Title:  Multivariate Imputation by Chained Equations 

Description:  Multiple imputation using Fully Conditional Specification (FCS) implemented by the MICE algorithm as described in Van Buuren and GroothuisOudshoorn (2011) <doi:10.18637/jss.v045.i03>. Each variable has its own imputation model. Builtin imputation models are provided for continuous data (predictive mean matching, normal), binary data (logistic regression), unordered categorical data (polytomous logistic regression) and ordered categorical data (proportional odds). MICE can also impute continuous twolevel data (normal model, pan, secondlevel variables). Passive imputation can be used to maintain consistency between variables. Various diagnostic plots are available to inspect the quality of the imputations. 
Authors:  Stef van Buuren [aut, cre], Karin GroothuisOudshoorn [aut], Gerko Vink [ctb], Rianne Schouten [ctb], Alexander Robitzsch [ctb], Patrick Rockenschaub [ctb], Lisa Doove [ctb], Shahab Jolani [ctb], Margarita MorenoBetancur [ctb], Ian White [ctb], Philipp Gaffert [ctb], Florian Meinfelder [ctb], Bernie Gray [ctb], Vincent ArelBundock [ctb], Mingyang Cai [ctb], Thom Volker [ctb], Edoardo Costantini [ctb], Caspar van Lissa [ctb], Hanne Oberman [ctb] 
Maintainer:  Stef van Buuren <[email protected]> 
License:  GPL (>= 2) 
Version:  3.16.10 
Built:  20240417 19:19:33 UTC 
Source:  https://github.com/amices/mice 
This function finds matches among the observed data in the predictive
mean metric. It selects the donors
closest matches, randomly
samples one of the donors, and returns the observed value of the
match.
.pmm.match(z, yhat = yhat, y = y, donors = 5, ...)
z 
A scalar containing the predicted value for the current case to be imputed. 
yhat 
A vector containing the predicted values for all cases with an observed outcome. 
y 
A vector of 
donors 
The size of the donor pool among which a draw is made. The default is

... 
Other parameters (not used). 
This function is included for backward compatibility. It was
used up to mice 2.21
. The current mice.impute.pmm()
function calls the faster C
function matcher
instead of
.pmm.match()
.
A scalar containing the observed value of the selected donor.
Stef van Buuren
Schenker N & Taylor JMG (1996) Partially parametric techniques for multiple imputation. Computational Statistics and Data Analysis, 22, 425446.
Little RJA (1988) Missingdata adjustments in large surveys (with discussion). Journal of Business Economics and Statistics, 6, 287301.
This function generates multivariate missing data under a MCAR, MAR or MNAR
missing data mechanism. Imputation of data sets containing missing values can
be performed with mice
.
ampute(
data,
prop = 0.5,
patterns = NULL,
freq = NULL,
mech = "MAR",
weights = NULL,
std = TRUE,
cont = TRUE,
type = NULL,
odds = NULL,
bycases = TRUE,
run = TRUE
)
data 
A complete data matrix or data frame. Values should be numeric. Categorical variables should have been transformed to dummies. 
prop 
A scalar specifying the proportion of missingness. Should be a value between 0 and 1. Default is a missingness proportion of 0.5. 
patterns 
A matrix or data frame of size #patterns by #variables where

freq 
A vector of length #patterns containing the relative frequency with
which the patterns should occur. For example, for three missing data patterns,
the vector could be 
mech 
A string specifying the missingness mechanism, either "MCAR" (Missing Completely At Random), "MAR" (Missing At Random) or "MNAR" (Missing Not At Random). Default is a MAR missingness mechanism. 
weights 
A matrix or data frame of size #patterns by #variables. The matrix
contains the weights that will be used to calculate the weighted sum scores. For
a MAR mechanism, the weights of the variables that will be made incomplete should be
zero. For a MNAR mechanism, these weights could have any possible value. Furthermore,
the weights may differ between patterns and between variables. They may be negative
as well. Within each pattern, the relative size of the values are of importance.
The default weights matrix is made with 
std 
Logical. Whether the weighted sum scores should be calculated with standardized data or with nonstandardized data. The latter is especially advised when making use of train and test sets in order to prevent leakage. 
cont 
Logical. Whether the probabilities should be based on a continuous
or a discrete distribution. If TRUE, the probabilities of being missing are based
on a continuous logistic distribution function. 
type 
A string or vector of strings containing the type of missingness for each
pattern. Either 
odds 
A matrix where #patterns defines the #rows. Each row should contain
the odds of being missing for the corresponding pattern. The number of odds values
defines in how many quantiles the sum scores will be divided. The odds values are
relative probabilities: a quantile with odds value 4 will have a probability of
being missing that is four times higher than a quantile with odds 1. The
number of quantiles may differ between the patterns, specify NA for cells remaining empty.
Default is 4 quantiles with odds values 1, 2, 3 and 4 and is created by

bycases 
Logical. If TRUE, the proportion of missingness is defined in terms of cases. If FALSE, the proportion of missingness is defined in terms of cells. Default is TRUE. 
run 
Logical. If TRUE, the amputations are implemented. If FALSE, the return object will contain everything except for the amputed data set. 
This function generates missing values in complete data sets. Amputation of complete
data sets is useful for the evaluation of imputation techniques, such as multiple
imputation (performed with function mice
in this package).
The basic strategy underlying multivariate imputation was suggested by Don Rubin during discussions in the 90's. Brand (1997) created one particular implementation, and his method found its way into the FCS paper (Van Buuren et al, 2006).
Until recently, univariate amputation procedures were used to generate missing data in complete, simulated data sets. With this approach, variables are made incomplete one variable at a time. When more than one variable needs to be amputed, the procedure is repeated multiple times.
With the univariate approach, it is difficult to relate the missingness on one
variable to the missingness on another variable. A multivariate amputation procedure
solves this issue and moreover, it does justice to the multivariate nature of
data sets. Hence, ampute
is developed to perform multivariate amputation.
The idea behind the function is the specification of several missingness
patterns. Each pattern is a combination of variables with and without missing
values (denoted by 0
and 1
respectively). For example, one might
want to create two missingness patterns on a data set with four variables. The
patterns could be something like: 0,0,1,1
and 1,0,1,0
.
Each combination of zeros and ones may occur.
Furthermore, the researcher specifies the proportion of missingness, either the proportion of missing cases or the proportion of missing cells, and the relative frequency each pattern occurs. Consequently, the data is split into multiple subsets, one subset per pattern. Now, each case is candidate for a certain missingness pattern, but whether the case will have missing values eventually depends on other specifications.
The first of these specifications is the missing mechanism. There are three possible mechanisms: the missingness depends completely on chance (MCAR), the missingness depends on the values of the observed variables (i.e. the variables that remain complete) (MAR) or on the values of the variables that will be made incomplete (MNAR). For a discussion on how missingness mechanisms are related to the observed data, we refer to doi:10.1177/0049124118799376Schouten and Vink, 2018.
When the user specifies the missingness mechanism to be "MCAR"
, the candidates
have an equal probability of becoming incomplete. For a "MAR"
or "MNAR"
mechanism,
weighted sum scores are calculated. These scores are a linear combination of the
variables.
In order to calculate the weighted sum scores, the data is standardized. For this reason,
the data has to be numeric. Second, for each case, the values in
the data set are multiplied with the weights, specified by argument weights
.
These weighted scores will be summed, resulting in a weighted sum score for each case.
The weights may differ between patterns and they may be negative or zero as well. Naturally, in case of a MAR mechanism, the weights corresponding to the variables that will be made incomplete, have a 0. Note that this may be different for each pattern. In case of MNAR missingness, especially the weights of the variables that will be made incomplete are of importance. However, the other variables may be weighted as well.
It is the relative difference between the weights that will result in an effect in the sum scores. For example, for the first missing data pattern mentioned above, the weights for the third and fourth variables could be set to 2 and 4. However, weight values of 0.2 and 0.4 will have the exact same effect on the weighted sum score: the fourth variable is weighted twice as much as variable 3.
Based on the weighted sum scores, either a discrete or continuous distribution of probabilities is used to calculate whether a candidate will have missing values.
For a discrete distribution of probabilities, the weighted sum scores are divided into subgroups of equal size (quantiles). Thereafter, the user specifies for each subgroup the odds of being missing. Both the number of subgroups and the odds values are important for the generation of missing data. For example, for a RIGHTlike mechanism, scoring in one of the higher quantiles should have high missingness odds, whereas for a MIDlike mechanism, the central groups should have higher odds. Again, not the size of the odds values are of importance, but the relative distance between the values.
The continuous distributions of probabilities are based on the logistic distribution function. The user can specify the type of missingness, which, again, may differ between patterns.
For an example and more explanation about how the arguments interact with each other, we refer to the vignette Generate missing values with ampute The amputation methodology is published in doi:10.1080/00949655.2018.1491577Schouten, Lugtig and Vink, 2018.
Returns an S3 object of class madsclass
(multivariate
amputed data set)
Rianne Schouten [aut, cre], Gerko Vink [aut], Peter Lugtig [ctb], 2016
Brand, J.P.L. (1999) Development, implementation and evaluation of multiple imputation strategies for the statistical analysis of incomplete data sets. pp. 110113. Dissertation. Rotterdam: Erasmus University.
Schouten, R.M., Lugtig, P and Vink, G. (2018) Generating missing values for simulation purposes: A multivariate amputation procedure.. Journal of Statistical Computation and Simulation, 88(15): 19091930. doi:10.1080/00949655.2018.1491577
Schouten, R.M. and Vink, G. (2018)The Dance of the Mechanisms: How Observed Information Influences the Validity of Missingness Assumptions. Sociological Methods and Research, 50(3): 12431258. doi:10.1177/0049124118799376
Van Buuren, S., Brand, J.P.L., GroothuisOudshoorn, C.G.M., Rubin, D.B. (2006) Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, 76(12): 10491064. doi:10.1080/10629360600810434
Van Buuren, S. (2018) Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Vink, G. (2016) Towards a standardized evaluation of multiple imputation routines.
madsclass
, bwplot
, xyplot
,
mice
# start with a complete data set
compl_boys < cc(boys)[1:3]
# Perform amputation with default settings
mads_boys < ampute(data = compl_boys)
mads_boys$amp
# Change default matrices as desired
my_patterns < mads_boys$patterns
my_patterns[1:3, 2] < 0
my_weights < mads_boys$weights
my_weights[2, 1] < 2
my_weights[3, 1] < 0.5
# Rerun amputation
my_mads_boys < ampute(
data = compl_boys, patterns = my_patterns, freq =
c(0.3, 0.3, 0.4), weights = my_weights, type = c("RIGHT", "TAIL", "LEFT")
)
my_mads_boys$amp
Compare several nested models
## S3 method for class 'mira'
anova(object, ..., method = "D1", use = "wald")
object 
Two or more objects of class 
... 
Other parameters passed down to 
method 
Either 
use 
An character indicating the test statistic 
Object of class mice.anova
A custom function to insert rows in long data with new pseudoobservations
that are being done on the specified break ages. There should be a
column called first
in data
with logical data that codes whether
the current row is the first for subject id
. Furthermore,
the function assumes that columns age
, occ
,
hgt.z
, wgt.z
and
bmi.z
are available. This function is used on the tbc
data in FIMD chapter 9. Check that out to see it in action.
appendbreak(data, brk, warp.model = warp.model, id = NULL, typ = "pred")
data 
A data frame in the long long format 
brk 
A vector of break ages 
warp.model 
A time warping model 
id 
The subject identifier 
typ 
Label to signal that this is a newly added observation 
A long data frame with additional rows for the break ages
mids
objectThis function converts imputed data stored in long format into
an object of class mids
. The original incomplete dataset
needs to be available so that we know where the missing data are.
The function is useful to convert back operations applied to
the imputed data back in a mids
object. It may also be
used to store multiply imputed data sets from other software
into the format used by mice
.
as.mids(long, where = NULL, .imp = ".imp", .id = ".id")
long 
A multiply imputed data set in long format, for example
produced by a call to 
where 
A data frame or matrix with logicals of the same dimensions
as 
.imp 
An optional column number or column name in 
.id 
An optional column number or column name in 
An object of class mids
The function expects the input data long
to be sorted by
imputation number (variable ".imp"
by default), and in the
same sequence within each imputation block.
Gerko Vink
# impute the nhanes dataset
imp < mice(nhanes, print = FALSE)
# extract the data in long format
X < complete(imp, action = "long", include = TRUE)
# create dataset with .imp variable as numeric
X2 < X
# nhanes example without .id
test1 < as.mids(X)
is.mids(test1)
identical(complete(test1, action = "long", include = TRUE), X)
# nhanes example without .id where .imp is numeric
test2 < as.mids(X2)
is.mids(test2)
identical(complete(test2, action = "long", include = TRUE), X)
# nhanes example, where we explicitly specify .id as column 2
test3 < as.mids(X, .id = ".id")
is.mids(test3)
identical(complete(test3, action = "long", include = TRUE), X)
# nhanes example with .id where .imp is numeric
test4 < as.mids(X2, .id = 6)
is.mids(test4)
identical(complete(test4, action = "long", include = TRUE), X)
# example without an .id variable
# variable .id not preserved
X3 < X[, 6]
test5 < as.mids(X3)
is.mids(test5)
identical(complete(test5, action = "long", include = TRUE)[, 6], X[, 6])
# as() syntax has fewer options
test7 < as(X, "mids")
test8 < as(X2, "mids")
test9 < as(X2[, 6], "mids")
rev < ncol(X):1
test10 < as(X[, rev], "mids")
# where argument copies also observed data into $imp element
where < matrix(TRUE, nrow = nrow(nhanes), ncol = ncol(nhanes))
colnames(where) < colnames(nhanes)
test11 < as.mids(X, where = where)
identical(complete(test11, action = "long", include = TRUE), X)
mira
object from repeated analysesThe as.mira()
function takes the results of repeated
completedata analysis stored as a list, and turns it
into a mira
object that can be pooled.
as.mira(fitlist)
fitlist 
A list containing $m$ fitted analysis objects 
An S3 object of class mira
.
Stef van Buuren
mitml.result
objectThe as.mitml.result()
function takes the results of repeated
completedata analysis stored as a list, and turns it
into an object of class mitml.result
.
as.mitml.result(x)
x 
An object of class 
An S3 object of class mitml.result
, a list
containing $m$ fitted analysis objects.
Stef van Buuren
Height, weight, head circumference and puberty of 748 Dutch boys.
A data frame with 748 rows on the following 9 variables:
Decimal age (021 years)
Height (cm)
Weight (kg)
Body mass index
Head circumference (cm)
Genital Tanner stage (G1G5)
Pubic hair (Tanner P1P6)
Testicular volume (ml)
Region (north, east, west, south, city)
Random sample of 10% from the crosssectional data used to construct the
Dutch growth references 1997. Variables gen
and phb
are ordered
factors. reg
is a factor.
Fredriks, A.M,, van Buuren, S., Burgmeijer, R.J., Meulmeester JF, Beuker, R.J., Brugman, E., Roede, M.J., VerlooveVanhorick, S.P., Wit, J.M. (2000) Continuing positive secular growth change in The Netherlands 19551997. Pediatric Research, 47, 316323.
Fredriks, A.M., van Buuren, S., Wit, J.M., VerlooveVanhorick, S.P. (2000). Body index measurements in 19967 compared with 1980. Archives of Disease in Childhood, 82, 107112.
# create two imputed data sets
imp < mice(boys, m = 1, maxit = 2)
z < complete(imp, 1)
# create imputations for age <8yrs
plot(z$age, z$gen,
col = mdc(1:2)[1 + is.na(boys$gen)],
xlab = "Age (years)", ylab = "Tanner Stage Genital"
)
# figure to show that the default imputation method does not impute BMI
# consistently
plot(z$bmi, z$wgt / (z$hgt / 100)^2,
col = mdc(1:2)[1 + is.na(boys$bmi)],
xlab = "Imputed BMI", ylab = "Calculated BMI"
)
# also, BMI distributions are somewhat different
oldpar < par(mfrow = c(1, 2))
MASS::truehist(z$bmi[!is.na(boys$bmi)],
h = 1, xlim = c(10, 30), ymax = 0.25,
col = mdc(1), xlab = "BMI observed"
)
MASS::truehist(z$bmi[is.na(boys$bmi)],
h = 1, xlim = c(10, 30), ymax = 0.25,
col = mdc(2), xlab = "BMI imputed"
)
par(oldpar)
# repair the inconsistency problem by passive imputation
meth < imp$meth
meth["bmi"] < "~I(wgt/(hgt/100)^2)"
pred < imp$predictorMatrix
pred["hgt", "bmi"] < 0
pred["wgt", "bmi"] < 0
imp2 < mice(boys, m = 1, maxit = 2, meth = meth, pred = pred)
z2 < complete(imp2, 1)
# show that new imputations are consistent
plot(z2$bmi, z2$wgt / (z2$hgt / 100)^2,
col = mdc(1:2)[1 + is.na(boys$bmi)],
ylab = "Calculated BMI"
)
# and compare distributions
oldpar < par(mfrow = c(1, 2))
MASS::truehist(z2$bmi[!is.na(boys$bmi)],
h = 1, xlim = c(10, 30), ymax = 0.25, col = mdc(1),
xlab = "BMI observed"
)
MASS::truehist(z2$bmi[is.na(boys$bmi)],
h = 1, xlim = c(10, 30), ymax = 0.25, col = mdc(2),
xlab = "BMI imputed"
)
par(oldpar)
Dataset with raw data from Snijders and Bosker (2012) containing data from 4106 pupils attending 216 schools. This dataset includes all pupils and schools with missing data.
brandsma
is a data frame with 4106 rows and 14 columns:
sch
School number
pup
Pupil ID
iqv
IQ verbal
iqp
IQ performal
sex
Sex of pupil
ses
SES score of pupil
min
Minority member 0/1
rpg
Number of repeated groups, 0, 1, 2
lpr
language score PRE
lpo
language score POST
apr
Arithmetic score PRE
apo
Arithmetic score POST
den
Denomination classification 14  at school level
ssi
School SES indicator  at school level
This dataset is constructed from the raw data. There are a few differences with the data set used in Chapter 4 and 5 of Snijders and Bosker:
All schools are included, including the five school with
missing values on langpost
.
Missing denomina
codes are left as missing.
Aggregates are undefined in the presence of missing data
in the underlying values.
Variables ses
, iqv
and iqp
are in their
original scale, and not globally centered.
No aggregate variables at the school level are included.
There is a wider selection of original variables. Note however that the source data contain an even wider set of variables.
Constructed from MLbook_2nded_total_410699.sav
from
https://www.stats.ox.ac.uk/~snijders/mlbook.htm by function
dataraw/R/brandsma.R
Brandsma, HP and Knuver, JWM (1989), Effects of school and classroom characteristics on pupil progress in language and arithmetic. International Journal of Educational Research, 13(7), 777  788.
Snijders, TAB and Bosker RJ (2012). Multilevel Analysis, 2nd Ed. Sage, Los Angeles, 2012.
Plotting method to investigate the relation between the data variables and the amputed data. The function shows how the amputed values are related to the variable values.
## S3 method for class 'mads'
bwplot(
x,
data,
which.pat = NULL,
standardized = TRUE,
descriptives = TRUE,
layout = NULL,
...
)
x 
A 
data 
A string or vector of variable names that needs to be plotted. As a default, all variables will be plotted. 
which.pat 
A scalar or vector indicating which patterns need to be plotted. As a default, all patterns are plotted. 
standardized 
Logical. Whether the boxandwhisker plots need to be created from standardized data or not. Default is TRUE. 
descriptives 
Logical. Whether the mean, variance and n of the variables need to be printed. This is useful to examine the effect of the amputation. Default is TRUE. 
layout 
A vector of two values indicating how the boxplots of one pattern
should be divided over the plot. For example, 
... 
Not used, but for consistency with generic 
A list containing the boxandwhisker plots. Note that a new pattern will always be shown in a new plot.
The mads
object contains all the information you need to
make any desired plots. Check madsclass
or the vignette Multivariate
Amputation using Ampute to understand the contents of class object mads
.
Rianne Schouten, 2016
ampute
, bwplot
, Lattice
for
an overview of the package, madsclass
Plotting methods for imputed data using lattice. bwplot
produces boxandwhisker plots. The function
automatically separates the observed and imputed data. The
functions extend the usual features of lattice.
## S3 method for class 'mids'
bwplot(
x,
data,
na.groups = NULL,
groups = NULL,
as.table = TRUE,
theme = mice.theme(),
mayreplicate = TRUE,
allow.multiple = TRUE,
outer = TRUE,
drop.unused.levels = lattice::lattice.getOption("drop.unused.levels"),
...,
subscripts = TRUE,
subset = TRUE
)
x 
A 
data 
Formula that selects the data to be plotted. This argument follows the lattice rules for formulas, describing the primary variables (used for the perpanel display) and the optional conditioning variables (which define the subsets plotted in different panels) to be used in the plot. The formula is evaluated on the complete data set in the Extended formula interface: The primary variable terms (both the LHS
For convenience, in 
na.groups 
An expression evaluating to a logical vector indicating
which two groups are distinguished (e.g. using different colors) in the
display. The environment in which this expression is evaluated in the
response indicator The default 
groups 
This is the usual 
as.table 
See 
theme 
A named list containing the graphical parameters. The default
function 
mayreplicate 
A logical indicating whether color, line widths, and so
on, may be replicated. The graphical functions attempt to choose
"intelligent" graphical parameters. For example, the same color can be
replicated for different element, e.g. use all reds for the imputed data.
Replication may be switched off by setting the flag to 
allow.multiple 
See 
outer 
See 
drop.unused.levels 
See 
... 
Further arguments, usually not directly processed by the highlevel functions documented here, but instead passed on to other functions. 
subscripts 
See 
subset 
See 
The argument na.groups
may be used to specify (combinations of)
missingness in any of the variables. The argument groups
can be used
to specify groups based on the variable values themselves. Only one of both
may be active at the same time. When both are specified, na.groups
takes precedence over groups
.
Use the subset
and na.groups
together to plots parts of the
data. For example, select the first imputed data set by by
subset=.imp==1
.
Graphical parameters like col
, pch
and cex
can be
specified in the arguments list to alter the plotting symbols. If
length(col)==2
, the color specification to define the observed and
missing groups. col[1]
is the color of the 'observed' data,
col[2]
is the color of the missing or imputed data. A convenient color
choice is col=mdc(1:2)
, a transparent blue color for the observed
data, and a transparent red color for the imputed data. A good choice is
col=mdc(1:2), pch=20, cex=1.5
. These choices can be set for the
duration of the session by running mice.theme()
.
The highlevel functions documented here, as well as other highlevel
Lattice functions, return an object of class "trellis"
. The
update
method can be used to
subsequently update components of the object, and the
print
method (usually called by default)
will plot it on an appropriate plotting device.
The first two arguments (x
and data
) are reversed
compared to the standard Trellis syntax implemented in lattice. This
reversal was necessary in order to benefit from automatic method dispatch.
In mice the argument x
is always a mids
object, whereas
in lattice the argument x
is always a formula.
In mice the argument data
is always a formula object, whereas in
lattice the argument data
is usually a data frame.
All other arguments have identical interpretation.
Stef van Buuren
Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
mice
, xyplot
, densityplot
,
stripplot
, lattice
for an overview of the
package, as well as bwplot
,
panel.bwplot
,
print.trellis
,
trellis.par.set
imp < mice(boys, maxit = 1)
### boxandwhisker plot per imputation of all numerical variables
bwplot(imp)
### tv (testicular volume), conditional on region
bwplot(imp, tv ~ .imp  reg)
### same data, organized in a different way
bwplot(imp, tv ~ reg  .imp, theme = list())
Functions cbind()
and rbind()
are defined in
the mice
package in order to
enable dispatch to cbind.mids()
and rbind.mids()
when one of the arguments is a data.frame
.
cbind(...)
rbind(...)
... 
Arguments passed on to

