mice
Multivariate Imputation by Chained Equations (MICE)
Generates Multivariate Imputations by Chained Equations (MICE)
 Keywords
 iteration
Usage
mice(data, m = 5, method = vector("character", length = ncol(data)), predictorMatrix = (1  diag(1, ncol(data))), visitSequence = (1:ncol(data))[apply(is.na(data), 2, any)], form = vector("character", length = ncol(data)), post = vector("character", length = ncol(data)), defaultMethod = c("pmm", "logreg", "polyreg", "polr"), maxit = 5, diagnostics = TRUE, printFlag = TRUE, seed = NA, imputationMethod = NULL, defaultImputationMethod = NULL, data.init = NULL, ...)
Arguments
 data
 A data frame or a matrix containing the incomplete data. Missing
values are coded as
NA
.  m
 Number of multiple imputations. The default is
m=5
.  method
 Can be either a single string, or a vector of strings with
length
ncol(data)
, specifying the elementary imputation method to be used for each column in data. If specified as a single string, the same method will be used for all columns. The default imputation method (when no argument is specified) depends on the measurement level of the target column and are specified by thedefaultMethod
argument. Columns that need not be imputed have the empty method''
. See details for more information.  predictorMatrix
 A square matrix of size
ncol(data)
containing 0/1 data specifying the set of predictors to be used for each target column. Rows correspond to target variables (i.e. variables to be imputed), in the sequence as they appear in data. A value of '1' means that the column variable is used as a predictor for the target variable (in the rows). The diagonal ofpredictorMatrix
must be zero. The default forpredictorMatrix
is that all other columns are used as predictors (sometimes called massive imputation). Note: For twolevel imputation codes '2' and '2' are also allowed.  visitSequence
 A vector of integers of arbitrary length, specifying the
column indices of the visiting sequence. The visiting sequence is the column
order that is used to impute the data during one pass through the data. A
column may be visited more than once. All incomplete columns that are used as
predictors should be visited, or else the function will stop with an error.
The default sequence
1:ncol(data)
implies that columns are imputed from left to right. It is possible to specify one of the keywords'roman'
(left to right),'arabic'
(right to left),'monotone'
(sorted in increasing amount of missingness) and'revmonotone'
(reverse of monotone). The keyword should be supplied as a string and may be abbreviated.  form
 A vector of strings with length
ncol(data)
, specifying formulae. Each string is parsed and executed within thesampler()
function to create terms for the predictor. The default is to do nothing, indicated by a vector of empty strings''
. The main value lies in the easy specification of interaction terms. The user must ensure that the set of variables in the formula match those inpredictors
.  post
 A vector of strings with length
ncol(data)
, specifying expressions. Each string is parsed and executed within thesampler()
function to postprocess imputed values. The default is to do nothing, indicated by a vector of empty strings''
.  defaultMethod
 A vector of three strings containing the default
imputation methods for numerical columns, factor columns with 2 levels, and
columns with (unordered or ordered) factors with more than two levels,
respectively. If nothing is specified, the following defaults will be used:
pmm
, predictive mean matching (numeric data)logreg
, logistic regression imputation (binary data, factor with 2 levels)polyreg
, polytomous regression imputation for unordered categorical data (factor >= 2 levels)polr
, proportional odds model for (ordered, >= 2 levels)  maxit
 A scalar giving the number of iterations. The default is 5.
 diagnostics
 A Boolean flag. If
TRUE
, diagnostic information will be appended to the value of the function. IfFALSE
, only the imputed data are saved. The default isTRUE
.  printFlag
 If
TRUE
,mice
will print history on console. Useprint=FALSE
for silent computation.  seed
 An integer that is used as argument by the
set.seed()
for offsetting the random number generator. Default is to leave the random number generator alone.  imputationMethod
 Same as
method
argument. Included for backwards compatibility.  defaultImputationMethod
 Same as
defaultMethod
argument. Included for backwards compatibility.  data.init
 A data frame of the same size and type as
data
, without missing data, used to initialize imputations before the start of the iterative process. The defaultNULL
implies that starting imputation are created by a simple random draw from the data. Note that specification ofdata.init
will start them
Gibbs sampling streams from the same imputations.  ...