The standard base::cbind()
and base::rbind()
always dispatch to
base::cbind.data.frame()
or base::rbind.data.frame()
if one of the arguments is a
data.frame
. The versions defined in the mice
package intercept the user command
and test whether the first argument has class "mids"
. If so,
function calls cbind.mids()
, respectively rbind.mids()
. In
all other cases, the call is forwarded to standard functions in the
base
package.
The cbind.mids()
function combines two mids
objects
columnwise into a single
object of class mids
, or combines a single mids
object with
a vector
, matrix
, factor
or data.frame
columnwise into a mids
object.
If both arguments of cbind.mids()
are mids
objects, the
data
list components should have the same number of rows. Also, the
number of imputations (m
) should be identical.
If the second argument is a matrix
,
factor
or vector
, it is transformed into a
data.frame
. The number of rows should match with the data
component of the first argument.
The cbind.mids()
function renames any duplicated variable or block names by
appending ".1"
, ".2"
to duplicated names.
The rbind.mids()
function combines two mids
objects rowwise into a single
mids
object, or combines a mids
object with a vector, matrix,
factor or data frame rowwise into a mids
object.
If both arguments of rbind.mids()
are mids
objects,
then rbind.mids()
requires that both have the same number of multiple
imputations. In addition, their data
components should match.
If the second argument of rbind.mids()
is not a mids
object,
the columns of the arguments should match. The where
matrix for the
second argument is set to FALSE
, signalling that any missing values in
that argument were not imputed. The ignore
vector for the second argument is
set to FALSE
. Rows inherited from the second argument will therefore
influence the parameter estimation of the imputation model in any future
iterations.
An S3 object of class mids
The cbind.mids()
function constructs the elements of the new mids
object as follows:
data 
Columnwise combination of the data in x and y

imp 
Combines the imputed values from x and y

m 
Taken from x$m

where 
Columnwise combination of x$where and y$where

blocks 
Combines x$blocks and y$blocks

call 
Vector, call[1] creates x , call[2]
is call to cbind.mids()

nmis 
Equals c(x$nmis, y$nmis)

method 
Combines x$method and y$method

predictorMatrix 
Combination with zeroes on the offdiagonal blocks 
visitSequence 
Combined as c(x$visitSequence, y$visitSequence)

formulas 
Combined as c(x$formulas, y$formulas)

post 
Combined as c(x$post, y$post)

blots 
Combined as c(x$blots, y$blots)

ignore 
Taken from x$ignore

seed 
Taken from x$seed

iteration 
Taken from x$iteration

lastSeedValue 
Taken from x$lastSeedValue

chainMean 
Combined from x$chainMean and y$chainMean

chainVar 
Combined from x$chainVar and y$chainVar

loggedEvents 
Taken from x$loggedEvents

version 
Current package version 
date 
Current date 
The rbind.mids()
function constructs the elements of the new mids
object as follows:
data 
Rowwise combination of the (incomplete) data in x and y

imp 
Equals rbind(x$imp[[j]], y$imp[[j]]) if y is mids object; otherwise
the data of y will be copied 
m 
Equals x$m

where 
Rowwise combination of where arguments 
blocks 
Equals x$blocks

call 
Vector, call[1] creates x , call[2] is call to rbind.mids

nmis 
x$nmis + y$nmis

method 
Taken from x$method

predictorMatrix 
Taken from x$predictorMatrix

visitSequence 
Taken from x$visitSequence

formulas 
Taken from x$formulas

post 
Taken from x$post

blots 
Taken from x$blots

ignore 
Concatenate x$ignore and y$ignore

seed 
Taken from x$seed

iteration 
Taken from x$iteration

lastSeedValue 
Taken from x$lastSeedValue

chainMean 
Set to NA

chainVar 
Set to NA

loggedEvents 
Taken from x$loggedEvents

version 
Taken from x$version

date 
Taken from x$date

Karin GroothuisOudshoorn, Stef van Buuren
van Buuren S and GroothuisOudshoorn K (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
#  cbind 
# impute four variables at once (default)
imp < mice(nhanes, m = 1, maxit = 1, print = FALSE)
imp$predictorMatrix
# impute two by two
data1 < nhanes[, c("age", "bmi")]
data2 < nhanes[, c("hyp", "chl")]
imp1 < mice(data1, m = 2, maxit = 1, print = FALSE)
imp2 < mice(data2, m = 2, maxit = 1, print = FALSE)
# Append two solutions
imp12 < cbind(imp1, imp2)
# This is a different imputation model
imp12$predictorMatrix
# Append the other way around
imp21 < cbind(imp2, imp1)
imp21$predictorMatrix
# Append 'forgotten' variable chl
data3 < nhanes[, 1:3]
imp3 < mice(data3, maxit = 1, m = 2, print = FALSE)
imp4 < cbind(imp3, chl = nhanes$chl)
# Of course, chl was not imputed
head(complete(imp4))
# Combine mids object with data frame
imp5 < cbind(imp3, nhanes2)
head(complete(imp5))
#  rbind 
imp1 < mice(nhanes[1:13, ], m = 2, maxit = 1, print = FALSE)
imp5 < mice(nhanes[1:13, ], m = 2, maxit = 2, print = FALSE)
mylist < list(age = NA, bmi = NA, hyp = NA, chl = NA)
nrow(complete(rbind(imp1, imp5)))
nrow(complete(rbind(imp1, mylist)))
nrow(complete(rbind(imp1, data.frame(mylist))))
nrow(complete(rbind(imp1, complete(imp5))))
Extracts the complete cases, also known as listwise deletion.
cc(x)
is similar to
na.omit(x)
, but returns an object of the same class
as the input data. Dimensions are not dropped. For extracting
incomplete cases, use ici
.
cc(x)
x 
An 
A vector
, matrix
or data.frame
containing the data of the complete cases.
Stef van Buuren, 2017.
# cc(nhanes) # get the 13 complete cases
# cc(nhanes$bmi) # extract complete bmi
The complete case indicator is useful for extracting the subset of complete cases. The function
cci(x)
calls complete.cases(x)
.
The companion function ici()
selects the incomplete cases.
cci(x)
x 
An 
Logical vector indicating the complete cases.
Stef van Buuren, 2017.
cci(nhanes) # indicator for 13 complete cases
cci(mice(nhanes, maxit = 0))
f < cci(nhanes[, c("bmi", "hyp")]) # complete data for bmi and hyp
nhanes[f, ] # obtain all data from those with complete bmi and hyp
mids
objectTakes an object of class mids
, fills in the missing data, and returns
the completed data in a specified format.
## S3 method for class 'mids'
complete(
data,
action = 1L,
include = FALSE,
mild = FALSE,
order = c("last", "first"),
...
)
data 
An object of class 
action 
A numeric vector or a keyword. Numeric
values between 1 and 
include 
A logical to indicate whether the original data with the missing values should be included. 
mild 
A logical indicating whether the return value should
always be an object of class 
order 
Either 
... 
Additional arguments. Not used. 
The argument action
can be length1 character, which is
matched to one of the following keywords:
"all"
produces a mild
object of imputed data sets. When
include = TRUE
, then the original data are appended as the first list
element;
"long"
produces a data set where imputed data sets
are stacked vertically. The columns are added: 1) .imp
, integer,
referring the imputation number, and 2) .id
, character, the row
names of data$data
;
"stacked"
same as "long"
but without the two
additional columns;
"broad"
produces a data set with where imputed data sets are stacked horizontally. Columns are ordered as in the original data. The imputation number is appended to each column name;
"repeated"
same as "broad"
, but with
columns in a different order.
Complete data set with missing values replaced by imputations.
A data.frame
, or a list of data frames of class mild
.
Technical note: mice 3.7.5
renamed the complete()
function
to complete.mids()
and exported it as an S3 method of the
generic tidyr::complete()
. Name clashes between
mice::complete()
and tidyr::complete()
should no
longer occur.
# obtain first imputed data set
sum(is.na(nhanes2))
imp < mice(nhanes2, print = FALSE, maxit = 1)
dat < complete(imp)
sum(is.na(dat))
# obtain stacked third and fifth imputation
dat < complete(imp, c(3, 5))
# obtain all datasets, with additional identifiers
head(complete(imp, "long"))
# same, but now as list, mild object
dslist < complete(imp, "all")
length(dslist)
# same, but also include the original data
dslist < complete(imp, "all", include = TRUE)
length(dslist)
# select original + 3 + 5, store as mild
dslist < complete(imp, c(0, 3, 5), mild = TRUE)
names(dslist)
formulas
and predictorMatrix
This helper function attempts to find blocks of variables in the
specification of the formulas
and/or predictorMatrix
objects. Blocks specified by formulas
may consist of
multiple variables. Blocks specified by predictorMatrix
are
assumed to consist of single variables. Any duplicates in names are
removed, and the formula specification is preferred.
predictorMatrix
and formulas
. When both arguments
specify models for the same block, the model for the
predictMatrix
is removed, and priority is given to the
specification given in formulas
.
construct.blocks(formulas = NULL, predictorMatrix = NULL)
formulas 
A named list of formula's, or expressions that
can be converted into formula's by 
predictorMatrix 
A numeric matrix of 
A blocks
object.
form < list(bmi + hyp ~ chl + age, chl ~ bmi)
pred < make.predictorMatrix(nhanes[, c("age", "chl")])
construct.blocks(formulas = form, pred = pred)
mids
objectTakes an object of class mids
, computes the autocorrelation
and/or potential scale reduction factor, and returns a data.frame
with the specified diagnostic(s) per iteration.
convergence(data, diagnostic = "all", parameter = "mean", ...)
data 
An object of class 
diagnostic 
A keyword. One of the following keywords: 
parameter 
A keyword. One of the following keywords: 
... 
Additional arguments. Not used. 
The argument diagnostic
can be length1 character, which is
matched to one of the following keywords:
"all"
computes both the lag1 autocorrelation as well as the potential scale reduction factor (cf. Vehtari et al., 2021) per iteration of the MICE algorithm;
"ac"
computes only the autocorrelation per iteration;
"psrf"
computes only the potential scale reduction factor per iteration;
"gr"
same as psrf
, the potential scale reduction
factor is colloquially called the GelmanRubin diagnostic.
In the unlikely event of perfect convergence, the autocorrelation equals zero and the potential scale reduction factor equals one. To interpret the convergence diagnostic(s) in the output of the function, it is recommended to plot the diagnostics (ac and/or psrf) against the iteration number (.it) per imputed variable (vrb). A persistently decreasing trend across iterations indicates potential nonconvergence.
A data.frame
with the autocorrelation and/or potential
scale reduction factor per iteration of the MICE algorithm.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Burkner, P.C. (2021). RankNormalization, Folding, and Localization: An Improved R for Assessing Convergence of MCMC. Bayesian Analysis, 1(1), 138. https://doi.org/10.1214/20BA1221
## Not run:
# obtain imputed data set
imp < mice(nhanes2, print = FALSE)
# compute convergence diagnostics
convergence(imp)
## End(Not run)
The D1statistics is the multivariate Wald test.
D1(fit1, fit0 = NULL, dfcom = NULL, df.com = NULL)
fit1 
An object of class 
fit0 
An object of class 
dfcom 
A single number denoting the
completedata degrees of freedom of model 
df.com 
Deprecated 
Warning: 'D1()' assumes that the order of the variables is the same in different models. See https://github.com/amices/mice/issues/420 for details.
Li, K. H., T. E. Raghunathan, and D. B. Rubin. 1991. LargeSample Significance Levels from Multiply Imputed Data Using MomentBased Statistics and an F Reference Distribution. Journal of the American Statistical Association, 86(416): 1065–73.
https://stefvanbuuren.name/fimd/secmultiparameter.html#sec:wald
# Compare two linear models:
imp < mice(nhanes2, seed = 51009, print = FALSE)
mi1 < with(data = imp, expr = lm(bmi ~ age + hyp + chl))
mi0 < with(data = imp, expr = lm(bmi ~ age + hyp))
D1(mi1, mi0)
## Not run:
# Compare two logistic regression models
imp < mice(boys, maxit = 2, print = FALSE)
fit1 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc + reg, family = binomial))
fit0 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc, family = binomial))
D1(fit1, fit0)
## End(Not run)
The D2statistic pools test statistics from the repeated analyses. The method is less powerful than the D1 and D3statistics.
D2(fit1, fit0 = NULL, use = "wald")
fit1 
An object of class 
fit0 
An object of class 
use 
A character string denoting Wald or likelihoodbased based tests. Can be either 
Warning: 'D2()' assumes that the order of the variables is the same in different models. See https://github.com/amices/mice/issues/420 for details.
Li, K. H., X. L. Meng, T. E. Raghunathan, and D. B. Rubin. 1991. Significance Levels from Repeated pValues with MultiplyImputed Data. Statistica Sinica 1 (1): 65–92.
https://stefvanbuuren.name/fimd/secmultiparameter.html#sec:chi
# Compare two linear models:
imp < mice(nhanes2, seed = 51009, print = FALSE)
mi1 < with(data = imp, expr = lm(bmi ~ age + hyp + chl))
mi0 < with(data = imp, expr = lm(bmi ~ age + hyp))
D2(mi1, mi0)
## Not run:
# Compare two logistic regression models
imp < mice(boys, maxit = 2, print = FALSE)
fit1 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc + reg, family = binomial))
fit0 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc, family = binomial))
D2(fit1, fit0)
## End(Not run)
The D3statistic is a likelihoodratio test statistic.
D3(fit1, fit0 = NULL, dfcom = NULL, df.com = NULL)
fit1 
An object of class 
fit0 
An object of class 
dfcom 
A single number denoting the
completedata degrees of freedom of model 
df.com 
Deprecated 
The D3()
function implement the LRmethod by
Meng and Rubin (1992). The implementation of the method relies
on the broom
package, the standard update
mechanism
for statistical models in R
and the offset
function.
The function calculates m
repetitions of the full
(or null) models, calculates the mean of the estimates of the
(fixed) parameter coefficients $\beta$
. For each imputed
imputed dataset, it calculates the likelihood for the model with
the parameters constrained to $\beta$
.
The mitml::testModels()
function offers similar functionality
for a subset of statistical models. Results of mice::D3()
and
mitml::testModels()
differ in multilevel models because the
testModels()
also constrains the variance components parameters.
For more details on
An object of class mice.anova
Meng, X. L., and D. B. Rubin. 1992. Performing Likelihood Ratio Tests with MultiplyImputed Data Sets. Biometrika, 79 (1): 103–11.
https://stefvanbuuren.name/fimd/secmultiparameter.html#sec:likelihoodratio
# Compare two linear models:
imp < mice(nhanes2, seed = 51009, print = FALSE)
mi1 < with(data = imp, expr = lm(bmi ~ age + hyp + chl))
mi0 < with(data = imp, expr = lm(bmi ~ age + hyp))
D3(mi1, mi0)
## Not run:
# Compare two logistic regression models
imp < mice(boys, maxit = 2, print = FALSE)
fit1 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc + reg, family = binomial))
fit0 < with(imp, glm(gen > levels(gen)[1] ~ hgt + hc, family = binomial))
D3(fit1, fit0)
## End(Not run)
Plotting methods for imputed data using lattice. densityplot
produces plots of the densities. The function
automatically separates the observed and imputed data. The
functions extend the usual features of lattice.
## S3 method for class 'mids'
densityplot(
x,
data,
na.groups = NULL,
groups = NULL,
as.table = TRUE,
plot.points = FALSE,
theme = mice.theme(),
mayreplicate = TRUE,
thicker = 2.5,
allow.multiple = TRUE,
outer = TRUE,
drop.unused.levels = lattice::lattice.getOption("drop.unused.levels"),
panel = lattice::lattice.getOption("panel.densityplot"),
default.prepanel = lattice::lattice.getOption("prepanel.default.densityplot"),
...,
subscripts = TRUE,
subset = TRUE
)
x 
A 
data 
Formula that selects the data to be plotted. This argument follows the lattice rules for formulas, describing the primary variables (used for the perpanel display) and the optional conditioning variables (which define the subsets plotted in different panels) to be used in the plot. The formula is evaluated on the complete data set in the Extended formula interface: The primary variable terms (both the LHS
The function 
na.groups 
An expression evaluating to a logical vector indicating
which two groups are distinguished (e.g. using different colors) in the
display. The environment in which this expression is evaluated in the
response indicator The default 
groups 
This is the usual 
as.table 
See 
plot.points 
A logical used in 
theme 
A named list containing the graphical parameters. The default
function 
mayreplicate 
A logical indicating whether color, line widths, and so
on, may be replicated. The graphical functions attempt to choose
"intelligent" graphical parameters. For example, the same color can be
replicated for different element, e.g. use all reds for the imputed data.
Replication may be switched off by setting the flag to 
thicker 
Used in 
allow.multiple 
See 
outer 
See 
drop.unused.levels 
See 
panel 
See 
default.prepanel 
See 
... 
Further arguments, usually not directly processed by the highlevel functions documented here, but instead passed on to other functions. 
subscripts 
See 
subset 
See 
The argument na.groups
may be used to specify (combinations of)
missingness in any of the variables. The argument groups
can be used
to specify groups based on the variable values themselves. Only one of both
may be active at the same time. When both are specified, na.groups
takes precedence over groups
.
Use the subset
and na.groups
together to plots parts of the
data. For example, select the first imputed data set by by
subset=.imp==1
.
Graphical parameters like col
, pch
and cex
can be
specified in the arguments list to alter the plotting symbols. If
length(col)==2
, the color specification to define the observed and
missing groups. col[1]
is the color of the 'observed' data,
col[2]
is the color of the missing or imputed data. A convenient color
choice is col=mdc(1:2)
, a transparent blue color for the observed
data, and a transparent red color for the imputed data. A good choice is
col=mdc(1:2), pch=20, cex=1.5
. These choices can be set for the
duration of the session by running mice.theme()
.
The highlevel functions documented here, as well as other highlevel
Lattice functions, return an object of class "trellis"
. The
update
method can be used to
subsequently update components of the object, and the
print
method (usually called by default)
will plot it on an appropriate plotting device.
The first two arguments (x
and data
) are reversed
compared to the standard Trellis syntax implemented in lattice. This
reversal was necessary in order to benefit from automatic method dispatch.
In mice the argument x
is always a mids
object, whereas
in lattice the argument x
is always a formula.
In mice the argument data
is always a formula object, whereas in
lattice the argument data
is usually a data frame.
All other arguments have identical interpretation.
densityplot
errs on empty groups, which occurs if all observations in
the subgroup contain NA
. The relevant error message is: Error in
density.default: ... need at least 2 points to select a bandwidth
automatically
. There is yet no workaround for this problem. Use the more
robust bwplot
or stripplot
as a replacement.
Stef van Buuren
Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
mice
, xyplot
, stripplot
,
bwplot
, lattice
for an overview of the
package, as well as densityplot
,
panel.densityplot
,
print.trellis
,
trellis.par.set
imp < mice(boys, maxit = 1)
### density plot of head circumference per imputation
### blue is observed, red is imputed
densityplot(imp, ~ hc  .imp)
### All combined in one panel.
densityplot(imp, ~hc)
A toy example from Craig Enders.
employee
A data frame with 20 rows and 3 variables:
candidate IQ score
candidate wellbeing score
candidate job performance score
Enders describes these data as follows: I designed these data to mimic an employee selection scenario in which prospective employees complete an IQ test and a psychological wellbeing questionnaire during their interview. The company subsequently hires the applications that score in the upper half of the IQ distribution, and a supervisor rates their job performance following a 6month probationary period. Note that the job performance scores are missing at random (MAR) (i.e. individuals in the lower half of the IQ distribution were never hired, and thus have no performance rating). In addition, I randomly deleted three of the wellbeing scores in order to mimic a situation where the applicant's wellbeing questionnaire is inadvertently lost.
A larger version of this data set in present as
data.enders.employee
.
Enders (2010), Applied Missing Data Analysis, p. 218
This function computes least squares estimates, variance/covariance matrices, residuals and degrees of freedom according to ridge regression, QR decomposition or Singular Value Decomposition. This function is internally called by .norm.draw(), but can be called by any userspecified imputation function.
estimice(x, y, ls.meth = "qr", ridge = 1e05, ...)
x 
Matrix ( 
y 
Incomplete data vector of length 
ls.meth 
the method to use for obtaining the least squares estimates. By default parameters are drawn by means of QR decomposition. 
ridge 
A small numerical value specifying the size of the ridge used.
The default value 
... 
Other named arguments. 
When calculating the inverse of the crossproduct of the predictor matrix, problems may arise. For example, taking the inverse is not possible when the predictor matrix is rank deficient, or when the estimation problem is computationally singular. This function detects such error cases and automatically falls back to adding a ridge penalty to the diagonal of the crossproduct to allow for proper calculation of the inverse.
A list
containing components c
(least squares estimate),
r
(residuals), v
(variance/covariance matrix) and df
(degrees of freedom).
This functions adds a star to variable names in the mice iteration
history to signal that a ridge penalty was added. In that case, it
also adds an entry to loggedEvents
.
Gerko Vink, 2018
lmer
objectExtract broken stick estimates from a lmer
object
extractBS(fit)
fit 
An object of class 
A matrix containing broken stick estimates
Stef van Buuren, 2012
Multiple outcomes of a randomized study to reduce posttraumatic stress.
fdd
is a data frame with 52 rows and 65 columns:
Client number
Treatment (E=EMDR, C=CBT)
Per protocol (Y/N)
Number of parental treatments
Sex: M/F
Ethnicity: NL/OTHER
Age (years)
Trauma count (15)
PROPS total score T1
PROPS total score T2
PROPS total score T3
CROPS total score T1
CROPS total score T2
CROPS total score T3
MASC score T1
MASC score T2
MASC score T3
CBCL T1
CBCL T3
PRS total score T1
PRS total score T2
PRS total score T3
PTSDRI B intrusive recollection parent T1
PTSDRI C avoidant/numbing parent T1
PTSDRI D hyperarousal parent T1
PTSDRI B+C+D parent T1
PTSDRI B intrusive recollection parent T2
PTSDRI C avoidant/numbing parent T2
PTSDRI D hyperarousal parent T2
PTSDRI B+C+D parent T1
PTSDRI B intrusive recollection parent T3
PTSDRI C avoidant/numbing parent T3
PTSDRI D hyperarousal parent T3
PTSDRI B+C+D parent T3
PTSDRI B intrusive recollection child T1
PTSDRI C avoidant/numbing child T1
PTSDRI D hyperarousal child T1
PTSDRI B+C+D child T1
PTSDRI B intrusive recollection child T2
PTSDRI C avoidant/numbing child T2
PTSDRI D hyperarousal child T2
PTSDRI B+C+D child T2
PTSDRI B intrusive recollection child T3
PTSDRI C avoidant/numbing child T3
PTSDRI D hyperarousal child T3
PTSDRI B+C+D child T3
PTSDRI parent full T1
PTSDRI parent full T2
PTSDRI parent full T3
PTSD parent partial T1
PTSD parent partial T2
PTSD parent partial T3
PTSD child full T1
PTSD child full T2
PTSD child full T3
PTSD child partial T1
PTSD child partial T2
PTSD child partial T3
CBCL Internalizing T1
CBCL Internalizing T3
CBCL Externalizing T1
CBCL Externalizing T3
Birlison T1
Birlison T2
Birlison T3
fdd.pred
is the 65 by 65 binary
predictor matrix used to impute fdd
.
Data from a randomized experiment to reduce posttraumatic stress by two treatments: Eye Movement Desensitization and Reprocessing (EMDR) (experimental treatment), and cognitive behavioral therapy (CBT) (control treatment). 52 children were randomized to one of these two treatments. Outcomes were measured at three time points: at baseline (pretreatment, T1), posttreatment (T2, 48 weeks), and at followup (T3, 3 months). For more details, see de Roos et al (2011). Some person covariates were reshuffled. The imputation methodology is explained in Chapter 9 of van Buuren (2012).
de Roos, C., Greenwald, R., den HollanderGijsman, M., Noorthoorn, E., van Buuren, S., de Jong, A. (2011). A Randomised Comparison of Cognitive Behavioral Therapy (CBT) and Eye Movement Desensitisation and Reprocessing (EMDR) in disasterexposed children. European Journal of Psychotraumatology, 2, 5694.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL. Boca Raton, FL.: Chapman & Hall/CRC Press.
data < fdd
md.pattern(fdd)
Age, height, weight and region of 10030 children measured within the Fifth Dutch Growth Study 2009
fdgs
is a data frame with 10030 rows and 8 columns:
Person number
Region (factor, 5 levels)
Age (years)
Sex (boy, girl)
Height (cm)
Weight (kg)
Height Zscore
Weight Zscore
The data set contains data from children of Dutch descent (biological parents are born in the Netherlands). Children with growthrelated diseases were excluded. The data were used to construct new growth charts of children of Dutch descent (Schonbeck 2013), and to calculate overweight and obesity prevalence (Schonbeck 2011).
Some groups were underrepresented. Multiple imputation was used to create synthetic cases that were used to correct for the nonresponse. See Van Buuren (2012), chapter 8 for details.
Schonbeck, Y., Talma, H., van Dommelen, P., Bakker, B., Buitendijk, S. E., Hirasing, R. A., van Buuren, S. (2011). Increase in prevalence of overweight in Dutch children and adolescents: A comparison of nationwide growth studies in 1980, 1997 and 2009. PLoS ONE, 6(11), e27608.
Schonbeck, Y., Talma, H., van Dommelen, P., Bakker, B., Buitendijk, S. E., Hirasing, R. A., van Buuren, S. (2013). The world's tallest nation has stopped growing taller: the height of Dutch children from 1955 to 2009. Pediatric Research, 73(3), 371377.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Boca Raton, FL.: Chapman & Hall/CRC Press.
data < data(fdgs)
summary(data)
FICO is an outbound statistic defined by the fraction of incomplete cases
among cases with Yj
observed (White and Carlin, 2010).
fico(data)
data 
A data frame or a matrix containing the incomplete data. Missing values are coded as NA's. 
A vector of length ncol(data)
of FICO statistics.
Stef van Buuren, 2012
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
White, I.R., Carlin, J.B. (2010). Bias and efficiency of multiple imputation compared with completecase analysis for missing covariate values. Statistics in Medicine, 29, 29202931.
mids
objectThis function takes a mids
object and returns a new
mids
object that pertains to the subset of the data
identified by the expression in .... The expression may use
column values from the incomplete data in .data$data
.
## S3 method for class 'mids'
filter(.data, ..., .preserve = FALSE)
.data 
A 
... 
Expressions that return a
logical value, and are defined in terms of the variables in 
.preserve 
Relevant when the 
An S3 object of class mids
The function calculates a logical vector include
of length nrow(.data$data)
.
The function constructs the elements of the filtered mids
object as follows:
data 
Select rows in .data$data for which include == TRUE

imp 
Select rows each imputation data.frame in .data$imp for which include == TRUE

m 
Equals .data$m

where 
Select rows in .data$where for which include == TRUE

blocks 
Equals .data$blocks

call 
Equals .data$call

nmis 
Recalculate nmis based on the selected data rows 
method 
Equals .data$method

predictorMatrix 
Equals .data$predictorMatrix

visitSequence 
Equals .data$visitSequence

formulas 
Equals .data$formulas

post 
Equals .data$post

blots 
Equals .data$blots

ignore 
Select positions in .data$ignore for which include == TRUE

seed 
Equals .data$seed

iteration 
Equals .data$iteration

lastSeedValue 
Equals .data$lastSeedValue

chainMean 
Set to NULL

chainVar 
Set to NULL

loggedEvents 
Equals .data$loggedEvents

version 
Replaced with current version 
date 
Replaced with current date 
Patrick Rockenschaub
imp < mice(nhanes, m = 2, maxit = 1, print = FALSE)
# example with external logical vector
imp_f < filter(imp, c(rep(TRUE, 13), rep(FALSE, 12)))
nrow(complete(imp))
nrow(complete(imp_f))
# example with calculated include vector
imp_f2 < filter(imp, age >= 2 & hyp == 1)
nrow(complete(imp_f2)) # should be 5
Refits a model with a specified set of coefficients.
fix.coef(model, beta = NULL)
model 
An R model, e.g., produced by 
beta 
A numeric vector with 
The function calculates the linear predictor using the new coefficients,
and reformulates the model using the offset
argument. The linear predictor is called
offset
, and its coefficient will be 1
by definition.
The new model only fits the intercept, which should be 0
if we set beta = coef(model)
.
An updated R model object
Stef van Buuren, 2018
model0 < lm(Volume ~ Girth + Height, data = trees)
formula(model0)
coef(model0)
deviance(model0)
# refit same model
model1 < fix.coef(model0)
formula(model1)
coef(model1)
deviance(model1)
# change the beta's
model2 < fix.coef(model0, beta = c(50, 5, 1))
coef(model2)
deviance(model2)
# compare predictions
plot(predict(model0), predict(model1))
abline(0, 1)
plot(predict(model0), predict(model2))
abline(0, 1)
# compare proportion explained variance
cor(predict(model0), predict(model0) + residuals(model0))^2
cor(predict(model1), predict(model1) + residuals(model1))^2
cor(predict(model2), predict(model2) + residuals(model2))^2
# extract offset from constrained model
summary(model2$offset)
# it also works with factors and missing data
model0 < lm(bmi ~ age + hyp + chl, data = nhanes2)
model1 < fix.coef(model0)
model2 < fix.coef(model0, beta = c(15, 8, 8, 2, 0.2))
Influx and outflux are statistics of the missing data pattern. These statistics are useful in selecting predictors that should go into the imputation model.
flux(data, local = names(data))
data 
A data frame or a matrix containing the incomplete data. Missing values are coded as NA's. 
local 
A vector of names of columns of 
Infux and outflux have been proposed by Van Buuren (2018), chapter 4.
Influx is equal to the number of variable pairs (Yj , Yk)
with
Yj
missing and Yk
observed, divided by the total number of
observed data cells. Influx depends on the proportion of missing data of the
variable. Influx of a completely observed variable is equal to 0, whereas for
completely missing variables we have influx = 1. For two variables with the
same proportion of missing data, the variable with higher influx is better
connected to the observed data, and might thus be easier to impute.
Outflux is equal to the number of variable pairs with Yj
observed and
Yk
missing, divided by the total number of incomplete data cells.
Outflux is an indicator of the potential usefulness of Yj
for imputing
other variables. Outflux depends on the proportion of missing data of the
variable. Outflux of a completely observed variable is equal to 1, whereas
outflux of a completely missing variable is equal to 0. For two variables
having the same proportion of missing data, the variable with higher outflux
is better connected to the missing data, and thus potentially more useful for
imputing other variables.
FICO is an outbound statistic defined by the fraction of incomplete cases
among cases with Yj
observed (White and Carlin, 2010).
A data frame with ncol(data)
rows and six columns:
pobs = Proportion observed,
influx = Influx
outflux = Outflux
ainb = Average inbound statistic
aout = Average outbound statistic
fico = Fraction of incomplete cases among cases with Yj
observed
Stef van Buuren, 2012
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
White, I.R., Carlin, J.B. (2010). Bias and efficiency of multiple imputation compared with completecase analysis for missing covariate values. Statistics in Medicine, 29, 29202931.
Influx and outflux are statistics of the missing data pattern. These statistics are useful in selecting predictors that should go into the imputation model.
fluxplot(
data,
local = names(data),
plot = TRUE,
labels = TRUE,
xlim = c(0, 1),
ylim = c(0, 1),
las = 1,
xlab = "Influx",
ylab = "Outflux",
main = paste("Influxoutflux pattern for", deparse(substitute(data))),
eqscplot = TRUE,
pty = "s",
lwd = 1,
...
)
data 
A data frame or a matrix containing the incomplete data. Missing values are coded as NA's. 
local 
A vector of names of columns of 
plot 
Should a graph be produced? 
labels 
Should the points be labeled? 
xlim 
See 
ylim 
See 
las 
See 
xlab 
See 
ylab 
See 
main 
See 
eqscplot 
Should a square plot be produced? 
pty 
See 
lwd 
See 
... 
Further arguments passed to 
Infux and outflux have been proposed by Van Buuren (2012), chapter 4.
Influx is equal to the number of variable pairs (Yj , Yk)
with
Yj
missing and Yk
observed, divided by the total number of
observed data cells. Influx depends on the proportion of missing data of the
variable. Influx of a completely observed variable is equal to 0, whereas for
completely missing variables we have influx = 1. For two variables with the
same proportion of missing data, the variable with higher influx is better
connected to the observed data, and might thus be easier to impute.
Outflux is equal to the number of variable pairs with Yj
observed and
Yk
missing, divided by the total number of incomplete data cells.
Outflux is an indicator of the potential usefulness of Yj
for imputing
other variables. Outflux depends on the proportion of missing data of the
variable. Outflux of a completely observed variable is equal to 1, whereas
outflux of a completely missing variable is equal to 0. For two variables
having the same proportion of missing data, the variable with higher outflux
is better connected to the missing data, and thus potentially more useful for
imputing other variables.
An invisible data frame with ncol(data)
rows and six columns:
pobs = Proportion observed,
influx = Influx
outflux = Outflux
ainb = Average inbound statistic
aout = Average outbound statistic
fico = Fraction of incomplete cases among cases with Yj
observed
Stef van Buuren, 2012
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
White, I.R., Carlin, J.B. (2010). Bias and efficiency of multiple imputation compared with completecase analysis for missing covariate values. Statistics in Medicine, 29, 29202931.
This is a wrapper function for mice
, using multiple cores to
execute mice
in parallel. As a result, the imputation
procedure can be sped up, which may be useful in general. By default,
futuremice
distributes the number of imputations m
about equally over the cores.
futuremice(
data,
m = 5,
parallelseed = NA,
n.core = NULL,
seed = NA,
use.logical = TRUE,
future.plan = "multisession",
packages = NULL,
globals = NULL,
...
)
data 
A data frame or matrix containing the incomplete data. Similar to
the first argument of 
m 
The number of desired imputated datasets. By default $m=5$ as with

parallelseed 
A scalar to be used to obtain reproducible results over
the futures. The default 
n.core 
A scalar indicating the number of cores that should be used. 
seed 
A scalar to be used as the seed value for the mice algorithm
within each parallel stream. Please note that the imputations will be the
same for all streams and, hence, this should be used if and only if

use.logical 
A logical indicating whether logical ( 
future.plan 
A character indicating how 
packages 
A character vector with additional packages to be used in

globals 
A character string with additional functions to be exported to each future (e.g., userwritten imputation functions). 
... 
Named arguments that are passed down to function 
This function relies on package furrr
, which is a
package for R versions 3.2.0 and later. We have chosen to use furrr function
future_map
to allow the use of futuremice
on Mac, Linux and
Windows systems.
This wrapper function combines the output of future_map
with
function ibind
from the mice
package. A
mids
object is returned and can be used for further analyses.
A seed value can be specified in the global environment, which will yield
reproducible results. A seed value can also be specified within the
futuremice
call, through specifying the argument
parallelseed
. If parallelseed
is not specified, a seed value is
drawn randomly by default, and accessible through $parallelseed
in the
output object. Hence, results will always be reproducible, regardless of
whether the seed is specified in the global environment, or by setting the
same seed within the function (potentially by extracting the seed from the
futuremice
output object.
A mids object as defined by midsclass
Thom Benjamin Volker, Gerko Vink
Volker, T.B. and Vink, G. (2022). futuremice: The future starts today. https://www.gerkovink.com/miceVignettes/futuremice/Vignette_futuremice.html
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
future
, furrr
, future_map
,
plan
, mice
, midsclass
# 150 imputations in dataset nhanes, performed by 3 cores
## Not run:
imp1 < futuremice(data = nhanes, m = 150, n.core = 3)
# Making use of arguments in mice.
imp2 < futuremice(data = nhanes, m = 100, method = "norm.nob")
imp2$method
fit < with(imp2, lm(bmi ~ hyp))
pool(fit)
## End(Not run)
Function getfit()
returns the list of objects containing the repeated analysis
results, or optionally, one of these fitted objects. The function looks for
a list element called analyses
, and return this component as a list with
mira
class. If element analyses
is not found in x
, then
it returns x
as a mira
object.
getfit(x, i = 1L, simplify = FALSE)
x 
An object of class 
i 
An integer between 1 and 
simplify 
Should the return value be unlisted? 
No checking is done for validity of objects. The function also processes
objects of class mitml.result
from the mitml
package.
If i = 1
an object of class mira
containing
all analyses. If i
selects one of the analyses, then it return
an object whose with class inherited from that element.
Stef van Buuren, 2012, 2020
imp < mice(nhanes, print = FALSE, seed = 21443)
fit < with(imp, lm(bmi ~ chl + hyp))
f1 < getfit(fit)
class(f1)
f2 < getfit(fit, 2)
class(f2)
mipo
objectgetqbar
returns a named vector of pooled estimates.
getqbar(x)
x 
An object of class 
mids
objectApplies glm()
to a multiply imputed data set
glm.mids(formula, family = gaussian, data, ...)
formula 
a formula expression as for other regression models, of the
form response ~ predictors. See the documentation of 
family 
The family of the glm model 
data 
An object of type 
... 
Additional parameters passed to 
This function is included for backward compatibility with V1.0. The function
is superseded by with.mids
.
An objects of class mira
, which stands for 'multiply imputed
repeated analysis'. This object contains data$m
distinct
glm.objects
, plus some descriptive information.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
Van Buuren, S., GroothuisOudshoorn, C.G.M. (2000) Multivariate Imputation by Chained Equations: MICE V1.0 User's manual. Leiden: TNO Quality of Life.
imp < mice(nhanes)
# logistic regression on the imputed data
fit < glm.mids((hyp == 2) ~ bmi + chl, data = imp, family = binomial)
fit
mids
objectsThis function combines two mids
objects x
and y
into a
single mids
object, with the objective of increasing the number of
imputed data sets. If the number of imputations in x
and y
are
m(x)
and m(y)
, then the combined object will have
m(x)+m(y)
imputations.
ibind(x, y)
x 
A 
y 
A 
The two mids
objects are required to
have the same underlying multiple imputation model and should
be fitted on the same data.
An S3 object of class mids
Karin GroothuisOudshoorn, Stef van Buuren
data(nhanes)
imp1 < mice(nhanes, m = 1, maxit = 2, print = FALSE)
imp1$m
imp2 < mice(nhanes, m = 3, maxit = 3, print = FALSE)
imp2$m
imp12 < ibind(imp1, imp2)
imp12$m
plot(imp12)
Extracts incomplete cases from a data set.
The companion function for selecting the complete cases is cc
.
ic(x)
x 
An 
A vector
, matrix
or data.frame
containing the data of the complete cases.
Stef van Buuren, 2017.
ic(nhanes) # get the 12 rows with incomplete cases
ic(nhanes[1:10, ]) # incomplete cases within the first ten rows
ic(nhanes[, c("bmi", "hyp")]) # restrict extraction to variables bmi and hyp
This array is useful for extracting the subset of incomplete cases.
The companion function cci()
selects the complete cases.
ici(x)
x 
An 
Logical vector indicating the incomplete cases,
Stef van Buuren, 2017.
ici(nhanes) # indicator for 12 rows with incomplete cases
mads
objectCheck for mads
object
is.mads(x)
x 
An object 
A logical indicating whether x
is an object of class mads
mids
objectCheck for mids
object
is.mids(x)
x 
An object 
A logical indicating whether x
is an object of class mids
mipo
objectCheck for mipo
object
is.mipo(x)
x 
An object 
A logical indicating whether x
is an object of class mipo
mira
objectCheck for mira
object
is.mira(x)
x 
An object 
A logical indicating whether x
is an object of class mira
mitml.result
objectCheck for mitml.result
object
is.mitml.result(x)
x 
An object 
A logical indicating whether x
is an object of class mitml.result
Subset of data from the Leiden 85+ study
leiden85
is a data frame with 956 rows and 336 columns.
The data set concerns of subset of 956 members of a very old (85+) cohort in Leiden.
Multiple imputation of this data set has been described in Boshuizen et al (1998), Van Buuren et al (1999) and Van Buuren (2012), chapter 7.
The data set is not available as part of mice
.
Lagaay, A. M., van der Meij, J. C., Hijmans, W. (1992). Validation of medical history taking as part of a population based survey in subjects aged 85 and over. Brit. Med. J., 304(6834), 10911092.
Izaks, G. J., van Houwelingen, H. C., Schreuder, G. M., Ligthart, G. J. (1997). The association between human leucocyte antigens (HLA) and mortality in community residents aged 85 and older. Journal of the American Geriatrics Society, 45(1), 5660.
Boshuizen, H. C., Izaks, G. J., van Buuren, S., Ligthart, G. J. (1998). Blood pressure and mortality in elderly people aged 85 and older: Community based study. Brit. Med. J., 316(7147), 17801784.
Van Buuren, S., Boshuizen, H.C., Knook, D.L. (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statistics in Medicine, 18, 681–694.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
mids
objectApplies lm()
to multiply imputed data set
lm.mids(formula, data, ...)
formula 
a formula object, with the response on the left of a ~
operator, and the terms, separated by + operators, on the right. See the
documentation of 
data 
An object of type 'mids', which stands for 'multiply imputed data
set', typically created by a call to function 
... 
Additional parameters passed to 
This function is included for backward compatibility with V1.0. The function
is superseded by with.mids
.
An objects of class mira
, which stands for 'multiply imputed
repeated analysis'. This object contains data$m
distinct
lm.objects
, plus some descriptive information.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
imp < mice(nhanes)
fit < lm.mids(bmi ~ hyp + chl, data = imp)
fit
mads
)The mads
object contains an amputed data set. The mads
object is
generated by the ampute
function. The mads
class of objects has
methods for the following generic functions: print
, summary
,
bwplot
and xyplot
.
call
:The function call.
prop
:Proportion of cases with missing values. Note: even when
the proportion is entered as the proportion of missing cells (when
bycases == TRUE
), this object contains the proportion of missing cases.
patterns
:A data frame of size #patterns by #variables where 0
indicates a variable has missing values and 1
indicates a variable remains
complete.
freq
:A vector of length #patterns containing the relative
frequency with which the patterns occur. For example, if the vector is
c(0.4, 0.4, 0.2)
, this means that of all cases with missing values,
40 percent is candidate for pattern 1, 40 percent for pattern 2 and 20
percent for pattern 3. The vector sums to 1.
mech
:A string specifying the missingness mechanism, either
"MCAR"
, "MAR"
or "MNAR"
.
weights
:A data frame of size #patterns by #variables. It contains the weights that were used to calculate the weighted sum scores. The weights may differ between patterns and between variables.
cont
:Logical, whether probabilities are based on continuous logit functions or on discrete odds distributions.
type
:A vector of strings containing the type of missingness
for each pattern. Either "LEFT"
, "MID"
, "TAIL"
or
"RIGHT"
. The first type refers to the first pattern, the second type
to the second pattern, etc.
odds
:A matrix where #patterns defines the #rows. Each row contains the odds of being missing for the corresponding pattern. The amount of odds values defines in how many quantiles the sum scores were divided. The values are relative probabilities: a quantile with odds value 4 will have a probability of being missing that is four times higher than a quantile with odds 1. The #quantiles may differ between patterns, NA is used for cells remaining empty.
amp
:A data frame containing the input data with NAs for the amputed values.
cand
:A vector that contains the pattern number for each case. A value between 1 and #patterns is given. For example, a case with value 2 is candidate for missing data pattern 2.
scores
:A list containing vectors with weighted sum scores of the candidates. The first vector refers to the candidates of the first pattern, the second vector refers to the candidates of the second pattern, etc. The length of the vectors differ because the number of candidates is different for each pattern.
data
:The complete data set that was entered in ampute
.
Many of the functions of the mice
package do not use the S4 class
definitions, and instead rely on the S3 list equivalent
oldClass(obj) < "mads"
.
Rianne Schouten, 2016
ampute
, Vignette titled "Multivariate Amputation using
Ampute".
blocks
argumentThis helper function generates a list of the type needed for
blocks
argument in the [=mice]{mice}
function.
make.blocks(
data,
partition = c("scatter", "collect", "void"),
calltype = "pred"
)
data 
A 
partition 
A character vector of length 1 used to assign
variables to blocks when 
calltype 
A character vector of 
Choices "scatter"
and "collect"
represent to two
extreme scenarios for assigning variables to imputation blocks.
Use "scatter"
to create an imputation model based on
fully conditionally specification (FCS). Use "collect"
to
gather all variables to be imputed by a joint model (JM).
Scenario's inbetween these two extremes represent
hybrid imputation models that combine FCS and JM.
Any variable not listed in will not be imputed.
Specification "void"
represents the extreme scenario that
skips imputation of all variables.
A variable may be a member of multiple blocks. The variable will be reimputed in each block, so the final imputations for variable will come from the last block that was executed. This scenario may be useful where the same complete background factors appear in multiple imputation blocks.
A variable may appear multiple times within a given block. If a univariate imputation model is applied to such a block, then the variable is reimputed each time as it appears in the block.
A named list of character vectors with variables names.
make.blocks(nhanes)
make.blocks(c("age", "sex", "edu"))
blots
argumentThis helper function creates a valid blots
object. The
blots
object is an argument to the mice
function.
The name blots
is a contraction of blocksdots.
Through blots
, the user can specify any additional
arguments that are specifically passed down to the lowest level
imputation function.
make.blots(data, blocks = make.blocks(data))
data 
A 
blocks 
An optional specification for blocks of variables in the rows. The default assigns each variable in its own block. 
A matrix
make.predictorMatrix(nhanes)
make.blots(nhanes, blocks = name.blocks(c("age", "hyp"), "xxx"))
formulas
argumentThis helper function creates a valid formulas
object. The
formulas
object is an argument to the mice
function.
It is a list of formula's that specifies the target variables and
the predictors by means of the standard ~
operator.
make.formulas(data, blocks = make.blocks(data), predictorMatrix = NULL)
data 
A 
blocks 
An optional specification for blocks of variables in the rows. The default assigns each variable in its own block. 
predictorMatrix 
A 
A list of formula's.
make.blocks
, make.predictorMatrix
f1 < make.formulas(nhanes)
f1
f2 < make.formulas(nhanes, blocks = make.blocks(nhanes, "collect"))
f2
# for editing, it may be easier to work with the character vector
c1 < as.character(f1)
c1
# fold it back into a formula list
f3 < name.formulas(lapply(c1, as.formula))
f3
method
argumentThis helper function creates a valid method
vector. The
method
vector is an argument to the mice
function that
specifies the method for each block.
make.method(
data,
where = make.where(data),
blocks = make.blocks(data),
defaultMethod = c("pmm", "logreg", "polyreg", "polr")
)
data 
A data frame or a matrix containing the incomplete data. Missing
values are coded as 
where 
A data frame or matrix with logicals of the same dimensions
as 
blocks 
List of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see 
defaultMethod 
A vector of length 4 containing the default
imputation methods for 1) numeric data, 2) factor data with 2 levels, 3)
factor data with > 2 unordered levels, and 4) factor data with > 2
ordered levels. By default, the method uses