 Named arguments that are passed down to the elementary imputation functions.
Details
Generates multiple imputations for incomplete multivariate data by Gibbs sampling. Missing data can occur anywhere in the data. The algorithm imputes an incomplete column (the target column) by generating 'plausible' synthetic values given other columns in the data. Each incomplete column must act as a target column, and has its own specific set of predictors. The default set of predictors for a given target consists of all other columns in the data. For predictors that are incomplete themselves, the most recently generated imputations are used to complete the predictors prior to imputation of the target column.
A separate univariate imputation model can be specified for each column. The default imputation method depends on the measurement level of the target column. In addition to these, several other methods are provided. You can also write their own imputation functions, and call these from within the algorithm.
The data may contain categorical variables that are used in a regressions on
other variables. The algorithm creates dummy variables for the categories of
these variables, and imputes these from the corresponding categorical
variable. The extended model containing the dummy variables is called the
padded model. Its structure is stored in the list component pad
.
Builtin elementary imputation methods are:
 pmm
 Predictive mean matching (any)
These corresponding functions are coded in the mice
library under
names mice.impute.method
, where method
is a string with the
name of the elementary imputation method name, for example norm
. The
method
argument specifies the methods to be used. For the j
'th
column, mice()
calls the first occurence of
paste('mice.impute.',method[j],sep='')
in the search path. The
mechanism allows uses to write customized imputation function,
mice.impute.myfunc
. To call it for all columns specify
method='myfunc'
. To call it only for, say, column 2 specify
method=c('norm','myfunc','logreg',...{})
.
Passive imputation: mice()
supports a special builtin method,
called passive imputation. This method can be used to ensure that a data
transform always depends on the most recently generated imputations. In some
cases, an imputation model may need transformed data in addition to the
original data (e.g. log, quadratic, recodes, interaction, sum scores, and so
on).
Passive imputation maintains consistency among different transformations of
the same data. Passive imputation is invoked if ~
is specified as the
first character of the string that specifies the elementary method.
mice()
interprets the entire string, including the ~
character,
as the formula argument in a call to model.frame(formula,
data[!r[,j],])
. This provides a simple mechanism for specifying determinstic
dependencies among the columns. For example, suppose that the missing entries
in variables data$height
and data$weight
are imputed. The body
mass index (BMI) can be calculated within mice
by specifying the
string '~I(weight/height^2)'
as the elementary imputation method for
the target column data$bmi
. Note that the ~
mechanism works
only on those entries which have missing values in the target column. You
should make sure that the combined observed and imputed parts of the target
column make sense. An easy way to create consistency is by coding all entries
in the target as NA
, but for large data sets, this could be
inefficient. Note that you may also need to adapt the default
predictorMatrix
to evade linear dependencies among the predictors that
could cause errors like Error in solve.default()
or Error:
system is exactly singular
. Though not strictly needed, it is often useful
to specify visitSequence
such that the column that is imputed by the
~
mechanism is visited each time after one of its predictors was
visited. In that way, deterministic relation between columns will always be
synchronized.
Value

Returns an S3 object of class
mids
(multiply imputed data set)
References
Van Buuren, S., GroothuisOudshoorn, K. (2011). mice
:
Multivariate Imputation by Chained Equations in R
. Journal of
Statistical Software, 45(3), 167.
http://www.jstatsoft.org/v45/i03/
van Buuren, S. (2012). Flexible Imputation of Missing Data. Boca Raton, FL: Chapman & Hall/CRC Press.
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.
Van Buuren, S. (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16, 3, 219242.
Van Buuren, S., Boshuizen, H.C., Knook, D.L. (1999) Multiple imputation of missing blood pressure covariates in survival analysis. Statistics in Medicine, 18, 681694.
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.
See Also
Examples
# do default multiple imputation on a numeric matrix
imp < mice(nhanes)
imp
# list the actual imputations for BMI
imp$imputations$bmi
# first completed data matrix
complete(imp)
# imputation on mixed data with a different method per column
mice(nhanes2, meth=c('sample','pmm','logreg','norm'))