Vector of length(blocks)
element with method names
make.method(nhanes2)
post
argumentThis helper function creates a valid post
vector. The
post
vector is an argument to the mice
function that
specifies postprocessing for a variable after each iteration of imputation.
make.post(data)
data 
A data frame or a matrix containing the incomplete data. Missing
values are coded as 
Character vector of ncol(data)
element
make.post(nhanes2)
predictorMatrix
argumentThis helper function creates a valid predictMatrix
. The
predictorMatrix
is an argument to the mice
function.
It specifies the target variable or block in the rows, and the
predictor variables on the columns. An entry of 0
means that
the column variable is NOT used to impute the row variable or block.
A nonzero value indicates that it is used.
make.predictorMatrix(data, blocks = make.blocks(data), predictorMatrix = NULL)
data 
A 
blocks 
An optional specification for blocks of variables in the rows. The default assigns each variable in its own block. 
predictorMatrix 
A predictor matrix from which rows with the same names are copied into the output predictor matrix. 
A matrix
make.predictorMatrix(nhanes)
make.predictorMatrix(nhanes, blocks = make.blocks(nhanes, "collect"))
visitSequence
argumentThis helper function creates a valid visitSequence
. The
visitSequence
is an argument to the mice
function that
specifies the sequence in which blocks are imputed.
make.visitSequence(data = NULL, blocks = NULL)
data 
A data frame or a matrix containing the incomplete data. Missing
values are coded as 
blocks 
List of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see 
Vector containing block names
make.visitSequence(nhanes)
where
argumentThis helper function creates a valid where
matrix. The
where
matrix is an argument to the mice
function.
It has the same size as data
and specifies which values
are to be imputed (TRUE
) or nor (FALSE
).
make.where(data, keyword = c("missing", "all", "none", "observed"))
data 
A 
keyword 
An optional keyword, one of 
A matrix with logical
make.blocks
, make.predictorMatrix
head(make.where(nhanes), 3)
# create & analyse synthetic data
where < make.where(nhanes2, "all")
imp < mice(nhanes2,
m = 10, where = where,
print = FALSE, seed = 123
)
fit < with(imp, lm(chl ~ bmi + age + hyp))
summary(pool.syn(fit))
Dataset from Allison and Cicchetti (1976) of 62 mammal species on the interrelationship between sleep, ecological, and constitutional variables. The dataset contains missing values on five variables.
mammalsleep
is a data frame with 62 rows and 11 columns:
Species of animal
Body weight (kg)
Brain weight (g)
Slow wave ("nondreaming") sleep (hrs/day)
Paradoxical ("dreaming") sleep (hrs/day)
Total sleep (hrs/day) (sum of slow wave and paradoxical sleep)
Maximum life span (years)
Gestation time (days)
Predation index (15), 1 = least likely to be preyed upon
Sleep exposure index (15), 1 = least exposed (e.g. animal sleeps in a wellprotected den), 5 = most exposed
Overall danger index (15) based on the above two indices and other information, 1 = least danger (from other animals), 5 = most danger (from other animals)
Allison and Cicchetti (1976) investigated the interrelationship between sleep, ecological, and constitutional variables. They assessed these variables for 39 mammalian species. The authors concluded that slowwave sleep is negatively associated with a factor related to body size. This suggests that large amounts of this sleep phase are disadvantageous in large species. Also, paradoxical sleep (REM sleep) was associated with a factor related to predatory danger, suggesting that large amounts of this sleep phase are disadvantageous in prey species.
Allison, T., Cicchetti, D.V. (1976). Sleep in Mammals: Ecological and Constitutional Correlates. Science, 194(4266), 732734.
sleep < data(mammalsleep)
Find index of matched donor units
matchindex(d, t, k = 5L)
d 
Numeric vector with values from donor cases. 
t 
Numeric vector with values from target cases. 
k 
Integer, number of unique donors from which a random draw is made.
For 
For each element in t
, the method finds the k
nearest
neighbours in d
, randomly draws one of these neighbours, and
returns its position in vector d
.
Fast predictive mean matching algorithm in seven steps:
1. Shuffle records to remove effects of ties
2. Obtain sorting order on shuffled data
3. Calculate index on input data and sort it
4. Presample vector h
with values between 1 and k
For each of the n0
elements in t
:
5. find the two adjacent neighbours
6. find the h_i
'th nearest neighbour
7. store the index of that neighbour
Return vector of n0
positions in d
.
We may use the function to perform predictive mean matching under a given
predictive model. To do so, specify both d
and t
as
predictions from the same model. Suppose that y
contains the observed
outcomes of the donor cases (in the same sequence as d
), then
y[matchindex(d, t)]
returns one matched outcome for every
target case.
See https://github.com/amices/mice/issues/236.
This function is a replacement for the matcher()
function that has
been in default in mice
since version 2.22
(June 2014).
An integer vector with length(t)
elements. Each
element is an index in the array d
.
Stef van Buuren, Nasinski Maciej, Alexander Robitzsch
set.seed(1)
# Inputs need not be sorted
d < c(5, 5, 0, 10, 12)
t < c(6, 4, 0, 2, 4, 2, 6)
# Index (in vector a) of closest match
idx < matchindex(d, t, 1)
idx
# To check: show values of closest match
# Random draw among indices of the 5 closest predictors
matchindex(d, t)
# An example
train < mtcars[1:20, ]
test < mtcars[21:32, ]
fit < lm(mpg ~ disp + cyl, data = train)
d < fitted.values(fit)
t < predict(fit, newdata = test) # note: not using mpg
idx < matchindex(d, t)
# Borrow values from train to produce 12 synthetic values for mpg in test.
# Synthetic values are plausible values that could have been observed if
# they had been measured.
train$mpg[idx]
# Exercise: Create a distribution of 1000 plausible values for each of the
# twelve mpg entries in test, and count how many times the true value
# (which we know here) is located within the interquartile range of each
# distribution. Is your count anywhere close to 500? Why? Why not?
Number of observations per variable pair.
md.pairs(data)
data 
A data frame or a matrix containing the incomplete data. Missing
values are coded as 
The four components in the output value is have the following interpretation:
responseresponse, both variables are observed
responsemissing, row observed, column missing
missing response, row missing, column observed
missing missing, both variables are missing
A list of four components named rr
, rm
, mr
and
mm
. Each component is square numerical matrix containing the number
observations within four missing data pattern.
Stef van Buuren, Karin GroothuisOudshoorn, 2009
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
pat < md.pairs(nhanes)
pat
# show that these four matrices decompose the total sample size
# for each pair
pat$rr + pat$rm + pat$mr + pat$mm
# percentage of usable cases to impute row variable from column variable
round(100 * pat$mr / (pat$mr + pat$mm))
Display missingdata patterns.
md.pattern(x, plot = TRUE, rotate.names = FALSE)
x 
A data frame or a matrix containing the incomplete data. Missing values are coded as NA's. 
plot 
Should the missing data pattern be made into a plot. Default is 'plot = TRUE'. 
rotate.names 
Whether the variable names in the plot should be placed horizontally or vertically. Default is 'rotate.names = FALSE'. 
This function is useful for investigating any structure of missing observations in the data. In specific case, the missing data pattern could be (nearly) monotone. Monotonicity can be used to simplify the imputation model. See Schafer (1997) for details. Also, the missing pattern could suggest which variables could potentially be useful for imputation of missing entries.
A matrix with ncol(x)+1
columns, in which each row corresponds
to a missing data pattern (1=observed, 0=missing). Rows and columns are
sorted in increasing amounts of missing information. The last column and row
contain row and column counts, respectively.
Gerko Vink, 2018, based on an earlier version of the same function by Stef van Buuren, Karin GroothuisOudshoorn, 2000
Schafer, J.L. (1997), Analysis of multivariate incomplete data. London: Chapman&Hall.
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
md.pattern(nhanes)
# age hyp bmi chl
# 13 1 1 1 1 0
# 1 1 1 0 1 1
# 3 1 1 1 0 1
# 1 1 0 0 1 2
# 7 1 0 0 0 3
# 0 8 9 10 27
mdc
returns colors used to distinguish observed, missing and combined
data in plotting. mice.theme
return a partial list of named objects
that can be used as a theme in stripplot
, bwplot
,
densityplot
and xyplot
.
mdc(
r = "observed",
s = "symbol",
transparent = TRUE,
cso = grDevices::hcl(240, 100, 40, 0.7),
csi = grDevices::hcl(0, 100, 40, 0.7),
csc = "gray50",
clo = grDevices::hcl(240, 100, 40, 0.8),
cli = grDevices::hcl(0, 100, 40, 0.8),
clc = "gray50"
)
r 
A numerical or character vector. The numbers 16 request colors as
follows: 1= 
s 
A character vector containing the strings ' 
transparent 
A logical indicating whether alphatransparency is
allowed. The default is 
cso 
The symbol color for the observed data. The default is a transparent blue. 
csi 
The symbol color for the missing or imputed data. The default is a transparent red. 
csc 
The symbol color for the combined observed and imputed data. The default is a grey color. 
clo 
The line color for the observed data. The default is a slightly darker transparent blue. 
cli 
The line color for the missing or imputed data. The default is a slightly darker transparent red. 
clc 
The line color for the combined observed and imputed data. The default is a grey color. 
This function eases consistent use of colors in plots. The default follows the Abayomi convention, which uses blue for observed data, red for missing or imputed data, and black for combined data.
mdc()
returns a vector containing color definitions. The length
of the output vector is calculate from the length of r
and s
.
Elements of the input vectors are repeated if needed.
Stef van Buuren, sept 2012.
Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer.
hcl
, rgb
,
xyplot.mids
, xyplot
,
trellis.par.set
# all six colors
mdc(1:6)
# lines color for observed and missing data
mdc(c("obs", "mis"), "lin")
glmer
Imputes univariate systematically and sporadically missing data
using a twolevel logistic model using lme4::glmer()
mice.impute.2l.bin(y, ry, x, type, wy = NULL, intercept = TRUE, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Vector of length 
wy 
Logical vector of length 
intercept 
Logical determining whether the intercept is automatically added. 
... 
Arguments passed down to 
Data are missing systematically if they have not been measured, e.g., in the case where we combine data from different sources. Data are missing sporadically if they have been partially observed.
Vector with imputed data, same type as y
, and of length
sum(wy)
Shahab Jolani, 2015; adapted to mice, SvB, 2018
Jolani S., Debray T.P.A., Koffijberg H., van Buuren S., Moons K.G.M. (2015). Imputation of systematically missing predictors in an individual participant data metaanalysis: a generalized approach using MICE. Statistics in Medicine, 34:18411863.
Other univariate2l:
mice.impute.2l.lmer()
,
mice.impute.2l.norm()
,
mice.impute.2l.pan()
library(tidyr)
library(dplyr)
data("toenail2")
data < tidyr::complete(toenail2, patientID, visit) %>%
tidyr::fill(treatment) %>%
dplyr::select(time) %>%
dplyr::mutate(patientID = as.integer(patientID))
## Not run:
pred < mice(data, print = FALSE, maxit = 0, seed = 1)$pred
pred["outcome", "patientID"] < 2
imp < mice(data, method = "2l.bin", pred = pred, maxit = 1, m = 1, seed = 1)
## End(Not run)
lmer
Imputes univariate systematically and sporadically missing data using a
twolevel normal model using lme4::lmer()
.
mice.impute.2l.lmer(y, ry, x, type, wy = NULL, intercept = TRUE, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Vector of length 
wy 
Logical vector of length 
intercept 
Logical determining whether the intercept is automatically added. 
... 
Arguments passed down to 
Data are missing systematically if they have not been measured, e.g., in the case where we combine data from different sources. Data are missing sporadically if they have been partially observed.
While the method is fully Bayesian, it may fix parameters of the variancecovariance matrix or the random effects to their estimated value in cases where creating draws from the posterior is not possible. The procedure throws a warning when this happens.
If lme4::lmer()
fails, the procedure prints the warning
"lmer does not run. Simplify imputation model"
and returns the
current imputation. If that happens we see flat lines in the
trace line plots. Thus, the appearance of flat trace lines should be taken
as an additional alert to a problem with imputation model fitting.
Vector with imputed data, same type as y
, and of length
sum(wy)
Shahab Jolani, 2017
Jolani S. (2017) Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations. Forthcoming.
Jolani S., Debray T.P.A., Koffijberg H., van Buuren S., Moons K.G.M. (2015). Imputation of systematically missing predictors in an individual participant data metaanalysis: a generalized approach using MICE. Statistics in Medicine, 34:18411863.
Van Buuren, S. (2011) Multiple imputation of multilevel data. In Hox, J.J. and and Roberts, J.K. (Eds.), The Handbook of Advanced Multilevel Analysis, Chapter 10, pp. 173–196. Milton Park, UK: Routledge.
Other univariate2l:
mice.impute.2l.bin()
,
mice.impute.2l.norm()
,
mice.impute.2l.pan()
Imputes univariate missing data using a twolevel normal model
mice.impute.2l.norm(y, ry, x, type, wy = NULL, intercept = TRUE, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Vector of length 
wy 
Logical vector of length 
intercept 
Logical determining whether the intercept is automatically added. 
... 
Other named arguments. 
Implements the Gibbs sampler for the linear multilevel model with heterogeneous withclass variance (Kasim and Raudenbush, 1998). Imputations are drawn as an extra step to the algorithm. For simulation work see Van Buuren (2011).
The random intercept is automatically added in mice.impute.2L.norm()
.
A model within a random intercept can be specified by mice(...,
intercept = FALSE)
.
Vector with imputed data, same type as y
, and of length
sum(wy)
Added June 25, 2012: The currently implemented algorithm does not
handle predictors that are specified as fixed effects (type=1). When using
mice.impute.2l.norm()
, the current advice is to specify all predictors
as random effects (type=2).
Warning: The assumption of heterogeneous variances requires that in every
class at least one observation has a response in y
.
Roel de Jong, 2008
Kasim RM, Raudenbush SW. (1998). Application of Gibbs sampling to nested variance components models with heterogeneous withingroup variance. Journal of Educational and Behavioral Statistics, 23(2), 93–116.
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
Van Buuren, S. (2011) Multiple imputation of multilevel data. In Hox, J.J. and and Roberts, J.K. (Eds.), The Handbook of Advanced Multilevel Analysis, Chapter 10, pp. 173–196. Milton Park, UK: Routledge.
Other univariate2l:
mice.impute.2l.bin()
,
mice.impute.2l.lmer()
,
mice.impute.2l.pan()
pan
Imputes univariate missing data using a twolevel normal model with
homogeneous within group variances. Aggregated group effects (i.e. group
means) can be automatically created and included as predictors in the
twolevel regression (see argument type
). This function needs the
pan
package.
mice.impute.2l.pan(
y,
ry,
x,
type,
intercept = TRUE,
paniter = 500,
groupcenter.slope = FALSE,
...
)
y 
Incomplete data vector of length 
ry 
Vector of missing data pattern ( 
x 
Matrix ( 
type 
Vector of length 
intercept 
Logical determining whether the intercept is automatically added. 
paniter 
Number of iterations in 
groupcenter.slope 
If 
... 
Other named arguments. 
Implements the Gibbs sampler for the linear twolevel model with homogeneous
within group variances which is a special case of a multivariate linear mixed
effects model (Schafer & Yucel, 2002). For a twolevel imputation with
heterogeneous withingroup variances see mice.impute.2l.norm
.
The random intercept is automatically added in
mice.impute.2l.norm()
.
A vector of length nmis
with imputations.
This function does not implement the where
functionality. It
always produces nmis
imputation, irrespective of the where
argument of the mice
function.
Alexander Robitzsch (IPN  Leibniz Institute for Science and Mathematics Education, Kiel, Germany), [email protected]
Alexander Robitzsch (IPN  Leibniz Institute for Science and Mathematics Education, Kiel, Germany), [email protected].
Schafer J L, Yucel RM (2002). Computational strategies for multivariate linear mixedeffects models with missing values. Journal of Computational and Graphical Statistics. 11, 437457.
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
Other univariate2l:
mice.impute.2l.bin()
,
mice.impute.2l.lmer()
,
mice.impute.2l.norm()
# simulate some data
# twolevel regression model with fixed slope
# number of groups
G < 250
# number of persons
n < 20
# regression parameter
beta < .3
# intraclass correlation
rho < .30
# correlation with missing response
rho.miss < .10
# missing proportion
missrate < .50
y1 < rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1  rho))
x < rnorm(G * n)
y < y1 + beta * x
dfr0 < dfr < data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1  rho.miss)) < qnorm(missrate), "y"] < NA
# empty imputation in mice
imp0 < mice(as.matrix(dfr), maxit = 0)
predM < imp0$predictorMatrix
impM < imp0$method
# specify predictor matrix and method
predM1 < predM
predM1["y", "group"] < 2
predM1["y", "x"] < 1 # fixed x effects imputation
impM1 < impM
impM1["y"] < "2l.pan"
# multilevel imputation
imp1 < mice(as.matrix(dfr),
m = 1, predictorMatrix = predM1,
method = impM1, maxit = 1
)
# multilevel analysis
library(lme4)
mod < lmer(y ~ (1 + x  group) + x, data = complete(imp1))
summary(mod)
# Examples of predictorMatrix specification
# random x effects
# predM1["y","x"] < 2
# fixed x effects and group mean of x
# predM1["y","x"] < 3
# random x effects and group mean of x
# predM1["y","x"] < 4
Method 2lonly.mean
replicates the most likely value within
a class of a secondlevel variable. It works for numeric and
factor data. The function is primarily useful as a quick fixup for
data in which the secondlevel variable is inconsistent.
mice.impute.2lonly.mean(y, ry, x, type, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Vector of length 
wy 
Logical vector of length 
... 
Other named arguments. 
Observed values in y
are averaged within the class, and
replicated to the missing y
within that class.
This function is primarily useful for repairing incomplete data
that are constant within the class, but vary over classes.
For numeric variables, mice.impute.2lonly.mean()
imputes the
class mean of y
. If y
is a secondlevel variable, then
conventionally all observed y
will be identical within the
class, and the function just provides a quick fix for any
missing y
by filling in the class mean.
For factor variables, mice.impute.2lonly.mean()
imputes the
most frequently occuring category within the class.
If there are no observed y
in the class, all entries of the
class are set to NA
. Note that this may produce problems
later on in mice
if imputation routines are called that
expects predictor data to be complete. Methods designed for
imputing this type of secondlevel variables include
mice.impute.2lonly.norm
and
mice.impute.2lonly.pmm
.
Vector with imputed data, same type as y
, and of length
sum(wy)
Gerko Vink, Stef van Buuren, 2019
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Boca Raton, FL.: Chapman & Hall/CRC Press.
Other univariate2lonly:
mice.impute.2lonly.norm()
,
mice.impute.2lonly.pmm()
Imputes univariate missing data at level 2 using Bayesian linear regression
analysis. Variables are level 1 are aggregated at level 2. The group
identifier at level 2 must be indicated by type = 2
in the
predictorMatrix
.
mice.impute.2lonly.norm(y, ry, x, type, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Group identifier must be specified by '2'. Predictors must be specified by '1'. 
wy 
Logical vector of length 
... 
Other named arguments. 
This function allows in combination with mice.impute.2l.pan
switching regression imputation between level 1 and level 2 as described in
Yucel (2008) or Gelman and Hill (2007, p. 541).
The function checks for partial missing level2 data. Level2 data
are assumed to be constant within the same cluster. If one or more
entries are missing, then the procedure aborts with an error
message that identifies the cluster with incomplete level2 data.
In such cases, one may first fill in the cluster mean (or mode) by
the 2lonly.mean
method to remove inconsistencies.
A vector of length nmis
with imputations.
For a more general approach, see
miceadds::mice.impute.2lonly.function()
.
Alexander Robitzsch (IPN  Leibniz Institute for Science and Mathematics Education, Kiel, Germany), [email protected]
Gelman, A. and Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge, Cambridge University Press.
Yucel, RM (2008). Multiple imputation inference for multivariate multilevel continuous data with ignorable nonresponse. Philosophical Transactions of the Royal Society A, 366, 23892404.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
mice.impute.norm
,
mice.impute.2lonly.pmm
, mice.impute.2l.pan
,
mice.impute.2lonly.mean
Other univariate2lonly:
mice.impute.2lonly.mean()
,
mice.impute.2lonly.pmm()
# simulate some data
# x,y ... level 1 variables
# v,w ... level 2 variables
G < 250 # number of groups
n < 20 # number of persons
beta < .3 # regression coefficient
rho < .30 # residual intraclass correlation
rho.miss < .10 # correlation with missing response
missrate < .50 # missing proportion
y1 < rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1  rho))
w < rep(round(rnorm(G), 2), each = n)
v < rep(round(runif(G, 0, 3)), each = n)
x < rnorm(G * n)
y < y1 + beta * x + .2 * w + .1 * v
dfr0 < dfr < data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y, "w" = w, "v" = v)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1  rho.miss)) < qnorm(missrate), "y"] < NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "w"] < NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "v"] < NA
# empty mice imputation
imp0 < mice(as.matrix(dfr), maxit = 0)
predM < imp0$predictorMatrix
impM < imp0$method
# multilevel imputation
predM1 < predM
predM1[c("w", "y", "v"), "group"] < 2
predM1["y", "x"] < 1 # fixed x effects imputation
impM1 < impM
impM1[c("y", "w", "v")] < c("2l.pan", "2lonly.norm", "2lonly.pmm")
# y ... imputation using pan
# w ... imputation at level 2 using norm
# v ... imputation at level 2 using pmm
imp1 < mice(as.matrix(dfr),
m = 1, predictorMatrix = predM1,
method = impM1, maxit = 1, paniter = 500
)
# Demonstration that 2lonly.norm aborts for partial missing data.
# Better use 2lonly.mean for repair.
data < data.frame(
patid = rep(1:4, each = 5),
sex = rep(c(1, 2, 1, 2), each = 5),
crp = c(
68, 78, 93, NA, 143,
5, 7, 9, 13, NA,
97, NA, 56, 52, 34,
22, 30, NA, NA, 45
)
)
pred < make.predictorMatrix(data)
pred[, "patid"] < 2
# only missing value (out of five) for patid == 1
data[3, "sex"] < NA
## Not run:
# The following fails because 2lonly.norm found partially missing
# level2 data
# imp < mice(data, method = c("", "2lonly.norm", "2l.pan"),
# predictorMatrix = pred, maxit = 1, m = 2)
# > iter imp variable
# > 1 1 sex crpError in .imputation.level2(y = y, ... :
# > Method 2lonly.norm found the following clusters with partially missing
# > level2 data: 1
# > Method 2lonly.mean can fix such inconsistencies.
## End(Not run)
# In contrast, if all sex values are missing for patid == 1, it runs fine,
# except on rpatchedsolarisx86. I used dontrun to evade CRAN errors.
## Not run:
data[1:5, "sex"] < NA
imp < mice(data,
method = c("", "2lonly.norm", "2l.pan"),
predictorMatrix = pred, maxit = 1, m = 2
)
## End(Not run)
Imputes univariate missing data at level 2 using predictive mean matching.
Variables are level 1 are aggregated at level 2. The group identifier at
level 2 must be indicated by type = 2
in the predictorMatrix
.
mice.impute.2lonly.pmm(y, ry, x, type, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
type 
Group identifier must be specified by '2'. Predictors must be specified by '1'. 
wy 
Logical vector of length 
... 
Other named arguments. 
This function allows in combination with mice.impute.2l.pan
switching regression imputation between level 1 and level 2 as described in
Yucel (2008) or Gelman and Hill (2007, p. 541).
The function checks for partial missing level2 data. Level2 data
are assumed to be constant within the same cluster. If one or more
entries are missing, then the procedure aborts with an error
message that identifies the cluster with incomplete level2 data.
In such cases, one may first fill in the cluster mean (or mode) by
the 2lonly.mean
method to remove inconsistencies.
A vector of length nmis
with imputations.
The extension to categorical variables transforms
a dependent factor variable by means of the as.integer()
function. This may make sense for categories that are
approximately ordered, but less so for pure nominal measures.
For a more general approach, see
miceadds::mice.impute.2lonly.function()
.
Alexander Robitzsch (IPN  Leibniz Institute for Science and Mathematics Education, Kiel, Germany), [email protected]
Gelman, A. and Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge, Cambridge University Press.
Yucel, RM (2008). Multiple imputation inference for multivariate multilevel continuous data with ignorable nonresponse. Philosophical Transactions of the Royal Society A, 366, 23892404.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
mice.impute.pmm
,
mice.impute.2lonly.norm
, mice.impute.2l.pan
,
mice.impute.2lonly.mean
Other univariate2lonly:
mice.impute.2lonly.mean()
,
mice.impute.2lonly.norm()
# simulate some data
# x,y ... level 1 variables
# v,w ... level 2 variables
G < 250 # number of groups
n < 20 # number of persons
beta < .3 # regression coefficient
rho < .30 # residual intraclass correlation
rho.miss < .10 # correlation with missing response
missrate < .50 # missing proportion
y1 < rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1  rho))
w < rep(round(rnorm(G), 2), each = n)
v < rep(round(runif(G, 0, 3)), each = n)
x < rnorm(G * n)
y < y1 + beta * x + .2 * w + .1 * v
dfr0 < dfr < data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y, "w" = w, "v" = v)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1  rho.miss)) < qnorm(missrate), "y"] < NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "w"] < NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "v"] < NA
# empty mice imputation
imp0 < mice(as.matrix(dfr), maxit = 0)
predM < imp0$predictorMatrix
impM < imp0$method
# multilevel imputation
predM1 < predM
predM1[c("w", "y", "v"), "group"] < 2
predM1["y", "x"] < 1 # fixed x effects imputation
impM1 < impM
impM1[c("y", "w", "v")] < c("2l.pan", "2lonly.norm", "2lonly.pmm")
# turn v into a categorical variable
dfr$v < as.factor(dfr$v)
levels(dfr$v) < LETTERS[1:4]
# y ... imputation using pan
# w ... imputation at level 2 using norm
# v ... imputation at level 2 using pmm
# skip imputation on solaris
is.solaris < function() grepl("SunOS", Sys.info()["sysname"])
if (!is.solaris()) {
imp < mice(dfr,
m = 1, predictorMatrix = predM1,
method = impM1, maxit = 1, paniter = 500
)
}
Imputes univariate missing data using classification and regression trees.
mice.impute.cart(y, ry, x, wy = NULL, minbucket = 5, cp = 1e04, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
minbucket 
The minimum number of observations in any terminal node used.
See 
cp 
Complexity parameter. Any split that does not decrease the overall
lack of fit by a factor of cp is not attempted. See 
... 
Other named arguments passed down to 
Imputation of y
by classification and regression trees. The procedure
is as follows:
Fit a classification or regression tree by recursive partitioning;
For each ymis
, find the terminal node they end up according to the fitted tree;
Make a random draw among the member in the node, and take the observed value from that draw as the imputation.
Vector with imputed data, same type as y
, and of length
sum(wy)
Numeric vector of length sum(!ry)
with imputations
Lisa Doove, Stef van Buuren, Elise Dusseldorp, 2012
Doove, L.L., van Buuren, S., Dusseldorp, E. (2014), Recursive partitioning for missing data imputation in the presence of interaction Effects. Computational Statistics & Data Analysis, 72, 92104.
Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984), Classification and regression trees, Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
mice
, mice.impute.rf
,
rpart
, rpart.control
Other univariate imputation functions:
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
imp < mice(nhanes2, meth = "cart", minbucket = 4)
plot(imp)
jomo
This function is a wrapper around the jomoImpute
function
from the mitml
package so that it can be called to
impute blocks of variables in mice
. The mitml::jomoImpute
function provides an interface to the jomo
package for
multiple imputation of multilevel data
https://CRAN.Rproject.org/package=jomo.
Imputations can be generated using type
or formula
,
which offer different options for model specification.
mice.impute.jomoImpute(
data,
formula,
type,
m = 1,
silent = TRUE,
format = "imputes",
...
)
data 
A data frame containing incomplete and auxiliary variables, the cluster indicator variable, and any other variables that should be present in the imputed datasets. 
formula 
A formula specifying the role of each variable
in the imputation model. The basic model is constructed
by 
type 
An integer vector specifying the role of each variable
in the imputation model (see 
m 
The number of imputed data sets to generate. Default is 10. 
silent 
(optional) Logical flag indicating if console output should be suppressed. Default is 
format 
A character vector specifying the type of object that should
be returned. The default is 
... 
Other named arguments: 
A list of imputations for all incomplete variables in the model,
that can be stored in the the imp
component of the mids
object.
The number of imputations m
is set to 1, and the function
is called m
times so that it fits within the mice
iteration scheme.
This is a multivariate imputation function using a joint model.
Stef van Buuren, 2018, building on work of Simon Grund,
Alexander Robitzsch and Oliver Luedtke (authors of mitml
package)
and Quartagno and Carpenter (authors of jomo
package).
Grund S, Luedtke O, Robitzsch A (2016). Multiple
Imputation of Multilevel Missing Data: An Introduction to the R
Package pan
. SAGE Open.
Quartagno M and Carpenter JR (2015). Multiple imputation for IPD metaanalysis: allowing for heterogeneity and studies with missing covariates. Statistics in Medicine, 35:29382954, 2015.
Other multivariate2l:
mice.impute.panImpute()
## Not run:
# Note: Requires mitml 0.35.7
blocks < list(c("bmi", "chl", "hyp"), "age")
method < c("jomoImpute", "pmm")
ini < mice(nhanes, blocks = blocks, method = method, maxit = 0)
pred < ini$pred
pred["B1", "hyp"] < 2
imp < mice(nhanes, blocks = blocks, method = method, pred = pred, maxit = 1)
## End(Not run)
Imputes univariate missing binary data using lasso logistic regression with bootstrap.
mice.impute.lasso.logreg(y, ry, x, wy = NULL, nfolds = 10, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nfolds 
The number of folds for the crossvalidation of the lasso penalty. The default is 10. 
... 
Other named arguments. 
The method consists of the following steps:
For a given y variable under imputation, draw a bootstrap version y*
with replacement from the observed cases y[ry]
, and stores in x* the
corresponding values from x[ry, ]
.
Fit a regularised (lasso) logistic regression with y* as the outcome, and x* as predictors. A vector of regression coefficients bhat is obtained. All of these coefficients are considered random draws from the imputation model parameters posterior distribution. Same of these coefficients will be shrunken to 0.
Compute predicted scores for m.d., i.e. logit1(X bhat)
Compare the score to a random (0,1) deviate, and impute.
The method is based on the Direct Use of Regularized Regression (DURR) proposed by Zhao & Long (2016) and Deng et al (2016).
Vector with imputed data, same type as y
, and of length
sum(wy)
Edoardo Costantini, 2021
Deng, Y., Chang, C., Ido, M. S., & Long, Q. (2016). Multiple imputation for general missing data patterns in the presence of highdimensional data. Scientific reports, 6(1), 110.
Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of highdimensional data. Statistical Methods in Medical Research, 25(5), 20212035.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing normal data using lasso linear regression with bootstrap.
mice.impute.lasso.norm(y, ry, x, wy = NULL, nfolds = 10, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nfolds 
The number of folds for the crossvalidation of the lasso penalty. The default is 10. 
... 
Other named arguments. 
The method consists of the following steps:
For a given y variable under imputation, draw a bootstrap version y*
with replacement from the observed cases y[ry]
, and stores in x* the
corresponding values from x[ry, ]
.
Fit a regularised (lasso) linear regression with y* as the outcome, and x* as predictors. A vector of regression coefficients bhat is obtained. All of these coefficients are considered random draws from the imputation model parameters posterior distribution. Same of these coefficients will be shrunken to 0.
Draw the imputed values from the predictive distribution defined by the original (nonbootstrap) data, bhat, and estimated error variance.
The method is based on the Direct Use of Regularized Regression (DURR) proposed by Zhao & Long (2016) and Deng et al (2016).
Vector with imputed data, same type as y
, and of length
sum(wy)
Edoardo Costantini, 2021
Deng, Y., Chang, C., Ido, M. S., & Long, Q. (2016). Multiple imputation for general missing data patterns in the presence of highdimensional data. Scientific reports, 6(1), 110.
Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of highdimensional data. Statistical Methods in Medical Research, 25(5), 20212035.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using logistic regression following a preprocessing lasso variable selection step.
mice.impute.lasso.select.logreg(y, ry, x, wy = NULL, nfolds = 10, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nfolds 
The number of folds for the crossvalidation of the lasso penalty. The default is 10. 
... 
Other named arguments. 
The method consists of the following steps:
For a given y
variable under imputation, fit a linear regression with lasso
penalty using y[ry]
as dependent variable and x[ry, ]
as predictors.
The coefficients that are not shrunk to 0 define the active set of predictors
that will be used for imputation.
Fit a logit with the active set of predictors, and find (bhat, V(bhat))
Draw BETA from N(bhat, V(bhat))
Compute predicted scores for m.d., i.e. logit1(X BETA)
Compare the score to a random (0,1) deviate, and impute.
The user can specify a predictorMatrix
in the mice
call
to define which predictors are provided to this univariate imputation method.
The lasso regularization will select, among the variables indicated by
the user, the ones that are important for imputation at any given iteration.
Therefore, users may force the exclusion of a predictor from a given
imputation model by speficing a 0
entry.
However, a nonzero entry does not guarantee the variable will be used,
as this decision is ultimately made by the lasso variable selection
procedure.
The method is based on the Indirect Use of Regularized Regression (IURR) proposed by Zhao & Long (2016) and Deng et al (2016).
Vector with imputed data, same type as y
, and of length
sum(wy)
Edoardo Costantini, 2021
Deng, Y., Chang, C., Ido, M. S., & Long, Q. (2016). Multiple imputation for general missing data patterns in the presence of highdimensional data. Scientific reports, 6(1), 110.
Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of highdimensional data. Statistical Methods in Medical Research, 25(5), 20212035.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using Bayesian linear regression following a preprocessing lasso variable selection step.
mice.impute.lasso.select.norm(y, ry, x, wy = NULL, nfolds = 10, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nfolds 
The number of folds for the crossvalidation of the lasso penalty. The default is 10. 
... 
Other named arguments. 
The method consists of the following steps:
For a given y
variable under imputation, fit a linear regression with lasso
penalty using y[ry]
as dependent variable and x[ry, ]
as predictors.
Coefficients that are not shrunk to 0 define an active set of predictors
that will be used for imputation
Define a Bayesian linear model using y[ry]
as the
dependent variable, the active set of x[ry, ]
as predictors, and standard
noninformative priors
Draw parameter values for the intercept, regression weights, and error variance from their posterior distribution
Draw imputations from the posterior predictive distribution
The user can specify a predictorMatrix
in the mice
call
to define which predictors are provided to this univariate imputation method.
The lasso regularization will select, among the variables indicated by
the user, the ones that are important for imputation at any given iteration.
Therefore, users may force the exclusion of a predictor from a given
imputation model by specifying a 0
entry.
However, a nonzero entry does not guarantee the variable will be used,
as this decision is ultimately made by the lasso variable selection
procedure.
The method is based on the Indirect Use of Regularized Regression (IURR) proposed by Zhao & Long (2016) and Deng et al (2016).
Vector with imputed data, same type as y
, and of length
sum(wy)
Edoardo Costantini, 2021
Deng, Y., Chang, C., Ido, M. S., & Long, Q. (2016). Multiple imputation for general missing data patterns in the presence of highdimensional data. Scientific reports, 6(1), 110.
Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of highdimensional data. Statistical Methods in Medical Research, 25(5), 20212035.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using linear discriminant analysis
mice.impute.lda(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. Not used. 
Imputation of categorical response variables by linear discriminant analysis.
This function uses the Venables/Ripley functions lda()
and
predict.lda()
to compute posterior probabilities for each incomplete
case, and draws the imputations from this posterior.
This function can be called from within the Gibbs sampler by specifying
"lda"
in the method
argument of mice()
. This method is usually
faster and uses fewer resources than calling the function, but the statistical
properties may not be as good (Brand, 1999).
mice.impute.polyreg
.
Vector with imputed data, of type factor, and of length
sum(wy)
The function does not incorporate the variability of the
discriminant weight, so it is not 'proper' in the sense of Rubin. For small
samples and rare categories in the y
, variability of the imputed data
could therefore be underestimated.
Added: SvB June 2009 Tried to include bootstrap, but disabled since bootstrapping may easily lead to constant variables within groups.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Brand, J.P.L. (1999). Development, Implementation and Evaluation of Multiple Imputation Strategies for the Statistical Analysis of Incomplete Data Sets. Ph.D. Thesis, TNO Prevention and Health/Erasmus University Rotterdam. ISBN 9074479081.
Venables, W.N. & Ripley, B.D. (1997). Modern applied statistics with SPLUS (2nd ed). Springer, Berlin.
mice
, link{mice.impute.polyreg}
,
lda
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using logistic regression.
mice.impute.logreg(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Imputation for binary response variables by the Bayesian logistic regression model (Rubin 1987, p. 169170). The Bayesian method consists of the following steps:
Fit a logit, and find (bhat, V(bhat))
Draw BETA from N(bhat, V(bhat))
Compute predicted scores for m.d., i.e. logit1(X BETA)
Compare the score to a random (0,1) deviate, and impute.
The method relies on the
standard glm.fit
function. Warnings from glm.fit
are
suppressed. Perfect prediction is handled by the data augmentation
method.
Vector with imputed data, same type as y
, and of length
sum(wy)
Stef van Buuren, Karin GroothuisOudshoorn
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Brand, J.P.L. (1999). Development, Implementation and Evaluation of Multiple Imputation Strategies for the Statistical Analysis of Incomplete Data Sets. Ph.D. Thesis, TNO Prevention and Health/Erasmus University Rotterdam. ISBN 9074479081.
Venables, W.N. & Ripley, B.D. (1997). Modern applied statistics with SPlus (2nd ed). Springer, Berlin.
White, I., Daniel, R. and Royston, P (2010). Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables. Computational Statistics and Data Analysis, 54:22672275.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using logistic regression
by a bootstrapped logistic regression model.
The bootstrap method draws a simple bootstrap sample with replacement
from the observed data y[ry]
and x[ry, ]
.
mice.impute.logreg.boot(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Vector with imputed data, same type as y
, and of length
sum(wy)
Stef van Buuren, Karin GroothuisOudshoorn, 2000, 2011
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes the arithmetic mean of the observed data
mice.impute.mean(y, ry, x = NULL, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Vector with imputed data, same type as y
, and of length
sum(wy)
Imputing the mean of a variable is almost never appropriate. See Little and Rubin (2002, p. 6162) or Van Buuren (2012, p. 1011)
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis with Missing Data. New York: John Wiley and Sons.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using predictive mean matching.
mice.impute.midastouch(
y,
ry,
x,
wy = NULL,
ridge = 1e05,
midas.kappa = NULL,
outout = TRUE,
neff = NULL,
debug = NULL,
...
)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
ridge 
The ridge penalty used in 
midas.kappa 
Scalar. If 
outout 
Logical. If 
neff 
FOR EXPERTS. Null or character string. The name of an existing
environment in which the effective sample size of the donors for each
loop (CE iterations times multiple imputations) is supposed to be written.
The effective sample size is necessary to compute the correction for the
total variance as originally suggested by Parzen, Lipsitz and
Fitzmaurice 2005. The objectname is 
debug 
FOR EXPERTS. Null or character string. The name of an existing
environment in which the input is supposed to be written. The objectname
is 
... 
Other named arguments. 
Imputation of y
by predictive mean matching, based on
Rubin (1987, p. 168, formulas a and b) and Siddique and Belin 2008.
The procedure is as follows:
Draw a bootstrap sample from the donor pool.
Estimate a beta matrix on the bootstrap sample by the leave one out principle.
Compute type II predicted values for yobs
(nobs x 1) and ymis
(nmis x nobs).
Calculate the distance between all yobs
and the corresponding ymis
.
Convert the distances in drawing probabilities.
For each recipient draw a donor from the entire pool while considering the probabilities from the model.
Take its observed value in y
as the imputation.
Vector with imputed data, same type as y
, and of
length sum(wy)
Philipp Gaffert, Florian Meinfelder, Volker Bosch 2015
Gaffert, P., Meinfelder, F., Bosch V. (2015) Towards an MIproper Predictive Mean Matching, Discussion Paper. https://www.unibamberg.de/fileadmin/uni/fakultaeten/sowi_lehrstuehle/statistik/Personen/Dateien_Florian/properPMM.pdf
Little, R.J.A. (1988), Missing data adjustments in large surveys (with discussion), Journal of Business Economics and Statistics, 6, 287–301.
Parzen, M., Lipsitz, S. R., Fitzmaurice, G. M. (2005), A note on reducing the bias of the approximate Bayesian bootstrap imputation variance estimator. Biometrika 92, 4, 971–974.
Rubin, D.B. (1987), Multiple imputation for nonresponse in surveys. New York: Wiley.
Siddique, J., Belin, T.R. (2008), Multiple imputation using an iterative hotdeck with distancebased donor selection. Statistics in medicine, 27, 1, 83–102
Van Buuren, S., Brand, J.P.L., GroothuisOudshoorn C.G.M., Rubin, D.B. (2006), Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, 76, 12, 1049–1064.
Van Buuren, S., GroothuisOudshoorn, K. (2011), mice
: Multivariate
Imputation by Chained Equations in R
. Journal of
Statistical Software, 45, 3, 1–67. doi:10.18637/jss.v045.i03
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
# do default multiple imputation on a numeric matrix
imp < mice(nhanes, method = "midastouch")
imp
# list the actual imputations for BMI
imp$imp$bmi
# first completed data matrix
complete(imp)
# imputation on mixed data with a different method per column
mice(nhanes2, method = c("sample", "midastouch", "logreg", "norm"))
Imputes univariate data under a userspecified MNAR mechanism by linear or logistic regression and NARFCS. Sensitivity analysis under different model specifications may shed light on the impact of different MNAR assumptions on the conclusions.
mice.impute.mnar.logreg(y, ry, x, wy = NULL, ums = NULL, umx = NULL, ...)
mice.impute.mnar.norm(y, ry, x, wy = NULL, ums = NULL, umx = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
ums 
A string containing the specification of the
unidentifiable part of the imputation model (the *unidentifiable
model specification"), that is, the desired 
umx 
An auxiliary data matrix containing variables that do
not appear in the identifiable part of the imputation procedure
but that have been specified via 
... 
Other named arguments. 
This function imputes data that are thought to be Missing Not at
Random (MNAR) by the NARFCS method. The NARFCS procedure
(Tompsett et al, 2018) generalises the socalled
$\delta$
adjustment sensitivity analysis method of Van Buuren,
Boshuizen & Knook (1999) to the case with multiple incomplete
variables within the FCS framework. In practical terms, the
NARFCS procedure shifts the imputations drawn at each
iteration of mice
by a userspecified quantity that can
vary across subjects, to reflect systematic departures of the
missing data from the data distribution imputed under MAR.
Specification of the NARFCS model is done by the blots
argument of mice()
. The blots
parameter is a named
list. For each variable to be imputed by
mice.impute.mnar.norm()
or mice.impute.mnar.logreg()
the corresponding element in blots
is a list with
at least one argument ums
and, optionally, a second
argument umx
.
For example, the highlevel call might like something like
mice(nhanes[, c(2, 4)], method = c("pmm", "mnar.norm"),
blots = list(chl = list(ums = "3+2*bmi")))
.
The ums
parameter is required, and might look like this:
"4+1*Y"
. The ums
specifcation must have the
following characteristics:
A single term corresponding to the intercept (constant) term, not multiplied by any variable name, must be included in the expression;
Each term in the expression (corresponding to the intercept
or a predictor variable) must be separated by either a "+"
or ""
sign, depending on the sign of the sensitivity
parameter;
Within each nonintercept term, the sensitivity parameter
value comes first and the predictor variable comes second, and these
must be separated by a "*"
sign;
For categorical predictors, for example a variable Z
with K + 1 categories ("Cat0","Cat1", ...,"CatK")
, K
categoryspecific terms are needed, and those not in umx
(see below) must be specified by concatenating the variable name
with the name of the category (e.g. ZCat1
) as this is how
they are named in the design matrix (argument x
) passed
to the univariate imputation function. An example is
"2+1*ZCat13*ZCat2"
.
If given, the umx
specification must have the following
characteristics:
It contains only complete variables, with no missing values;
It is a numeric matrix. In particular, categorical variables
must be represented as dummy indicators with names corresponding
to what is used in ums
to refer to the categoryspecific terms
(see above);
It has the same number of rows as the data
argument
passed on to the main mice
function;
It does not contain variables that were already predictors in the identifiable part of the model for the variable under imputation.
Limitation: The present implementation can only condition on variables
that appear in the identifiable part of the imputation model (x
) or
in complete auxiliary variables passed on via the umx
argument.
It is not possible to specify models where the offset depends on
incomplete auxiliary variables.
For an MNAR alternative see also mice.impute.ri
.
Vector with imputed data, same type as y
, and of length
sum(wy)
Margarita MorenoBetancur, Stef van Buuren, Ian R. White, 2020.
Tompsett, D. M., Leacy, F., MorenoBetancur, M., Heron, J., & White, I. R. (2018). On the use of the notatrandom fully conditional specification (NARFCS) procedure in practice. Statistics in Medicine, 37(15), 23382353. doi:10.1002/sim.7643.
Van Buuren, S., Boshuizen, H.C., Knook, D.L. (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statistics in Medicine, 18, 681–694.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
# 1: Example with no auxiliary data: only pass unidentifiable model specification (ums)
# Specify argument to pass on to mnar imputation functions via "blots" argument
mnar.blot < list(X = list(ums = "4"), Y = list(ums = "2+1*ZCat13*ZCat2"))
# Run NARFCS by using mnar imputation methods and passing argument via blots
impNARFCS < mice(mnar_demo_data,
method = c("mnar.logreg", "mnar.norm", ""),
blots = mnar.blot, seed = 234235, print = FALSE
)
# Obtain MI results: Note they coincide with those from old version at
# https://github.com/morenobetancur/NARFCS
pool(with(impNARFCS, lm(Y ~ X + Z)))$pooled$estimate
# 2: Example passing also auxiliary data to MNAR procedure (umx)
# Assumptions:
#  Auxiliary data are complete, no missing values
#  Auxiliary data are a numeric matrix
#  Auxiliary data have same number of rows as x
#  Auxiliary data have no overlapping variable names with x
# Specify argument to pass on to mnar imputation functions via "blots" argument
aux < matrix(0:1, nrow = nrow(mnar_demo_data))
dimnames(aux) < list(NULL, "even")
mnar.blot < list(
X = list(ums = "4"),
Y = list(ums = "2+1*ZCat13*ZCat2+0.5*even", umx = aux)
)
# Run NARFCS by using mnar imputation methods and passing argument via blots
impNARFCS < mice(mnar_demo_data,
method = c("mnar.logreg", "mnar.norm", ""),
blots = mnar.blot, seed = 234235, print = FALSE
)
# Obtain MI results: As expected they differ (slightly) from those
# from old version at https://github.com/morenobetancur/NARFCS
pool(with(impNARFCS, lm(Y ~ X + Z)))$pooled$estimate
Imputes multivariate incomplete data among which there are specific relations, for instance, polynomials, interactions, range restrictions and sum scores.
mice.impute.mpmm(data, format = "imputes", ...)
data 
matrix with exactly two missing data patterns 
format 
A character vector specifying the type of object that should
be returned. The default is 
... 
Other named arguments. 
This function implements the predictive mean matching and applies canonical regression analysis to select donors fora set of missing variables. In general, canonical regressionanalysis looks for a linear combination of covariates that predicts a linear combination of outcomes (a set of missing variables) optimally in a leastsquare sense (Israels, 1987). The predicted value of the linear combination of the set of missing variables would be applied to perform predictive mean matching.
A matrix with imputed data, which has ncol(y)
columns and
sum(wy)
rows.
The function requires variables in the block have the same missingness pattern. If there are more than one missingness pattern, the function will return a warning.
Mingyang Cai and Gerko Vink
mice.impute.pmm
Van Buuren, S. (2018).
Flexible Imputation of Missing Data. Second Edition.
Chapman & Hall/CRC. Boca Raton, FL.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
# simulate data
beta2 < beta1 < .5
x < rnorm(1000)
e < rnorm(1000, 0, 1)
y < beta1 * x + beta2 * x^2 + e
dat < data.frame(y = y, x = x, x2 = x^2)
m < as.logical(rbinom(1000, 1, 0.25))
dat[m, c("x", "x2")] < NA
# impute
blk < list("y", c("x", "x2"))
meth < c("", "mpmm")
imp < mice(dat, blocks = blk, method = meth, print = FALSE,
m = 2, maxit = 2)
# analyse and check
summary(pool(with(imp, lm(y ~ x + x2))))
with(dat, plot(x, x2, col = mdc(1)))
with(complete(imp), points(x[m], x2[m], col = mdc(2)))
Calculates imputations for univariate missing data by Bayesian linear regression, also known as the normal model.
mice.impute.norm(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Imputation of y
by the normal model by the method defined by
Rubin (1987, p. 167). The procedure is as follows:
Calculate the crossproduct matrix $S=X_{obs}'X_{obs}$
.
Calculate $V = (S+{diag}(S)\kappa)^{1}$
, with some small ridge
parameter $\kappa$
.
Calculate regression weights $\hat\beta = VX_{obs}'y_{obs}.$
Draw a random variable $\dot g \sim \chi^2_\nu$
with $\nu=n_1  q$
.
Calculate $\dot\sigma^2 = (y_{obs}  X_{obs}\hat\beta)'(y_{obs}  X_{obs}\hat\beta)/\dot g.$
Draw $q$
independent $N(0,1)$
variates in vector $\dot z_1$
.
Calculate $V^{1/2}$
by Cholesky decomposition.
Calculate $\dot\beta = \hat\beta + \dot\sigma\dot z_1 V^{1/2}$
.
Draw $n_0$
independent $N(0,1)$
variates in vector $\dot z_2$
.
Calculate the $n_0$
values $y_{imp} = X_{mis}\dot\beta + \dot z_2\dot\sigma$
.
Using mice.impute.norm
for all columns emulates Schafer's NORM method (Schafer, 1997).
Vector with imputed data, same type as y
, and of length
sum(wy)
Stef van Buuren, Karin GroothuisOudshoorn
Rubin, D.B (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley & Sons.
Schafer, J.L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using linear regression with bootstrap
mice.impute.norm.boot(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Draws a bootstrap sample from x[ry,]
and y[ry]
, calculates
regression weights and imputes with normal residuals.
Vector with imputed data, same type as y
, and of length
sum(wy)
Gerko Vink, Stef van Buuren, 2018
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes univariate missing data using linear regression analysis without accounting for the uncertainty of the model parameters.
mice.impute.norm.nob(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
This function creates imputations using the spread around the
fitted linear regression line of y
given x
, as
fitted on the observed data.
This function is provided mainly to allow comparison between proper (e.g.,
as implemented in mice.impute.norm
and improper (this function)
normal imputation methods.
For large data, having many rows, differences between proper and improper
methods are small, and in those cases one may opt for speed by using
mice.impute.norm.nob
.
Vector with imputed data, same type as y
, and of length
sum(wy)
The function does not incorporate the variability of the regression weights, so it is not 'proper' in the sense of Rubin. For small samples, variability of the imputed data is therefore underestimated.
Gerko Vink, Stef van Buuren, Karin GroothuisOudshoorn, 2018
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Brand, J.P.L. (1999). Development, Implementation and Evaluation of Multiple Imputation Strategies for the Statistical Analysis of Incomplete Data Sets. Ph.D. Thesis, TNO Prevention and Health/Erasmus University Rotterdam.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes the "best value" according to the linear regression model, also known as regression imputation.
mice.impute.norm.predict(y, ry, x, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
Calculates regression weights from the observed data and returns predicted values to as imputations. This method is known as regression imputation.
Vector with imputed data, same type as y
, and of length
sum(wy)
THIS METHOD SHOULD NOT BE USED FOR DATA ANALYSIS.
This method is seductive because it imputes the most
likely value according to the model. However, it ignores the uncertainty
of the missing values and artificially
amplifies the relations between the columns of the data. Application of
richer models having more parameters does not help to evade these issues.
Stochastic regression methods, like mice.impute.pmm
or
mice.impute.norm
, are generally preferred.
At best, prediction can give reasonable estimates of the mean, especially if normality assumptions are plausible. See Little and Rubin (2002, p. 6264) or Van Buuren (2012, p. 1113, p. 4546) for a discussion of this method.
Gerko Vink, Stef van Buuren, 2018
Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis with Missing Data. New York: John Wiley and Sons.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
pan
This function is a wrapper around the panImpute
function
from the mitml
package so that it can be called to
impute blocks of variables in mice
. The mitml::panImpute
function provides an interface to the pan
package for
multiple imputation of multilevel data (Schafer & Yucel, 2002).
Imputations can be generated using type
or formula
,
which offer different options for model specification.
mice.impute.panImpute(
data,
formula,
type,
m = 1,
silent = TRUE,
format = "imputes",
...
)
data 
A data frame containing incomplete and auxiliary variables, the cluster indicator variable, and any other variables that should be present in the imputed datasets. 
formula 
A formula specifying the role of each variable
in the imputation model. The basic model is constructed
by 
type 
An integer vector specifying the role of each variable
in the imputation model (see 
m 
The number of imputed data sets to generate. 
silent 
(optional) Logical flag indicating if console output should be suppressed. Default is to 
format 
A character vector specifying the type of object that should
be returned. The default is 
... 
Other named arguments: 
A list of imputations for all incomplete variables in the model,
that can be stored in the the imp
component of the mids
object.
The number of imputations m
is set to 1, and the function
is called m
times so that it fits within the mice
iteration scheme.
This is a multivariate imputation function using a joint model.
Stef van Buuren, 2018, building on work of Simon Grund,
Alexander Robitzsch and Oliver Luedtke (authors of mitml
package)
and Joe Schafer (author of pan
package).
Grund S, Luedtke O, Robitzsch A (2016). Multiple
Imputation of Multilevel Missing Data: An Introduction to the R
Package pan
. SAGE Open.
Schafer JL (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall.
Schafer JL, and Yucel RM (2002). Computational strategies for multivariate linear mixedeffects models with missing values. Journal of Computational and Graphical Statistics, 11, 437457.
Other multivariate2l:
mice.impute.jomoImpute()
blocks < list(c("bmi", "chl", "hyp"), "age")
method < c("panImpute", "pmm")
ini < mice(nhanes, blocks = blocks, method = method, maxit = 0)
pred < ini$pred
pred["B1", "hyp"] < 2
imp < mice(nhanes, blocks = blocks, method = method, pred = pred, maxit = 1)
Calculate new variable during imputation
mice.impute.passive(data, func)
data 
A data frame 
func 
A 
Passive imputation is a special internal imputation function. Using this
facility, the user can specify, at any point in the mice
Gibbs
sampling algorithm, a function on the imputed data. This is useful, for
example, to compute a cubic version of a variable, a transformation like
Q = W/H^2
based on two variables, or a mean variable like
(x_1+x_2+x_3)/3
. The so derived variables might be used in other
places in the imputation model. The function allows to dynamically derive
virtually any function of the imputed data at virtually any time.
The result of applying formula
Stef van Buuren, Karin GroothuisOudshoorn, 2000
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Imputation by predictive mean matching
mice.impute.pmm(
y,
ry,
x,
wy = NULL,
donors = 5L,
matchtype = 1L,
exclude = NULL,
quantify = TRUE,
trim = 1L,
ridge = 1e05,
use.matcher = FALSE,
...
)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
donors 
The size of the donor pool among which a draw is made.
The default is 
matchtype 
Type of matching distance. The default choice
( 
exclude 
Dependent values to exclude from the imputation model and the collection of donor values 
quantify 
Logical. If 
trim 
Scalar integer. Minimum number of observations required in a
category in order to be considered as a potential donor value.
Relevant only of 
ridge 
The ridge penalty used in 
use.matcher 
Logical. Set 
... 
Other named arguments. 
Imputation of y
by predictive mean matching, based on
van Buuren (2012, p. 73). The procedure is as follows:
Calculate the crossproduct matrix $S=X_{obs}'X_{obs}$
.
Calculate $V = (S+{diag}(S)\kappa)^{1}$
, with some small ridge
parameter $\kappa$
.
Calculate regression weights $\hat\beta = VX_{obs}'y_{obs}.$
Draw $q$
independent $N(0,1)$
variates in vector $\dot z_1$
.
Calculate $V^{1/2}$
by Cholesky decomposition.
Calculate $\dot\beta = \hat\beta + \dot\sigma\dot z_1 V^{1/2}$
.
Calculate $\dot\eta(i,j)=X_{{obs},[i]}\hat\betaX_{{mis},[j]}\dot\beta$
with $i=1,\dots,n_1$
and $j=1,\dots,n_0$
.
Construct $n_0$
sets $Z_j$
, each containing $d$
candidate donors, from Y_obs such that $\sum_d\dot\eta(i,j)$
is minimum for all $j=1,\dots,n_0$
. Break ties randomly.
Draw one donor $i_j$
from $Z_j$
randomly for $j=1,\dots,n_0$
.
Calculate imputations $\dot y_j = y_{i_j}$
for $j=1,\dots,n_0$
.
The name predictive mean matching was proposed by Little (1988).
Vector with imputed data, same type as y
, and of length
sum(wy)
Gerko Vink, Stef van Buuren, Karin GroothuisOudshoorn
Little, R.J.A. (1988), Missing data adjustments in large surveys (with discussion), Journal of Business Economics and Statistics, 6, 287–301.
Morris TP, White IR, Royston P (2015). Tuning multiple imputation by predictive mean matching and local residual draws. BMC Med Res Methodol. ;14:75.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
# We normally call mice.impute.pmm() from within mice()
# But we may call it directly as follows (not recommended)
set.seed(53177)
xname < c("age", "hgt", "wgt")
r < stats::complete.cases(boys[, xname])
x < boys[r, xname]
y < boys[r, "tv"]
ry < !is.na(y)
table(ry)
# percentage of missing data in tv
sum(!ry) / length(ry)
# Impute missing tv data
yimp < mice.impute.pmm(y, ry, x)
length(yimp)
hist(yimp, xlab = "Imputed missing tv")
# Impute all tv data
yimp < mice.impute.pmm(y, ry, x, wy = rep(TRUE, length(y)))
length(yimp)
hist(yimp, xlab = "Imputed missing and observed tv")
plot(jitter(y), jitter(yimp),
main = "Predictive mean matching on age, height and weight",
xlab = "Observed tv (n = 224)",
ylab = "Imputed tv (n = 224)"
)
abline(0, 1)
cor(y, yimp, use = "pair")
# Use blots to exclude different values per column
# Create blots object
blots < make.blots(boys)
# Exclude ml 1 through 5 from tv donor pool
blots$tv$exclude < c(1:5)
# Exclude 100 random observed heights from tv donor pool
blots$hgt$exclude < sample(unique(boys$hgt), 100)
imp < mice(boys, method = "pmm", print = FALSE, blots = blots, seed=123)
blots$hgt$exclude %in% unlist(c(imp$imp$hgt)) # MUST be all FALSE
blots$tv$exclude %in% unlist(c(imp$imp$tv)) # MUST be all FALSE
# Factor quantification
xname < c("age", "hgt", "wgt")
br < boys[c(1:10, 101:110, 501:510, 601:620, 701:710), ]
r < stats::complete.cases(br[, xname])
x < br[r, xname]
y < factor(br[r, "tv"])
ry < !is.na(y)
table(y)
# impute factor by optimizing canonical correlation y, x
mice.impute.pmm(y, ry, x)
# only categories with at least 2 cases can be donor
mice.impute.pmm(y, ry, x, trim = 2L)
# in addition, eliminate category 20
mice.impute.pmm(y, ry, x, trim = 2L, exclude = 20)
# to get old behavior: as.integer(y))
mice.impute.pmm(y, ry, x, quantify = FALSE)
Imputes missing data in a categorical variable using polytomous regression
mice.impute.polr(
y,
ry,
x,
wy = NULL,
nnet.maxit = 100,
nnet.trace = FALSE,
nnet.MaxNWts = 1500,
polr.to.loggedEvents = FALSE,
...
)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nnet.maxit 
Tuning parameter for 
nnet.trace 
Tuning parameter for 
nnet.MaxNWts 
Tuning parameter for 
polr.to.loggedEvents 
A logical indicating whether each fallback
to the 
... 
Other named arguments. 
The function mice.impute.polr()
imputes for ordered categorical response
variables by the proportional odds logistic regression (polr) model. The
function repeatedly applies logistic regression on the successive splits. The
model is also known as the cumulative link model.
By default, ordered factors with more than two levels are imputed by
mice.impute.polr
.
The algorithm of mice.impute.polr
uses the function polr()
from
the MASS
package.
In order to avoid bias due to perfect prediction, the algorithm augment the data according to the method of White, Daniel and Royston (2010).
The call to polr
might fail, usually because the data are very sparse.
In that case, multinom
is tried as a fallback.
If the local flag polr.to.loggedEvents
is set to TRUE,
a record is written
to the loggedEvents
component of the mids
object.
Use mice(data, polr.to.loggedEvents = TRUE)
to set the flag.
Vector with imputed data, same type as y
, and of length
sum(wy)
In December 2019 Simon White alerted that the
polr
could always fail silently. I can confirm this behaviour for
versions mice 3.0.0  mice 3.6.6
, so any method requests
for polr
in these versions were in fact handled by multinom
.
See https://github.com/amices/mice/issues/206 for details.
Stef van Buuren, Karin GroothuisOudshoorn, 20002010
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
Brand, J.P.L. (1999) Development, implementation and evaluation of multiple imputation strategies for the statistical analysis of incomplete data sets. Dissertation. Rotterdam: Erasmus University.
White, I.R., Daniel, R. Royston, P. (2010). Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables. Computational Statistics and Data Analysis, 54, 22672275.
Venables, W.N. & Ripley, B.D. (2002). Modern applied statistics with SPlus (4th ed). Springer, Berlin.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes missing data in a categorical variable using polytomous regression
mice.impute.polyreg(
y,
ry,
x,
wy = NULL,
nnet.maxit = 100,
nnet.trace = FALSE,
nnet.MaxNWts = 1500,
...
)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
nnet.maxit 
Tuning parameter for 
nnet.trace 
Tuning parameter for 
nnet.MaxNWts 
Tuning parameter for 
... 
Other named arguments. 
The function mice.impute.polyreg()
imputes categorical response
variables by the Bayesian polytomous regression model. See J.P.L. Brand
(1999), Chapter 4, Appendix B.
By default, unordered factors with more than two levels are imputed by
mice.impute.polyreg()
.
The method consists of the following steps:
Fit categorical response as a multinomial model
Compute predicted categories
Add appropriate noise to predictions
The algorithm of mice.impute.polyreg
uses the function
multinom()
from the nnet
package.
In order to avoid bias due to perfect prediction, the algorithm augment the data according to the method of White, Daniel and Royston (2010).
Vector with imputed data, same type as y
, and of length
sum(wy)
Stef van Buuren, Karin GroothuisOudshoorn, 20002010
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
Brand, J.P.L. (1999) Development, implementation and evaluation of multiple imputation strategies for the statistical analysis of incomplete data sets. Dissertation. Rotterdam: Erasmus University.
White, I.R., Daniel, R. Royston, P. (2010). Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables. Computational Statistics and Data Analysis, 54, 22672275.
Venables, W.N. & Ripley, B.D. (2002). Modern applied statistics with SPlus (4th ed). Springer, Berlin.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.quadratic()
,
mice.impute.rf()
,
mice.impute.ri()
Imputes incomplete variable that appears as both main effect and quadratic effect in the completedata model.
mice.impute.quadratic(y, ry, x, wy = NULL, quad.outcome = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
quad.outcome 
The name of the outcome in the quadratic analysis as a
character string. For example, if the substantive model of interest is

... 
Other named arguments. 
This function implements the "polynomial combination" method.
First, the polynomial
combination $Z = Y \beta_1 + Y^2 \beta_2$
is formed.
$Z$
is imputed by
predictive mean matching, followed by a decomposition of the imputed
data $Z$
into components $Y$
and $Y^2$
.
See Van Buuren (2012, pp. 139141) and Vink
et al (2012) for more details. The method ensures that 1) the imputed data
for $Y$
and $Y^2$
are mutually consistent, and 2) that provides unbiased
estimates of the regression weights in a completedata linear regression that
use both $Y$
and $Y^2$
.
Vector with imputed data, same type as y
, and of length
sum(wy)
There are two situations to consider. If only the linear term Y
is present in the data, calculate the quadratic term YY
after
imputation. If both the linear term Y
and the the quadratic term
YY
are variables in the data, then first impute Y
by calling
mice.impute.quadratic()
on Y
, and then impute YY
by
passive imputation as meth["YY"] < "~I(Y^2)"
. See example section
for details. Generally, we would like YY
to be present in the data if
we need to preserve quadratic relations between YY
and any third
variables in the multivariate incomplete data that we might wish to impute.
Mingyang Cai and Gerko Vink
mice.impute.pmm
Van Buuren, S. (2018).
Flexible Imputation of Missing Data. Second Edition.
Chapman & Hall/CRC. Boca Raton, FL.
Vink, G., van Buuren, S. (2013). Multiple Imputation of Squared Terms. Sociological Methods & Research, 42:598607.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.rf()
,
mice.impute.ri()
# Create Data
B1 < .5
B2 < .5
X < rnorm(1000)
XX < X^2
e < rnorm(1000, 0, 1)
Y < B1 * X + B2 * XX + e
dat < data.frame(x = X, xx = XX, y = Y)
# Impose 25 percent MCAR Missingness
dat[0 == rbinom(1000, 1, 1  .25), 1:2] < NA
# Prepare data for imputation
ini < mice(dat, maxit = 0)
meth < c("quadratic", "~I(x^2)", "")
pred < ini$pred
pred[, "xx"] < 0
# Impute data
imp < mice(dat, meth = meth, pred = pred, quad.outcome = "y")
# Pool results
pool(with(imp, lm(y ~ x + xx)))
# Plot results
stripplot(imp)
plot(dat$x, dat$xx, col = mdc(1), xlab = "x", ylab = "xx")
cmp < complete(imp)
points(cmp$x[is.na(dat$x)], cmp$xx[is.na(dat$x)], col = mdc(2))
Imputes univariate missing data using random forests.
mice.impute.rf(
y,
ry,
x,
wy = NULL,
ntree = 10,
rfPackage = c("ranger", "randomForest"),
...
)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
ntree 
The number of trees to grow. The default is 10. 
rfPackage 
A single string specifying the backend for estimating the
random forest. The default backend is the 
... 
Other named arguments passed down to

Imputation of y
by random forests. The method
calls randomForrest()
which implements Breiman's random forest
algorithm (based on Breiman and Cutler's original Fortran code)
for classification and regression. See Appendix A.1 of Doove et al.
(2014) for the definition of the algorithm used.
Vector with imputed data, same type as y
, and of length
sum(wy)
An alternative implementation was independently
developed by Shah et al (2014). This were available as
functions CALIBERrfimpute::mice.impute.rfcat
and
CALIBERrfimpute::mice.impute.rfcont
(now archived).
Simulations by Shah (Feb 13, 2014) suggested that
the quality of the imputation for 10 and 100 trees was identical,
so mice 2.22 changed the default number of trees from ntree = 100
to
ntree = 10
.
Lisa Doove, Stef van Buuren, Elise Dusseldorp, 2012; Patrick Rockenschaub, 2021
Doove, L.L., van Buuren, S., Dusseldorp, E. (2014), Recursive partitioning for missing data imputation in the presence of interaction Effects. Computational Statistics & Data Analysis, 72, 92104.
Shah, A.D., Bartlett, J.W., Carpenter, J., Nicholas, O., Hemingway, H. (2014), Comparison of random forest and parametric imputation models for imputing missing data using MICE: A CALIBER study. American Journal of Epidemiology, doi:10.1093/aje/kwt312.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
mice
, mice.impute.cart
,
randomForest
ranger
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.ri()
## Not run:
imp < mice(nhanes2, meth = "rf", ntree = 3)
plot(imp)
## End(Not run)
Imputes nonignorable missing data by the random indicator method.
mice.impute.ri(y, ry, x, wy = NULL, ri.maxit = 10, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
ri.maxit 
Number of inner iterations 
... 
Other named arguments. 
The random indicator method estimates an offset between the distribution of the observed and missing data using an algorithm that iterates over the response and imputation models.
This routine assumes that the response model and imputation model have same predictors.
For an MNAR alternative see also mice.impute.mnar.logreg
.
Vector with imputed data, same type as y
, and of length
sum(wy)
Shahab Jolani (University of Utrecht)
Jolani, S. (2012). Dual Imputation Strategies for Analyzing Incomplete Data. Dissertation. University of Utrecht, Dec 7 2012.
Other univariate imputation functions:
mice.impute.cart()
,
mice.impute.lasso.logreg()
,
mice.impute.lasso.norm()
,
mice.impute.lasso.select.logreg()
,
mice.impute.lasso.select.norm()
,
mice.impute.lda()
,
mice.impute.logreg()
,
mice.impute.logreg.boot()
,
mice.impute.mean()
,
mice.impute.midastouch()
,
mice.impute.mnar.logreg()
,
mice.impute.mpmm()
,
mice.impute.norm()
,
mice.impute.norm.boot()
,
mice.impute.norm.nob()
,
mice.impute.norm.predict()
,
mice.impute.pmm()
,
mice.impute.polr()
,
mice.impute.polyreg()
,
mice.impute.quadratic()
,
mice.impute.rf()
Imputes a random sample from the observed y
data
mice.impute.sample(y, ry, x = NULL, wy = NULL, ...)
y 
Vector to be imputed 
ry 
Logical vector of length 
x 
Numeric design matrix with 
wy 
Logical vector of length 
... 
Other named arguments. 
This function takes a simple random sample from the observed values in
y
, and returns these as imputations.
Vector with imputed data, same type as y
, and of length
sum(wy)
Stef van Buuren, Karin GroothuisOudshoorn, 2000, 2017
van Buuren S and GroothuisOudshoorn K (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
Takes a mids
object, and produces a new object of class mids
.
mice.mids(obj, newdata = NULL, maxit = 1, printFlag = TRUE, ...)
obj 
An object of class 
newdata 
An optional 
maxit 
The number of additional Gibbs sampling iterations. 
printFlag 
A Boolean flag. If 
... 
Named arguments that are passed down to the univariate imputation functions. 
This function enables the user to split up the computations of the Gibbs sampler into smaller parts. This is useful for the following reasons:
RAM memory may become easily exhausted if the number of iterations is large. Returning to prompt/session level may alleviate these problems.
The user can compute customized convergence statistics at specific points, e.g. after each iteration, for monitoring convergence.  For computing a 'few extra iterations'.
Note: The imputation model itself
is specified in the mice()
function and cannot be changed with
mice.mids
. The state of the random generator is saved with the
mids
object.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
complete
, mice
, set.seed
,
mids
imp1 < mice(nhanes, maxit = 1, seed = 123)
imp2 < mice.mids(imp1)
# yields the same result as
imp < mice(nhanes, maxit = 2, seed = 123)
# verification
identical(imp$imp, imp2$imp)
#
The mice.theme()
function sets default choices for
Trellis plots that are built into mice.
mice.theme(transparent = TRUE, alpha.fill = 0.3)
transparent 
A logical indicating whether alphatransparency is
allowed. The default is 
alpha.fill 
A numerical values between 0 and 1 that indicates the default alpha value for fills. 
mice.theme()
returns a named list that can be used as a theme in the functions in
lattice. By default, the mice.theme()
function sets
transparent < TRUE
if the current device .Device
supports
semitransparent colors.
Stef van Buuren 2011
mids
)The mids
object contains a multiply imputed data set. The mids
object is
generated by functions mice()
, mice.mids()
, cbind.mids()
,
rbind.mids()
and ibind.mids()
.
The mids
class of objects has methods for the following generic functions:
print
, summary
, plot
.
The loggedEvents
entry is a matrix with five columns containing a
record of automatic removal actions. It is NULL
is no action was
made. At initialization the program does the following three actions:
A variable that contains missing values, that is not imputed and that is used as a predictor is removed
A constant variable is removed
A collinear variable is removed.
During iteration, the program does the following actions:
One or more variables that are linearly dependent are removed (for categorical data, a 'variable' corresponds to a dummy variable)
Proportional odds regression imputation that does not converge
and is replaced by polyreg
.
Explanation of elements in loggedEvents
:
it
iteration number at which the record was added,
im
imputation number,
dep
name of the dependent variable,
meth
imputation method used,
out
a (possibly long) character vector with the names of the altered or removed predictors.
.Data
:Object of class "list"
containing the
following slots:
data
:Original (incomplete) data set.
imp
:A list of ncol(data)
components with
the generated multiple imputations. Each list component is a
data.frame
(nmis[j]
by m
) of imputed values
for variable j
. A NULL
component is used for
variables for which not imputations are generated.
m
:Number of imputations.
where
:The where
argument of the
mice()
function.
blocks
:The blocks
argument of the
mice()
function.
call
:Call that created the object.
nmis
:An array containing the number of missing observations per column.
method
:A vector of strings of length(blocks
specifying the imputation method per block.
predictorMatrix
:A numerical matrix of containing integers specifying the predictor set.
visitSequence
:A vector of variable and block names that specifies how variables and blocks are visited in one iteration throuh the data.
formulas
:A named list of formula's, or expressions that
can be converted into formula's by as.formula
. List elements
correspond to blocks. The block to which the list element applies is
identified by its name, so list names must correspond to block names.
post
:A vector of strings of length length(blocks)
with commands for postprocessing.
blots
:"Block dots". The blots
argument to the mice()
function.
ignore
:A logical vector of length nrow(data)
indicating
the rows in data
used to build the imputation model. (new in mice 3.12.0
)
seed
:The seed value of the solution.
iteration
:Last Gibbs sampling iteration number.
lastSeedValue
:The most recent seed value.
chainMean
:An array of dimensions ncol
by
maxit
by m
elements containing the mean of
the generated multiple imputations.
The array can be used for monitoring convergence.
Note that observed data are not present in this mean.
chainVar
:An array with similar structure as
chainMean
, containing the variance of the imputed values.
loggedEvents
:A data.frame
with five columns
containing warnings, corrective actions, and other inside info.
version
:Version number of mice
package that
created the object.
date
:Date at which the object was created.
The mice
package does not use
the S4 class definitions, and instead relies on the S3 list
equivalent oldClass(obj) < "mids"
.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
van Buuren S and GroothuisOudshoorn K (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
mids
object to MplusConverts a mids
object into a format recognized by Mplus, and writes
the data and the Mplus input files
mids2mplus(
imp,
file.prefix = "imp",
path = getwd(),
sep = "\t",
dec = ".",
silent = FALSE
)
imp 
The 
file.prefix 
A character string describing the prefix of the output data files. 
path 
A character string containing the path of the output file. By
default, files are written to the current 
sep 
The separator between the data fields. 
dec 
The decimal separator for numerical data. 
silent 
A logical flag stating whether the names of the files should be printed. 
This function automates most of the work needed to export a mids
object to Mplus
. The function writes the multiple imputation datasets,
the file that contains the names of the multiple imputation data sets and an
Mplus
input file. The Mplus
input file has the proper file
names, so in principle it should run and read the data without alteration.
Mplus
will recognize the data set as a multiply imputed data set, and
do automatic pooling in procedures where that is supported.
The return value is NULL
.
Gerko Vink, 2011.
mids
object to SPSSConverts a mids
object into a format recognized by SPSS, and writes
the data and the SPSS syntax files.
mids2spss(
imp,
filename = "midsdata",
path = getwd(),
compress = FALSE,
silent = FALSE
)
imp 
The 
filename 
A character string describing the name of the output data file and its extension. 
path 
A character string containing the path of the output file. The
value in 
compress 
A logical flag stating whether the resulting SPSS set should
be a compressed 
silent 
A logical flag stating whether the location of the saved file should be printed. 
This function automates most of the work needed to export a mids
object to SPSS. It uses haven::write_sav()
to facilitate the export to an
SPSS .sav
or .zsav
file.
Below are some things to pay attention to.
The SPSS
syntax file has the proper file names and separators set, so
in principle it should run and read the data without alteration. SPSS
is more strict than R
with respect to the paths. Always use the full
path, otherwise SPSS
may not be able to find the data file.
Factors in R
translate into categorical variables in SPSS
. The
internal coding of factor levels used in R
is exported. This is
generally acceptable for SPSS
. However, when the data are to be
combined with existing SPSS
data, watch out for any changes in the
factor levels codes.
SPSS
will recognize the data set as a multiply imputed data set, and
do automatic pooling in procedures where that is supported. Note however that
pooling is an extra option only available to those who license the
MISSING VALUES
module. Without this license, SPSS
will still
recognize the structure of the data, but it will not pool the multiply imputed
estimates into a single inference.
The return value is NULL
.
Gerko Vink, dec 2020.
mira
)The mira
object is generated by the with.mids()
function.
The as.mira()
function takes the results of repeated completedata analysis stored as a
list, and turns it into a mira
object that can be pooled.
In versions prior to mice 3.0
pooling required only that
coef()
and vcov()
methods were available for fitted
objects. This feature is no longer supported. The reason is that vcov()
methods are inconsistent across packages, leading to buggy behaviour
of the pool()
function. Since mice 3.0+
, the broom
package takes care of filtering out the relevant parts of the
completedata analysis. It may happen that you'll see the messages
like No method for tidying an S3 object of class ...
or
Error: No glance method for objects of class ...
. The royal
way to solve this problem is to write your own glance()
and tidy()
methods and add these to broom
according to the specifications
given in https://broom.tidymodels.org.
The mira
class of objects has methods for the
following generic functions: print
, summary
.
Many of the functions of the mice
package do not use the
S4 class definitions, and instead rely on the S3 list equivalent
oldClass(obj) < "mira"
.
#'
.Data
:Object of class "list"
containing the
following slots:
call
:The call that created the object.
call1
:The call that created the mids
object that was used
in call
.
nmis
:An array containing the number of missing observations per column.
analyses
:A list of m
components containing the individual
fit objects from each of the m
complete data analyses.
Stef van Buuren, Karin GroothuisOudshoorn, 2000
van Buuren S and GroothuisOudshoorn K (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
A toy example from Margarita MorenoBetancur for checking NARFCS.
mnar_demo_data
An object of class data.frame
with 500 rows and 3 columns.
A small dataset with just three columns.
https://github.com/morenobetancur/NARFCS/blob/master/datmis.csv
This helper function names any unnamed elements in the blocks
specification. This is a convenience function.
name.blocks(blocks, prefix = "B")
blocks 
List of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see 
prefix 
A character vector of length 1 with the prefix to be using for naming any unnamed blocks with two or more variables. 
This function will name any unnamed list elements specified in
the optional argument blocks
. Unnamed blocks
consisting of just one variable will be named after this variable.
Unnamed blocks containing more than one variables will be named
by the prefix
argument, padded by an integer sequence
stating at 1.
A named list of character vectors with variables names.
blocks < list(c("hyp", "chl"), AGE = "age", c("bmi", "hyp"), "edu")
name.blocks(blocks)
This helper function names any unnamed elements in the formula
list. This is a convenience function.
name.formulas(formulas, prefix = "F")
formulas 
A named list of formula's, or expressions that
can be converted into formula's by 
prefix 
A character vector of length 1 with the prefix to be using for naming any unnamed blocks with two or more variables. 
This function will name any unnamed list elements specified in
the optional argument formula
. Unnamed formula's
consisting with just one response variable will be named
after this variable. Unnamed formula's containing more
than one variable will be named by the prefix
argument, padded by an integer sequence stating at 1.
Named list of formulas
# fully conditionally specified main effects model
form1 < list(
bmi ~ age + chl + hyp,
hyp ~ age + bmi + chl,
chl ~ age + bmi + hyp
)
form1 < name.formulas(form1)
imp1 < mice(nhanes, formulas = form1, print = FALSE, m = 1, seed = 12199)
# same model using dot notation
form2 < list(bmi ~ ., hyp ~ ., chl ~ .)
form2 < name.formulas(form2)
imp2 < mice(nhanes, formulas = form2, print = FALSE, m = 1, seed = 12199)
identical(complete(imp1), complete(imp2))
# same model using repeated multivariate imputation
form3 < name.blocks(list(all = bmi + hyp + chl ~ .))
imp3 < mice(nhanes, formulas = form3, print = FALSE, m = 1, seed = 12199)
cmp3 < complete(imp3)
identical(complete(imp1), complete(imp3))
# same model using predictorMatrix
imp4 < mice(nhanes, print = FALSE, m = 1, seed = 12199, auxiliary = TRUE)
identical(complete(imp1), complete(imp4))
# different model: multivariate imputation for chl and bmi
form5 < list(chl + bmi ~ ., hyp ~ bmi + age)
form5 < name.formulas(form5)
imp5 < mice(nhanes, formulas = form5, print = FALSE, m = 1, seed = 71712)
Calculates the number of complete cases.
ncc(x)
x 
An 
Number of elements in x
with complete data.
Stef van Buuren, 2017
ncc(nhanes) # 13 complete cases
Calculates the cumulative hazard rate (NelsonAalen estimator)
nelsonaalen(data, timevar, statusvar)
data 
A data frame containing the data. 
timevar 
The name of the time variable in 
statusvar 
The name of the event variable, e.g. death in 
This function is useful for imputing variables that depend on survival time. White and Royston (2009) suggested using the cumulative hazard to the survival time H0(T) rather than T or log(T) as a predictor in imputation models. See section 7.1 of Van Buuren (2012) for an example.
A vector with nrow(data)
elements containing the NelsonAalen
estimates of the cumulative hazard function.
Stef van Buuren, 2012
White, I. R., Royston, P. (2009). Imputing missing covariate values for the Cox model. Statistics in Medicine, 28(15), 19821998.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
require(MASS)
leuk$status < 1 ## no censoring occurs in leuk data (MASS)
ch < nelsonaalen(leuk, time, status)
plot(x = leuk$time, y = ch, ylab = "Cumulative hazard", xlab = "Time")
### See example on http://www.engineeredsoftware.com/lmar/pe_cum_hazard_function.htm
time < c(43, 67, 92, 94, 149, rep(149, 7))
status < c(rep(1, 5), rep(0, 7))
eng < data.frame(time, status)
ch < nelsonaalen(eng, time, status)
plot(x = time, y = ch, ylab = "Cumulative hazard", xlab = "Time")
A small data set with nonmonotone missing values.
A data frame with 25 observations on the following 4 variables.
Age group (1=2039, 2=4059, 3=60+)
Body mass index (kg/m**2)
Hypertensive (1=no,2=yes)
Total serum cholesterol (mg/dL)
A small data set with all numerical variables. The data set nhanes2
is
the same data set, but with age
and hyp
treated as factors.
Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall. Table 6.14.
# create 5 imputed data sets
imp < mice(nhanes)
# print the first imputed data set
complete(imp)
A small data set with nonmonotone missing values.
A data frame with 25 observations on the following 4 variables.
Age group (1=2039, 2=4059, 3=60+)
Body mass index (kg/m**2)
Hypertensive (1=no,2=yes)
Total serum cholesterol (mg/dL)
A small data set with missing data and mixed numerical and discrete
variables. The data set nhanes
is the same data set, but with all data
treated as numerical.
Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall. Table 6.14.
# create 5 imputed data sets
imp < mice(nhanes2)
# print the first imputed data set
complete(imp)
Calculates the number of incomplete cases.
nic(x)
x 
An 
Number of elements in x
with incomplete data.
Stef van Buuren, 2017
nic(nhanes) # the remaining 12 rows
nic(nhanes[, c("bmi", "hyp")]) # number of cases with incomplete bmi and hyp
Calculates the number of cells within a block for which imputation is requested.
nimp(where, blocks = make.blocks(where))
where 
A data frame or matrix with logicals of the same dimensions
as 
blocks 
List of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see 
A numeric vector of length length(blocks)
containing
the number of cells that need to be imputed within a block.
where < is.na(nhanes)
# standard FCS
nimp(where)
# userdefined blocks
nimp(where, blocks = name.blocks(list(c("bmi", "hyp"), "age", "chl")))
This function draws random values of beta and sigma under the Bayesian linear regression model as described in Rubin (1987, p. 167). This function can be called by userspecified imputation functions.
norm.draw(y, ry, x, rank.adjust = TRUE, ...)
.norm.draw(y, ry, x, rank.adjust = TRUE, ...)
y 
Incomplete data vector of length 
ry 
Vector of missing data pattern ( 
x 
Matrix ( 
rank.adjust 
Argument that specifies whether 
... 
Other named arguments. 
A list
containing components coef
(least squares estimate),
beta
(drawn regression weights) and sigma
(drawn value of the
residual standard deviation).
Gerko Vink, 2018, for this version, based on earlier versions written by Stef van Buuren, Karin GroothuisOudshoorn, 2017
Rubin, D.B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.
This function is included for backward compatibility. The function
is superseded by futuremice
.
parlmice(
data,
m = 5,
seed = NA,
cluster.seed = NA,
n.core = NULL,
n.imp.core = NULL,
cl.type = "PSOCK",
...
)
data 
A data frame or matrix containing the incomplete data. Similar to
the first argument of 
m 
The number of desired imputated datasets. By default $m=5$ as with 
seed 
A scalar to be used as the seed value for the mice algorithm within
each parallel stream. Please note that the imputations will be the same for all
streams and, hence, this should be used if and only if 
cluster.seed 
A scalar to be used as the seed value. It is recommended to put the seed value here and not outside this function, as otherwise the parallel processes will be performed with separate, random seeds. 
n.core 
A scalar indicating the number of cores that should be used. 
n.imp.core 
A scalar indicating the number of imputations per core. 
cl.type 
The cluster type. Default value is 
... 
Named arguments that are passed down to function 
This function relies on package parallel
, which is a base
package for R versions 2.14.0 and later. We have chosen to use parallel function
parLapply
to allow the use of parlmice
on Mac, Linux and Windows
systems. For the same reason, we use the Parallel Socket Cluster (PSOCK) type by default.
On systems other than Windows, it can be hugely beneficial to change the cluster type to
FORK
, as it generally results in improved memory handling. When memory issues
arise on a Windows system, we advise to store the multiply imputed datasets,
clean the memory by using rm
and gc
and make another
run using the same settings.
This wrapper function combines the output of parLapply
with
function ibind
in mice
. A mids
object is returned
and can be used for further analyses.
Note that if a seed value is desired, the seed should be entered to this function
with argument seed
. Seed values outside the wrapper function (in an
Rscript or passed to mice
) will not result to reproducible results.
We refer to the manual of parallel
for an explanation on this matter.
A mids object as defined by midsclass
Gerko Vink, Rianne Schouten
Schouten, R. and Vink, G. (2017). parlmice: faster, paraleller, micer. https://www.gerkovink.com/parlMICE/Vignette_parlMICE.html
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
parallel
, parLapply
, makeCluster
,
mice
, midsclass
# 150 imputations in dataset nhanes, performed by 3 cores
## Not run:
imp1 < parlmice(data = nhanes, n.core = 3, n.imp.core = 50)
# Making use of arguments in mice.
imp2 < parlmice(data = nhanes, method = "norm.nob", m = 100)
imp2$method
fit < with(imp2, lm(bmi ~ hyp))
pool(fit)
## End(Not run)
Four simple datasets with various missing data patterns
Data with a univariate missing data pattern
Data with a monotone missing data pattern
Data with a file matching missing data pattern
Data with a general missing data pattern
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Van Buuren (2012) uses these four artificial datasets to illustrate various missing data patterns.
pattern4
data < rbind(pattern1, pattern2, pattern3, pattern4)
mdpat < cbind(expand.grid(rec = 8:1, pat = 1:4, var = 1:3), r = as.numeric(as.vector(is.na(data))))
types < c("Univariate", "Monotone", "File matching", "General")
tp41 < lattice::levelplot(r ~ var + rec  as.factor(pat),
data = mdpat,
as.table = TRUE, aspect = "iso",
shrink = c(0.9),
col.regions = mdc(1:2),
colorkey = FALSE,
scales = list(draw = FALSE),
xlab = "", ylab = "",
between = list(x = 1, y = 0),
strip = lattice::strip.custom(
bg = "grey95", style = 1,
factor.levels = types
)
)
print(tp41)
md.pattern(pattern4)
p < md.pairs(pattern4)
p
### proportion of usable cases
p$mr / (p$mr + p$mm)
### outbound statistics
p$rm / (p$rm + p$rr)
fluxplot(pattern2)
Trace line plots portray the value of an estimate
against the iteration number. The estimate can be anything that you can calculate, but
typically are chosen as parameter of scientific interest. The plot
method for
a mids
object plots the mean and standard deviation of the imputed (not observed)
values against the iteration number for each of the $m$ replications. By default,
the function plot the development of the mean and standard deviation for each incomplete
variable. On convergence, the streams should intermingle and be free of any trend.
## S3 method for class 'mids'
plot(
x,
y = NULL,
theme = mice.theme(),
layout = c(2, 3),
type = "l",
col = 1:10,
lty = 1,
...
)
x 
An object of class 
y 
A formula that specifies which variables, stream and iterations are plotted. If omitted, all streams, variables and iterations are plotted. 
theme 
The trellis theme to applied to the graphs. The default is 
layout 
A vector of length 2 given the number of columns and rows in the plot.
The default is 
type 
Parameter 
col 
Parameter 
lty 
Parameter 
... 
Extra arguments for 
An object of class "trellis"
.
Stef van Buuren 2011
imp < mice(nhanes, print = FALSE)
plot(imp, bmi + chl ~ .it  .ms, layout = c(2, 1))
The pool()
function combines the estimates from m
repeated complete data analyses. The typical sequence of steps to
perform a multiple imputation analysis is:
Impute the missing data by the mice()
function, resulting in
a multiple imputed data set (class mids
);
Fit the model of interest (scientific model) on each imputed data set
by the with()
function, resulting an object of class mira
;
Pool the estimates from each model into a single set of estimates
and standard errors, resulting in an object of class mipo
;
Optionally, compare pooled estimates from different scientific models
by the D1()
or D3()
functions.
A common error is to reverse steps 2 and 3, i.e., to pool the
multiplyimputed data instead of the estimates. Doing so may severely bias
the estimates of scientific interest and yield incorrect statistical
intervals and pvalues. The pool()
function will detect
this case.
pool(object, dfcom = NULL, rule = NULL, custom.t = NULL)
pool.syn(object, dfcom = NULL, rule = "reiter2003")
object 
An object of class 
dfcom 
A positive number representing the degrees of freedom in the
completedata analysis. Normally, this would be the number of independent
observation minus the number of fitted parameters. The default
( 
rule 
A string indicating the pooling rule. Currently supported are

custom.t 
A custom character string to be parsed as a calculation rule
for the total variance 
The pool()
function averages the estimates of the complete
data model, computes the total variance over the repeated analyses
by Rubin's rules (Rubin, 1987, p. 76), and computes the following
diagnostic statistics per estimate:
Relative increase in variance due to nonresponse r
;
Residual degrees of freedom for hypothesis testing df
;
Proportion of total variance due to missingness lambda
;
Fraction of missing information fmi
.
The degrees of freedom calculation for the pooled estimates uses the BarnardRubin adjustment for small samples (Barnard and Rubin, 1999).
The pool.syn()
function combines estimates by Reiter's partially
synthetic data pooling rules (Reiter, 2003). This combination rule
assumes that the data that is synthesised is completely observed.
Pooling differs from Rubin's method in the calculation of the total
variance and the degrees of freedom.
Pooling requires the following input from each fitted model:
the estimates of the model;
the standard error of each estimate;
the residual degrees of freedom of the model.
The pool()
and pool.syn()
functions rely on the
broom::tidy
and broom::glance
for extracting these
parameters.
Since mice 3.0+
, the broom
package takes care of filtering out the relevant parts of the
completedata analysis. It may happen that you'll see the messages
like Error: No tidy method for objects of class ...
or
Error: No glance method for objects of class ...
. The message
means that your completedata method used in with(imp, ...)
has
no tidy
or glance
method defined in the broom
package.
The broom.mixed
package contains tidy
and glance
methods
for mixed models. If you are using a mixed model, first run
library(broom.mixed)
before calling pool()
.
If no tidy
or glance
methods are defined for your analysis
tabulate the m
parameter estimates and their variance
estimates (the square of the standard errors) from the m
fitted
models stored in fit$analyses
. For each parameter, run
pool.scalar
to obtain the pooled parameters estimate, its variance, the
degrees of freedom, the relative increase in variance and the fraction of missing
information.
An alternative is to write your own glance()
and tidy()
methods and add these to broom
according to the specifications
given in https://broom.tidymodels.org.
In versions prior to mice 3.0
pooling required that
coef()
and vcov()
methods were available for fitted
objects. This feature is no longer supported. The reason is that
vcov()
methods are inconsistent across packages, leading to
buggy behaviour of the pool()
function.
Since mice 3.13.2
function pool()
uses the robust
the standard error estimate for pooling when it can extract
robust.se
from the tidy()
object.
An object of class mipo
, which stands for 'multiple imputation
pooled outcome'.
For rule "reiter2003"
values for lambda
and fmi
are
set to 'NA', as these statistics do not apply for data synthesised from
fully observed data.
Barnard, J. and Rubin, D.B. (1999). Small sample degrees of freedom with multiple imputation. Biometrika, 86, 948955.
Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons.
Reiter, J.P. (2003). Inference for Partially Synthetic, Public Use Microdata Sets. Survey Methodology, 29, 181189.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
with.mids
, as.mira
, pool.scalar
,
glance
, tidy
https://github.com/amices/mice/issues/142,
https://github.com/amices/mice/issues/274
# impute missing data, analyse and pool using the classic MICE workflow
imp < mice(nhanes, maxit = 2, m = 2)
fit < with(data = imp, exp = lm(bmi ~ hyp + chl))
summary(pool(fit))
# generate fully synthetic data, analyse and pool
imp < mice(cars,
maxit = 2, m = 2,
where = matrix(TRUE, nrow(cars), ncol(cars))
)
fit < with(data = imp, exp = lm(speed ~ dist))
summary(pool.syn(fit))
# use a custom pooling rule for the total variance about the estimate
# e.g. use t = b + b/m instead of t = ubar + b + b/m
imp < mice(nhanes, maxit = 2, m = 2)
fit < with(data = imp, exp = lm(bmi ~ hyp + chl))
pool(fit, custom.t = ".data$b + .data$b / .data$m")
This function is deprecated in V3. Use D1
or
D3
instead.
pool.compare(fit1, fit0, method = c("wald", "likelihood"), data = NULL)
fit1 
An object of class 'mira', produced by 
fit0 
An object of class 'mira', produced by 
method 
Either 
data 
No longer used. 
Compares two nested models after m repeated complete data analysis
The function is based on the article of Meng and Rubin (1992). The
Waldmethod can be found in paragraph 2.2 and the likelihood method can be
found in paragraph 3. One could use the Wald method for comparison of linear
models obtained with e.g. lm
(in with.mids()
). The likelihood
method should be used in case of logistic regression models obtained with
glm()
in with.mids()
.
The function assumes that fit1
is the
larger model, and that model fit0
is fully contained in fit1
.
In case of method='wald'
, the null hypothesis is tested that the extra
parameters are all zero.
A list containing several components. Component call
is
the call to the pool.compare
function. Component call11
is
the call that created fit1
. Component call12
is the
call that created the imputations. Component call01
is the
call that created fit0
. Component call02
is the
call that created the imputations. Components method
is the
method used to compare two models: 'Wald' or 'likelihood'. Component
nmis
is the number of missing entries for each variable.
Component m
is the number of imputations.
Component qhat1
is a matrix, containing the estimated coefficients of the
m repeated complete data analyses from fit1
.
Component qhat0
is a matrix, containing the estimated coefficients of the
m repeated complete data analyses from fit0
.
Component ubar1
is the mean of the variances of fit1
,
formula (3.1.3), Rubin (1987).
Component ubar0
is the mean of the variances of fit0
,
formula (3.1.3), Rubin (1987).
Component qbar1
is the pooled estimate of fit1
, formula (3.1.2) Rubin
(1987).
Component qbar0
is the pooled estimate of fit0
, formula (3.1.2) Rubin
(1987).
Component Dm
is the test statistic.
Component rm
is the relative increase in variance due to nonresponse, formula
(3.1.7), Rubin (1987).
Component df1
: df1 = under the null hypothesis it is assumed that Dm
has an F
distribution with (df1,df2) degrees of freedom.
Component df2
: df2.
Component pvalue
is the Pvalue of testing whether the model fit1
is
statistically different from the smaller fit0
.
Karin GroothuisOudshoorn and Stef van Buuren, 2009
Li, K.H., Meng, X.L., Raghunathan, T.E. and Rubin, D. B. (1991). Significance levels from repeated pvalues with multiplyimputed data. Statistica Sinica, 1, 6592.
Meng, X.L. and Rubin, D.B. (1992). Performing likelihood ratio tests with multipleimputed data sets. Biometrika, 79, 103111.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
The function pools the coefficients of determination R^2 or the adjusted
coefficients of determination (R^2_a) obtained with the lm
modeling
function. For pooling it uses the Fisher ztransformation.
pool.r.squared(object, adjusted = FALSE)
object 
An object of class 'mira' or 'mipo', produced by 
adjusted 
A logical value. If adjusted=TRUE then the adjusted R^2 is calculated. The default value is FALSE. 
Returns a 1x4 table with components. Component est
is the
pooled R^2 estimate. Component lo95
is the 95 % lower bound of the pooled R^2.
Component hi95
is the 95 % upper bound of the pooled R^2.
Component fmi
is the fraction of missing information due to nonresponse.
Karin GroothuisOudshoorn and Stef van Buuren, 2009
Harel, O (2009). The estimation of R^2 and adjusted R^2 in incomplete data sets using multiple imputation, Journal of Applied Statistics, 36:11091118.
Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
imp < mice(nhanes, print = FALSE, seed = 16117)
fit < with(imp, lm(chl ~ age + hyp + bmi))
# input: mira object
pool.r.squared(fit)
pool.r.squared(fit, adjusted = TRUE)
# input: mipo object
est < pool(fit)
pool.r.squared(est)
pool.r.squared(est, adjusted = TRUE)
Pools univariate estimates of m repeated complete data analysis
pool.scalar(Q, U, n = Inf, k = 1, rule = c("rubin1987", "reiter2003"))
pool.scalar.syn(Q, U, n = Inf, k = 1, rule = "reiter2003")
Q 
A vector of univariate estimates of 
U 
A vector containing the corresponding 
n 
A number providing the sample size. If nothing is specified,
an infinite sample 
k 
A number indicating the number of parameters to be estimated.
By default, 
rule 
A string indicating the pooling rule. Currently supported are

The function averages the univariate estimates of the complete data model, computes the total variance over the repeated analyses, and computes the relative increase in variance due to missing data or data synthesisation and the fraction of missing information.
Returns a list with components.
m
:Number of imputations.
qhat
:The m
univariate estimates of repeated completedata analyses.
u
:The corresponding m
variances of the univariate estimates.
qbar
:The pooled univariate estimate, formula (3.1.2) Rubin (1987).
ubar
:The mean of the variances (i.e. the pooled withinimputation variance), formula (3.1.3) Rubin (1987).
b
:The betweenimputation variance, formula (3.1.4) Rubin (1987).
t
:The total variance of the pooled estimated, formula (3.1.5) Rubin (1987).
r
:The relative increase in variance due to nonresponse, formula (3.1.7) Rubin (1987).
df
:The degrees of freedom for t reference distribution by the method of BarnardRubin (1999).
fmi
:The fraction missing information due to nonresponse, formula (3.1.10) Rubin (1987). (Not defined for synthetic data.)
Karin GroothuisOudshoorn and Stef van Buuren, 2009; Thom Volker, 2021
Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons.
Reiter, J.P. (2003). Inference for Partially Synthetic, Public Use Microdata Sets. Survey Methodology, 29, 181189.
# missing data imputation with with manual pooling
imp < mice(nhanes, maxit = 2, m = 2, print = FALSE, seed = 18210)
fit < with(data = imp, lm(bmi ~ age))
# manual pooling
summary(fit$analyses[[1]])
summary(fit$analyses[[2]])
pool.scalar(Q = c(1.5457, 1.428), U = c(0.9723^2, 1.041^2), n = 25, k = 2)
# check: automatic pooling using broom
pool(fit)
# manual pooling for synthetic data created from complete data
imp < mice(cars,
maxit = 2, m = 2, print = FALSE, seed = 18210,
where = matrix(TRUE, nrow(cars), ncol(cars))
)
fit < with(data = imp, lm(speed ~ dist))
# manual pooling: extract Q and U
summary(fit$analyses[[1]])
summary(fit$analyses[[2]])
pool.scalar.syn(Q = c(0.12182, 0.13209), U = c(0.02121^2, 0.02516^2), n = 50, k = 2)
# check: automatic pooling using broom
pool.syn(fit)
Combines estimates from a tidy table
pool.table(
w,
type = c("all", "minimal", "tests"),
conf.int = TRUE,
conf.level = 0.95,
exponentiate = FALSE,
dfcom = Inf,
custom.t = NULL,
rule = c("rubin1987", "reiter2003"),
...
)
w 
A 
type 
A string, either 
conf.int 
Logical indicating whether to include a confidence interval. 
conf.level 
Confidence level of the interval, used only if

exponentiate 
Flag indicating whether to exponentiate the coefficient estimates and confidence intervals (typical for logistic regression). 
dfcom 
A positive number representing the degrees of freedom of the
residuals in the completedata analysis. The 
custom.t 
A custom character string to be parsed as a calculation
rule for the total variance 
rule 
A string indicating the pooling rule. Currently supported are

... 
Arguments passed down 
The input data w
is a data.frame
with columns named:
term 
a character or factor with the parameter names 
estimate 
a numeric vector with parameter estimates 
std.error 
a numeric vector with standard errors of estimate

residual.df 
a numeric vector with the degrees of freedom 
Columns 13 are obligatory. Column 4 is optional. Usually,
all entries in column 4 are the same. The user can omit column 4,
and specify argument pool.table(..., dfcom = ...)
instead.
If both are given, then column residual.df
takes precedence.
If neither are specified, then mice
tries to calculate the
residual degrees of freedom. If that fails (e.g. because there is
no information on sample size), mice
sets dfcom = Inf
.
The value dfcom = Inf
is acceptable for large samples
(n > 1000) and relatively concise parametric models.
pool.table()
returns a data.frame
with aggregated
estimates, standard errors, confidence intervals and statistical tests.
The meaning of the columns is as follows:
term 
Parameter name 
m 
Number of multiple imputations 
estimate 
Pooled complete data estimate 
std.error 
Standard error of estimate

statistic 
tstatistic = estimate / std.error

df 
Degrees of freedom for statistic

p.value 
Onesided Pvalue under null hypothesis 
conf.low 
Lower bound of c.i. (default 95 pct) 
conf.high 
Upper bound of c.i. (default 95 pct) 
riv 
Relative increase in variance 
fmi 
Fraction of missing information 
ubar 
Withinimputation variance of estimate

b 
Betweenimputation variance of estimate

t 
Total variance, of estimate

dfcom 
Residual degrees of freedom in complete data 
# conventional mice workflow
imp < mice(nhanes2, m = 2, maxit = 2, seed = 1, print = FALSE)
fit < with(imp, lm(chl ~ age + bmi + hyp))
pld1 < pool(fit)
pld1$pooled
# using pool.table() on tidy table
tbl < summary(fit)[, c("term", "estimate", "std.error", "df.residual")]
tbl
pld2 < pool.table(tbl, type = "minimal")
pld2
identical(pld1$pooled, pld2)
# conventional workflow: all numerical output
all1 < summary(pld1, type = "all", conf.int = TRUE)
all1
# pool.table workflow: all numerical output
all2 < pool.table(tbl)
all2
identical(data.frame(all1), all2)
Hox pupil popularity data with some missing popularity scores
A data frame with 2000 rows and 7 columns:
Pupil number within school
School number
Pupil popularity with 848 missing entries
Pupil gender
Teacher experience (years)
Constant intercept term
Teacher popularity
The original, complete dataset was generated by Joop Hox as an example of wellbehaved multilevel data set. The distributed data contains missing data in pupil popularity.
Hox, J. J. (2002) Multilevel analysis. Techniques and applications. Mahwah, NJ: Lawrence Erlbaum.
popmis[1:3, ]
Subset of data from the POPS study, a national, prospective study on preterm children, including all liveborn infants <32 weeks gestational age and/or <1500 g from 1983 (n = 1338).
pops
is a data frame with 959 rows and 86 columns.
pops.pred
is the 86 by 86 binary predictor matrix used for specifying
the multiple imputation model.
The data set concerns of subset of 959 children that survived up to the age of 19 years.
Hille et al (2005) divided the 959 survivors into three groups: Full responders (examined at an outpatient clinic and completed the questionnaires, n = 596), postal responders (only completed the mailed questionnaires, n = 109), nonresponders (did not respond to any of the mailed requests or telephone calls, or could not be traced, n = 254).
Compared to the postal and nonresponders, the full response group consists of more girls, contains more Dutch children, has higher educational and social economic levels and has fewer handicaps. The responders form a highly selective subgroup in the total cohort.
Multiple imputation of this data set has been described in Hille et al (2007) and Van Buuren (2012), chapter 8.
This dataset is not part of mice
.
Hille, E. T. M., Elbertse, L., Bennebroek Gravenhorst, J., Brand, R., VerlooveVanhorick, S. P. (2005). Nonresponse bias in a followup study of 19yearold adolescents born as preterm infants. Pediatrics, 116(5):662666.
Hille, E. T. M., WeisglasKuperus, N., Van Goudoever, J. B., Jacobusse, G. W., EnsDokkum, M. H., De Groot, L., Wit, J. M., Geven, W. B., Kok, J. H., De Kleine, M. J. K., Kollee, L. A. A., Mulder, A. L. M., Van Straaten, H. L. M., De Vries, L. S., Van Weissenbruch, M. M., VerlooveVanhorick, S. P. (2007). Functional outcomes and participation in young adulthood for very preterm and very low birth weight infants: The Dutch project on preterm and small for gestational age infants at 19 years of age. Pediatrics, 120(3):587595.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
pops < data(pops)
Data from PotthoffRoy (1964) with repeated measures on dental fissures.
tbs
is a data frame with 27 rows and 6 columns:
Person number
Sex M/F
Distance at age 8 years
Distance at age 10 years
Distance at age 12 years
Distance at age 14 years
This data set is the famous PotthoffRoy data, used to demonstrate MANOVA on repeated measure data. Potthoff and Roy (1964) published classic data on a study in 16 boys and 11 girls, who at ages 8, 10, 12, and 14 had the distance (mm) from the center of the pituitary gland to the pteryomaxillary fissure measured. Changes in pituitarypteryomaxillary distances during growth is important in orthodontic therapy. The goals of the study were to describe the distance in boys and girls as simple functions of age, and then to compare the functions for boys and girls. The data have been reanalyzed by many authors including Jennrich and Schluchter (1986), Little and Rubin (1987), Pinheiro and Bates (2000), Verbeke and Molenberghs (2000) and Molenberghs and Kenward (2007). See Chapter 9 of Van Buuren (2012) for a challenging exercise using these data.
Potthoff, R. F., Roy, S. N. (1964). A generalized multivariate analysis of variance model usefully especially for growth curve problems. Biometrika, 51(3), 313326.
Little, R. J. A., Rubin, D. B. (1987). Statistical Analysis with Missing Data. New York: John Wiley & Sons.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
### create missing values at age 10 as in Little and Rubin (1987)
phr < potthoffroy
idmis < c(3, 6, 9, 10, 13, 16, 23, 24, 27)
phr[idmis, 4] < NA
phr
md.pattern(phr)
mads
objectPrint a mads
object
## S3 method for class 'mads'
print(x, ...)
x 
Object of class 
... 
Other parameters passed down to 
NULL
mids
objectPrint a mids
object
Print a mira
object
Print a mice.anova
object
Print a summary.mice.anova
object
## S3 method for class 'mids'
print(x, ...)
## S3 method for class 'mira'
print(x, ...)
## S3 method for class 'mice.anova'
print(x, ...)
## S3 method for class 'mice.anova.summary'
print(x, ...)
x 
Object of class 
... 
Other parameters passed down to 
NULL
NULL
NULL
NULL
Selects predictors according to simple statistics
quickpred(
data,
mincor = 0.1,
minpuc = 0,
include = "",
exclude = "",
method = "pearson"
)
data 
Matrix or data frame with incomplete data. 
mincor 
A scalar, numeric vector (of size 
minpuc 
A scalar, vector (of size 
include 
A string or a vector of strings containing one or more
variable names from 
exclude 
A string or a vector of strings containing one or more
variable names from 
method 
A string specifying the type of correlation. Use

This function creates a predictor matrix using the variable selection procedure described in Van Buuren et al.~(1999, p.~687–688). The function is designed to aid in setting up a good imputation model for data with many variables.
Basic workings: The procedure calculates for each variable pair (i.e.
targetpredictor pair) two correlations using all available cases per pair.
The first correlation uses the values of the target and the predictor
directly. The second correlation uses the (binary) response indicator of the
target and the values of the predictor. If the largest (in absolute value) of
these correlations exceeds mincor
, the predictor will be added to the
imputation set. The default value for mincor
is 0.1.
In addition, the procedure eliminates predictors whose proportion of usable
cases fails to meet the minimum specified by minpuc
. The default value
is 0, so predictors are retained even if they have no usable case.
Finally, the procedure includes any predictors named in the include
argument (which is useful for background variables like age and sex) and
eliminates any predictor named in the exclude
argument. If a variable
is listed in both include
and exclude
arguments, the
include
argument takes precedence.
Advanced topic: mincor
and minpuc
are typically specified as
scalars, but vectors and squares matrices of appropriate size will also work.
Each element of the vector corresponds to a row of the predictor matrix, so
the procedure can effectively differentiate between different target
variables. Setting a high values for can be useful for auxiliary, less
important, variables. The set of predictor for those variables can remain
relatively small. Using a square matrix extends the idea to the columns, so
that one can also apply cellwise thresholds.
A square binary matrix of size ncol(data)
.
quickpred()
uses data.matrix
to convert
factors to numbers through their internal codes. Especially for unordered
factors the resulting quantification may not make sense.
Stef van Buuren, Aug 2009
van Buuren, S., Boshuizen, H.C., Knook, D.L. (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statistics in Medicine, 18, 681–694.
van Buuren, S. and GroothuisOudshoorn, K. (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
# default: include all predictors with absolute correlation over 0.1
quickpred(nhanes)
# all predictors with absolute correlation over 0.4
quickpred(nhanes, mincor = 0.4)
# include age and bmi, exclude chl
quickpred(nhanes, mincor = 0.4, inc = c("age", "bmi"), exc = "chl")
# only include predictors with at least 30% usable cases
quickpred(nhanes, minpuc = 0.3)
# use low threshold for bmi, and high thresholds for hyp and chl
pred < quickpred(nhanes, mincor = c(0, 0.1, 0.5, 0.5))
pred
# use it directly from mice
imp < mice(nhanes, pred = quickpred(nhanes, minpuc = 0.25, include = "age"))
Dataset containing height and weight data (measured, selfreported) from two studies.
A data frame with 2060 rows and 15 variables:
Study, either krul
or mgg
(factor)
Person identification number
Population, all NL
(factor)
Age of respondent in years
Sex of respondent (factor)
Height measured (cm)
Weight measured (kg)
Height reported (cm)
Weight reported (kg)
Pregnancy (factor), all Not pregnant
Educational level (factor)
Ethnicity (factor)
Obtained through web survey (factor)
BMI measured (kg/m2)
BMI reported (kg/m2)
This dataset combines two datasets: krul
data (Krul, 2010) (1257
persons) and the mgg
data (Van Keulen 2011; Van der Klauw 2011) (803
persons). The krul
dataset contains height and weight (both measures
and selfreported) from 1257 Dutch adults, whereas the mgg
dataset
contains selfreported height and weight for 803 Dutch adults. Section 7.3 in
Van Buuren (2012) shows how the missing measured data can be imputed in the
mgg
data, so corrected prevalence estimates can be calculated.
Krul, A., Daanen, H. A. M., Choi, H. (2010). Selfreported and measured weight, height and body mass index (BMI) in Italy, The Netherlands and North America. European Journal of Public Health, 21(4), 414419.
Van Keulen, H.M.,, Chorus, A.M.J., Verheijden, M.W. (2011). Monitor Convenant Gezond Gewicht Nulmeting (determinanten van) beweeg en eetgedrag van kinderen (411 jaar), jongeren (1217 jaar) en volwassenen (18+ jaar). TNO/LS 2011.016. Leiden: TNO.
Van der Klauw, M., Van Keulen, H.M., Verheijden, M.W. (2011). Monitor Convenant Gezond Gewicht Beweeg en eetgedrag van kinderen (411 jaar), jongeren (1217 jaar) en volwassenen (18+ jaar) in 2010 en 2011. TNO/LS 2011.055. Leiden: TNO. (in Dutch)
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
md.pattern(selfreport[, c("age", "sex", "hm", "hr", "wm", "wr")])
### FIMD Section 7.3.5 Application
bmi < function(h, w) {
return(w / (h / 100)^2)
}
init < mice(selfreport, maxit = 0)
meth < init$meth
meth["bm"] < "~bmi(hm,wm)"
pred < init$pred
pred[, c("src", "id", "web", "bm", "br")] < 0
imp < mice(selfreport, pred = pred, meth = meth, seed = 66573, maxit = 2, m = 1)
## imp < mice(selfreport, pred=pred, meth=meth, seed=66573, maxit=20, m=10)
### Like FIMD Figure 7.6
cd < complete(imp, 1)
xy < xy.coords(cd$bm, cd$br  cd$bm)
plot(xy,
col = mdc(2), xlab = "Measured BMI", ylab = "Reported  Measured BMI",
xlim = c(17, 45), ylim = c(5, 5), type = "n", lwd = 0.7
)
polygon(x = c(30, 20, 30), y = c(0, 10, 10), col = "grey95", border = NA)
polygon(x = c(30, 40, 30), y = c(0, 10, 10), col = "grey95", border = NA)
abline(0, 0, lty = 2, lwd = 0.7)
idx < cd$src == "krul"
xyc < xy
xyc$x < xy$x[idx]
xyc$y < xy$y[idx]
xys < xy
xys$x < xy$x[!idx]
xys$y < xy$y[!idx]
points(xyc, col = mdc(1), cex = 0.7)
points(xys, col = mdc(2), cex = 0.7)
lines(lowess(xyc), col = mdc(4), lwd = 2)
lines(lowess(xys), col = mdc(5), lwd = 2)
text(1:4, x = c(40, 28, 20, 32), y = c(4, 4, 4, 4), cex = 3)
box(lwd = 1)
This function replaces any values in x
that are lower than
bounds[1]
by bounds[1]
, and replaces any values higher
than bounds[2]
by bounds[2]
.
squeeze(x, bounds = c(min(x[r]), max(x[r])), r = rep.int(TRUE, length(x)))
x 
A numerical vector with values 
bounds 
A numerical vector of length 2 containing the lower and upper bounds.
By default, the bounds are to the minimum and maximum values in 
r 
A logical vector of length 
A vector of length length(x)
.
Stef van Buuren, 2011.
Plotting methods for imputed data using lattice.
stripplot
produces onedimensional
scatterplots. The function
automatically separates the observed and imputed data. The
functions extend the usual features of lattice.
## S3 method for class 'mids'
stripplot(
x,
data,
na.groups = NULL,
groups = NULL,
as.table = TRUE,
theme = mice.theme(),
allow.multiple = TRUE,
outer = TRUE,
drop.unused.levels = lattice::lattice.getOption("drop.unused.levels"),
panel = lattice::lattice.getOption("panel.stripplot"),
default.prepanel = lattice::lattice.getOption("prepanel.default.stripplot"),
jitter.data = TRUE,
horizontal = FALSE,
...,
subscripts = TRUE,
subset = TRUE
)
x 
A 
data 
Formula that selects the data to be plotted. This argument follows the lattice rules for formulas, describing the primary variables (used for the perpanel display) and the optional conditioning variables (which define the subsets plotted in different panels) to be used in the plot. The formula is evaluated on the complete data set in the Extended formula interface: The primary variable terms (both the LHS
For convenience, in 
na.groups 
An expression evaluating to a logical vector indicating
which two groups are distinguished (e.g. using different colors) in the
display. The environment in which this expression is evaluated in the
response indicator The default 
groups 
This is the usual 
as.table 
See 
theme 
A named list containing the graphical parameters. The default
function 
allow.multiple 
See 
outer 
See 
drop.unused.levels 
See 
panel 
See 
default.prepanel 
See 
jitter.data 
See 
horizontal 
See 
... 
Further arguments, usually not directly processed by the highlevel functions documented here, but instead passed on to other functions. 
subscripts 
See 
subset 
See 
The argument na.groups
may be used to specify (combinations of)
missingness in any of the variables. The argument groups
can be used
to specify groups based on the variable values themselves. Only one of both
may be active at the same time. When both are specified, na.groups
takes precedence over groups
.
Use the subset
and na.groups
together to plots parts of the
data. For example, select the first imputed data set by by
subset=.imp==1
.
Graphical parameters like col
, pch
and cex
can be
specified in the arguments list to alter the plotting symbols. If
length(col)==2
, the color specification to define the observed and
missing groups. col[1]
is the color of the 'observed' data,
col[2]
is the color of the missing or imputed data. A convenient color
choice is col=mdc(1:2)
, a transparent blue color for the observed
data, and a transparent red color for the imputed data. A good choice is
col=mdc(1:2), pch=20, cex=1.5
. These choices can be set for the
duration of the session by running mice.theme()
.
The highlevel functions documented here, as well as other highlevel
Lattice functions, return an object of class "trellis"
. The
update
method can be used to
subsequently update components of the object, and the
print
method (usually called by default)
will plot it on an appropriate plotting device.
The first two arguments (x
and data
) are reversed
compared to the standard Trellis syntax implemented in lattice. This
reversal was necessary in order to benefit from automatic method dispatch.
In mice the argument x
is always a mids
object, whereas
in lattice the argument x
is always a formula.
In mice the argument data
is always a formula object, whereas in
lattice the argument data
is usually a data frame.
All other arguments have identical interpretation.
Stef van Buuren
Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
mice
, xyplot
, densityplot
,
bwplot
, lattice
for an overview of the
package, as well as stripplot
,
panel.stripplot
,
print.trellis
,
trellis.par.set
imp < mice(boys, maxit = 1)
### stripplot, all numerical variables
## Not run:
stripplot(imp)
## End(Not run)
### same, but with improved display
## Not run:
stripplot(imp, col = c("grey", mdc(2)), pch = c(1, 20))
## End(Not run)
### distribution per imputation of height, weight and bmi
### labeled by their own missingness
## Not run:
stripplot(imp, hgt + wgt + bmi ~ .imp,
cex = c(2, 4), pch = c(1, 20), jitter = FALSE,
layout = c(3, 1)
)
## End(Not run)
### same, but labeled with the missingness of wgt (just four cases)
## Not run:
stripplot(imp, hgt + wgt + bmi ~ .imp,
na = wgt, cex = c(2, 4), pch = c(1, 20), jitter = FALSE,
layout = c(3, 1)
)
## End(Not run)
### distribution of age and height, labeled by missingness in height
### most height values are missing for those around
### the age of two years
### some additional missings occur in region WEST
## Not run:
stripplot(imp, age + hgt ~ .imp  reg, hgt,
col = c(grDevices::hcl(0, 0, 40, 0.2), mdc(2)), pch = c(1, 20)
)
## End(Not run)
### heavily jitted relation between two categorical variables
### labeled by missingness of gen
### aggregated over all imputed data sets
## Not run:
stripplot(imp, gen ~ phb, factor = 2, cex = c(8, 1), hor = TRUE)
## End(Not run)
### circle fun
stripplot(imp, gen ~ .imp,
na = wgt, factor = 2, cex = c(8.6),
hor = FALSE, outer = TRUE, scales = "free", pch = c(1, 19)
)
mira
objectSummary of a mira
object
Summary of a mids
object
Summary of a mads
object
Print a mice.anova
object
## S3 method for class 'mira'
summary(object, type = c("tidy", "glance", "summary"), ...)
## S3 method for class 'mids'
summary(object, ...)
## S3 method for class 'mads'
summary(object, ...)
## S3 method for class 'mice.anova'
summary(object, ...)
object 
A 
type 
A length1 character vector indicating the
type of summary. There are three choices: 
... 
Other parameters passed down to 
NULL
NULL
NULL
NULL
This function is used by mdc()
to find out whether the current device
supports semitransparent foreground colors.
supports.transparent()
The function calls the function dev.capabilities()
from the package
grDevices
. The function return FALSE
if the status of the
current device is unknown.
TRUE
or FALSE
supports.transparent()
Data of subset of the Terneuzen Birth Cohort data on child growth.
tbs
is a data frame with 3951 rows and 11 columns:
Person number
Occasion number
Number of occasions
Is this the first record for this person? (TRUE/FALSE)
Type of data (all observed)
Age (years)
Sex 1=M, 2=F
Height Zscore
Weight Zscore
BMI Zscore
Adult overweight (0=no, 1=yes)
tbc.target
is a data frame with 2612 rows and 3 columns:
Person number
Adult overweight (0=no, 1=yes)
BMI Zscore as young adult (1829 years)
This tbc
data set is a random subset of persons from a much larger
collection of data from the Terneuzen Birth Cohort. The total cohort
comprises of 2604 unique persons, whereas the subset in tbc
covers 306
persons. The tbc.target
is an auxiliary data set containing two
outcomes at adult age. For more details, see De Kroon et al (2008, 2010,
2011). The imputation methodology is explained in Chapter 9 of Van Buuren
(2012).
De Kroon, M. L. A., Renders, C. M., Kuipers, E. C., van Wouwe, J. P., van Buuren, S., de Jonge, G. A., Hirasing, R. A. (2008). Identifying metabolic syndrome without blood tests in young adults  The Terneuzen birth cohort. European Journal of Public Health, 18(6), 656660.
De Kroon, M. L. A., Renders, C. M., Van Wouwe, J. P., Van Buuren, S., Hirasing, R. A. (2010). The Terneuzen birth cohort: BMI changes between 2 and 6 years correlate strongest with adult overweight. PLoS ONE, 5(2), e9155.
De Kroon, M. L. A. (2011). The Terneuzen Birth Cohort. Detection and Prevention of Overweight and Cardiometabolic Risk from Infancy Onward. Dissertation, Vrije Universiteit, Amsterdam. https://research.vu.nl/en/publications/theterneuzenbirthcohortdetectionandpreventionofoverweight
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
data < tbc
md.pattern(data)
The toenail data come from a Multicenter study comparing two oral treatments for toenail infection. Patients were evaluated for the degree of separation of the nail. Patients were randomized into two treatments and were followed over seven visits  four in the first year and yearly thereafter. The patients have not been treated prior to the first visit so this should be regarded as the baseline.
A data frame with 1908 observations on the following 5 variables:
ID
a numeric vector giving the ID of patient
outcome
a numeric vector giving the response (0=none or mild seperation, 1=moderate or severe)
treatment
a numeric vector giving the treatment group
month
a numeric vector giving the time of the visit (not exactly monthly intervals hence not round numbers)
visit
a numeric vector giving the number of the visit
This dataset was copied from the DPpackage
, which is
scheduled to be discontinued from CRAN in August 2019.
De Backer, M., De Vroey, C., Lesaffre, E., Scheys, I., and De Keyser, P. (1998). Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: A doubleblind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. Journal of the American Academy of Dermatology, 38, 5763.
Lesaffre, E. and Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic randomeffects model: An example. Journal of the Royal Statistical Society, Series C, 50, 325335.
G. Fitzmaurice, N. Laird and J. Ware (2004) Applied Longitudinal Analysis, Wiley and Sons, New York, USA.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
The toenail data come from a Multicenter study comparing two oral treatments for toenail infection. Patients were evaluated for the degree of separation of the nail. Patients were randomized into two treatments and were followed over seven visits  four in the first year and yearly thereafter. The patients have not been treated prior to the first visit so this should be regarded as the baseline.
A data frame with 1908 observations on the following 5 variables:
patientID
a numeric vector giving the ID of patient
outcome
a factor with 2 levels giving the response
treatment
a factor with 2 levels giving the treatment group
time
a numeric vector giving the time of the visit (not exactly monthly intervals hence not round numbers)
visit
an integer giving the number of the visit
Apart from formatting, this dataset is identical to
toenail
. The formatting is taken identical to
data("toenail", package = "HSAUR3")
.
De Backer, M., De Vroey, C., Lesaffre, E., Scheys, I., and De Keyser, P. (1998). Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: A doubleblind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. Journal of the American Academy of Dermatology, 38, 5763.
Lesaffre, E. and Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic randomeffects model: An example. Journal of the Royal Statistical Society, Series C, 50, 325335.
G. Fitzmaurice, N. Laird and J. Ware (2004) Applied Longitudinal Analysis, Wiley and Sons, New York, USA.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Echoes the package version number
version(pkg = "mice")
pkg 
A character vector with the package name. 
A character vector containing the package name, version number and installed directory.
Stef van Buuren, Oct 2010
version()
version("base")
Two items YA and YB measuring walking disability in samples A, B and E.
A data frame with 890 rows on the following 5 variables:
Sex of respondent (factor)
Age of respondent
Item administered in samples A and E (factor)
Item administered in samples B and E (factor)
Source: Sample A, B or E (factor)
Example dataset to demonstrate imputation of two items (YA and YB). Item YA is administered to sample A and sample E, item YB is administered to sample B and sample E, so sample E acts as a bridge study. Imputation using a bridge study is better than simple equating or than imputation under independence.
Item YA corresponds to the HAQ8 item, and item YB corresponds to the GAR9 items from Van Buuren et al (2005). Sample E (as well as sample B) is the Euridiss study (n=292), sample A is the ERGOPLUS study (n=306).
See Van Buuren (2018) section 9.4 for more details on the imputation methodology.
van Buuren, S., Eyres, S., Tennant, A., HopmanRock, M. (2005). Improving comparability of existing data by Response Conversion. Journal of Official Statistics, 21(1), 5372.
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
md.pattern(walking)
micemill < function(n) {
for (i in 1:n) {
imp << mice.mids(imp) # global assignment
cors < with(imp, cor(as.numeric(YA),
as.numeric(YB),
method = "kendall"
))
tau << rbind(tau, getfit(cors, s = TRUE)) # global assignment
}
}
plotit < function() {
matplot(
x = 1:nrow(tau), y = tau,
ylab = expression(paste("Kendall's ", tau)),
xlab = "Iteration", type = "l", lwd = 1,
lty = 1:10, col = "black"
)
}
tau < NULL
imp < mice(walking, max = 0, m = 10, seed = 92786)
pred < imp$pred
pred[, c("src", "age", "sex")] < 0
imp < mice(walking, max = 0, m = 3, seed = 92786, pred = pred)
micemill(5)
plotit()
### to get figure 9.8 van Buuren (2018) use m=10 and micemill(20)
Subset of Irish wind speed data
A data frame with 433 rows and 6 columns containing the daily average wind speeds within the period 19611978 at meteorological stations in the Republic of Ireland. The data are a random sample from a larger data set.
Roche Point
Rosslare
Shannon
Dublin
Clones
Malin Head
The original data set is much larger and was analyzed in detail by Haslett and Raftery (1989). Van Buuren et al (2006) used this subset to investigate the influence of extreme MAR mechanisms on the quality of imputation.
Haslett, J. and Raftery, A. E. (1989). Spacetime Modeling with Longmemory Dependence: Assessing Ireland's Wind Power Resource (with Discussion). Applied Statistics 38, 150. http://lib.stat.cmu.edu/datasets/wind.desc and http://lib.stat.cmu.edu/datasets/wind.data
van Buuren, S., Brand, J.P.L., GroothuisOudshoorn C.G.M., Rubin, D.B. (2006) Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, 76, 12, 1049–1064.
windspeed[1:3, ]
Performs a computation of each of imputed datasets in data.
## S3 method for class 'mids'
with(data, expr, ...)
data 
An object of type 
expr 
An expression to evaluate for each imputed data set. Formula's containing a dot (notation for "all other variables") do not work. 
... 
Not used 
An object of S3 class mira
Version 3.11.10 changed to tidy evaluation on a quosure. This change
should not affect any code that worked on previous versions.
It turned out that the latter statement was not true (#292).
Version 3.12.2 reverts to the old with()
function.
Karin Oudshoorn, Stef van Buuren 2009, 2012, 2020
van Buuren S and GroothuisOudshoorn K (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
doi:10.18637/jss.v045.i03
mids
, mira
, pool
,
D1
, D3
, pool.r.squared
imp < mice(nhanes2, m = 2, print = FALSE, seed = 14221)
# descriptive statistics
getfit(with(imp, table(hyp, age)))
# model fitting and testing
fit1 < with(imp, lm(bmi ~ age + hyp + chl))
fit2 < with(imp, glm(hyp ~ age + chl, family = binomial))
fit3 < with(imp, anova(lm(bmi ~ age + chl)))
Plotting method to investigate relation between amputed data and the weighted sum
scores. Based on lattice
. xyplot
produces scatterplots.
The function plots the variables against the weighted sum scores. The function
automatically separates the amputed and nonamputed data to see the relation between
the amputation and the weighted sum scores.
## S3 method for class 'mads'
xyplot(
x,
data,
which.pat = NULL,
standardized = TRUE,
layout = NULL,
colors = mdc(1:2),
...
)
x 
A 
data 
A string or vector of variable names that needs to be plotted. As a default, all variables will be plotted. 
which.pat 
A scalar or vector indicating which patterns need to be plotted. As a default, all patterns are plotted. 
standardized 
Logical. Whether the scatterplots need to be created from standardized data or not. Default is TRUE. 
layout 
A vector of two values indicating how the scatterplots of one
pattern should be divided over the plot. For example, 
colors 
A vector of two RGB values defining the colors of the nonamputed and
amputed data respectively. RGB values can be obtained with 
... 
Not used, but for consistency with generic 
A list containing the scatterplots. Note that a new pattern will always be shown in a new plot.
The mads
object contains all the information you need to
make any desired plots. Check madsclass
or the vignette Multivariate
Amputation using Ampute to understand the contents of class object mads
.
Rianne Schouten, 2016
ampute
, bwplot
, Lattice
for
an overview of the package, madsclass
Plotting methods for imputed data using lattice.
xyplot()
produces a conditional scatterplots. The function
automatically separates the observed (blue) and imputed (red) data. The
function extends the usual features of lattice.
## S3 method for class 'mids'
xyplot(
x,
data,
na.groups = NULL,
groups = NULL,
as.table = TRUE,
theme = mice.theme(),
allow.multiple = TRUE,
outer = TRUE,
drop.unused.levels = lattice::lattice.getOption("drop.unused.levels"),
...,
subscripts = TRUE,
subset = TRUE
)
x 
A 
data 
Formula that selects the data to be plotted. This argument follows the lattice rules for formulas, describing the primary variables (used for the perpanel display) and the optional conditioning variables (which define the subsets plotted in different panels) to be used in the plot. The formula is evaluated on the complete data set in the Extended formula interface: The primary variable terms (both the LHS

na.groups 
An expression evaluating to a logical vector indicating
which two groups are distinguished (e.g. using different colors) in the
display. The environment in which this expression is evaluated in the
response indicator The default 
groups 
This is the usual 
as.table 
See 
theme 
A named list containing the graphical parameters. The default
function 
allow.multiple 
See 
outer 
See 
drop.unused.levels 
See 
... 
Further arguments, usually not directly processed by the highlevel functions documented here, but instead passed on to other functions. 
subscripts 
See 
subset 
See 
The argument na.groups
may be used to specify (combinations of)
missingness in any of the variables. The argument groups
can be used
to specify groups based on the variable values themselves. Only one of both
may be active at the same time. When both are specified, na.groups
takes precedence over groups
.
Use the subset
and na.groups
together to plots parts of the
data. For example, select the first imputed data set by by
subset=.imp==1
.
Graphical parameters like col
, pch
and cex
can be
specified in the arguments list to alter the plotting symbols. If
length(col)==2
, the color specification to define the observed and
missing groups. col[1]
is the color of the 'observed' data,
col[2]
is the color of the missing or imputed data. A convenient color
choice is col=mdc(1:2)
, a transparent blue color for the observed
data, and a transparent red color for the imputed data. A good choice is
col=mdc(1:2), pch=20, cex=1.5
. These choices can be set for the
duration of the session by running mice.theme()
.
The highlevel functions documented here, as well as other highlevel
Lattice functions, return an object of class "trellis"
. The
update
method can be used to
subsequently update components of the object, and the
print
method (usually called by default)
will plot it on an appropriate plotting device.
The first two arguments (x
and data
) are reversed
compared to the standard Trellis syntax implemented in lattice. This
reversal was necessary in order to benefit from automatic method dispatch.
In mice the argument x
is always a mids
object, whereas
in lattice the argument x
is always a formula.
In mice the argument data
is always a formula object, whereas in
lattice the argument data
is usually a data frame.
All other arguments have identical interpretation.
Stef van Buuren
Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer.
van Buuren S and GroothuisOudshoorn K (2011). mice
: Multivariate
Imputation by Chained Equations in R
. Journal of Statistical
Software, 45(3), 167. doi:10.18637/jss.v045.i03
mice
, stripplot
, densityplot
,
bwplot
, lattice
for an overview of the
package, as well as xyplot
,
panel.xyplot
,
print.trellis
,
trellis.par.set
imp < mice(boys, maxit = 1)
# xyplot: scatterplot by imputation number
# observe the erroneous outlying imputed values
# (caused by imputing hgt from bmi)
xyplot(imp, hgt ~ age  .imp, pch = c(1, 20), cex = c(1, 1.5))
# same, but label with missingness of wgt (four cases)
xyplot(imp, hgt ~ age  .imp, na.group = wgt, pch = c(1, 20), cex = c(1, 1.5))