The mice package implements a method to deal with missing data. The package creates multiple imputations (replacement values) for multivariate missing data. The method is based on Fully Conditional Specification, where each incomplete variable is imputed by a separate model. The MICE algorithm can impute mixes of continuous, binary, unordered categorical and ordered categorical data. In addition, MICE can impute continuous two-level data, and maintain consistency between imputations by means of passive imputation. Many diagnostic plots are implemented to inspect the quality of the imputations.
Generates Multivariate Imputations by Chained Equations (MICE)
mice(
data,
m = 5,
method = NULL,
predictorMatrix,
ignore = NULL,
where = NULL,
blocks,
visitSequence = NULL,
formulas,
blots = NULL,
post = NULL,
defaultMethod = c("pmm", "logreg", "polyreg", "polr"),
maxit = 5,
printFlag = TRUE,
seed = NA,
data.init = NULL,
...
)Returns an S3 object of class mids
(multiply imputed data set)
A data frame or a matrix containing the incomplete data. Missing
values are coded as NA.
Number of multiple imputations. The default is m=5.
Can be either a single string, or a vector of strings with
length length(blocks), specifying the imputation method to be
used for each column in data. If specified as a single string, the same
method will be used for all blocks. The default imputation method (when no
argument is specified) depends on the measurement level of the target column,
as regulated by the defaultMethod argument. Columns that need
not be imputed have the empty method "". See details.
A numeric matrix of length(blocks) rows
and ncol(data) columns, containing 0/1 data specifying
the set of predictors to be used for each target column.
Each row corresponds to a variable block, i.e., a set of variables
to be imputed. A value of 1 means that the column
variable is used as a predictor for the target block (in the rows).
By default, the predictorMatrix is a square matrix of ncol(data)
rows and columns with all 1's, except for the diagonal.
Note: For two-level imputation models (which have "2l" in their names)
other codes (e.g, 2 or -2) are also allowed.
A logical vector of nrow(data) elements indicating
which rows are ignored when creating the imputation model. The default
NULL includes all rows that have an observed value of the variable
to imputed. Rows with ignore set to TRUE do not influence the
parameters of the imputation model, but are still imputed. We may use the
ignore argument to split data into a training set (on which the
imputation model is built) and a test set (that does not influence the
imputation model estimates).
Note: Multivariate imputation methods, like mice.impute.jomoImpute()
or mice.impute.panImpute(), do not honour the ignore argument.
A data frame or matrix with logicals of the same dimensions
as data indicating where in the data the imputations should be
created. The default, where = is.na(data), specifies that the
missing data should be imputed. The where argument may be used to
overimpute observed data, or to skip imputations for selected missing values.
Note: Imputation methods that generate imptutations outside of
mice, like mice.impute.panImpute() may depend on a complete
predictor space. In that case, a custom where matrix can not be
specified.
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 method argument). By default each variable is placed
into its own block, which is effectively
fully conditional specification (FCS) by univariate models
(variable-by-variable imputation). Only variables whose names appear in
blocks are imputed. The relevant columns in the where
matrix are set to FALSE of variables that are not block members.
A variable may appear in multiple blocks. In that case, it is
effectively re-imputed each time that it is visited.
A vector of block names of arbitrary length, specifying the
sequence of blocks that are imputed during one iteration of the Gibbs
sampler. A block is a collection of variables. All variables that are
members of the same block are imputed
when the block is visited. A variable that is a member of multiple blocks
is re-imputed within the same iteration.
The default visitSequence = "roman" visits the blocks (left to right)
in the order in which they appear in blocks.
One may also use one of the following keywords: "arabic"
(right to left), "monotone" (ordered low to high proportion
of missing data) and "revmonotone" (reverse of monotone).
Special case: If you specify both visitSequence = "monotone" and
maxit = 1, then the procedure will edit the predictorMatrix
to conform to the monotone pattern. Realize that convergence in one
iteration is only guaranteed if the missing data pattern is actually
monotone. The procedure does not check this.
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.
The formulas argument is an alternative to the
predictorMatrix argument that allows for more flexibility in
specifying imputation models, e.g., for specifying interaction terms.
A named list of alist's that can be used
to pass down arguments to lower level imputation function. The entries
of element blots[[blockname]] are passed down to the function
called for block blockname.
A vector of strings with length ncol(data) specifying
expressions as strings. Each string is parsed and
executed within the sampler() function to post-process
imputed values during the iterations.
The default is a vector of empty strings, indicating no post-processing.
Multivariate (block) imputation methods ignore the post parameter.
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
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).
A scalar giving the number of iterations. The default is 5.
If TRUE, mice will print history on console.
Use print=FALSE for silent computation.
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.
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 default NULL implies that starting imputation
are created by a simple random draw from the data. Note that specification of
data.init will start all m Gibbs sampling streams from the same
imputation.
Named arguments that are passed down to the univariate imputation functions.
The main functions are:
mice() | Impute the missing data *m* times |
with() | Analyze completed data sets |
pool() | Combine parameter estimates |
complete() | Export imputed data |
ampute() | Generate missing data |
There is a detailed series of six online vignettes that walk you through solving realistic inference problems with mice.
We suggest going through these vignettes in the following order
#'Van Buuren, S. (2018). Boca Raton, FL.: Chapman & Hall/CRC Press. The book Flexible Imputation of Missing Data. Second Edition. contains a lot of example code.
The mice software was published in the Journal of Statistical Software (Van Buuren and Groothuis-Oudshoorn, 2011). tools:::Rd_expr_doi("10.18637/jss.v045.i03") The first application of the method concerned missing blood pressure data (Van Buuren et. al., 1999). The term Fully Conditional Specification was introduced in 2006 to describe a general class of methods that specify imputations model for multivariate data as a set of conditional distributions (Van Buuren et. al., 2006). Further details on mixes of variables and applications can be found in the book Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Updating the BLAS can improve speed of R, sometime considerably. The details depend on the operating system. See the discussion in the "R Installation and Administration" guide for further information.
Stef van Buuren stef.vanbuuren@tno.nl, Karin Groothuis-Oudshoorn c.g.m.oudshoorn@utwente.nl, 2000-2010, with contributions of Alexander Robitzsch, Gerko Vink, Shahab Jolani, Roel de Jong, Jason Turner, Lisa Doove, John Fox, Frank E. Harrell, and Peter Malewski.
The mice package contains functions to
Inspect the missing data pattern
Impute the missing data m times, resulting in m completed data sets
Diagnose the quality of the imputed values
Analyze each completed data set
Pool the results of the repeated analyses
Store and export the imputed data in various formats
Generate simulated incomplete data
Incorporate custom imputation methods
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.
Built-in univariate imputation methods are:
pmm | any | Predictive mean matching |
midastouch | any | Weighted predictive mean matching |
sample | any | Random sample from observed values |
cart | any | Classification and regression trees |
rf | any | Random forest imputations |
mean | numeric | Unconditional mean imputation |
norm | numeric | Bayesian linear regression |
norm.nob | numeric | Linear regression ignoring model error |
norm.boot | numeric | Linear regression using bootstrap |
norm.predict | numeric | Linear regression, predicted values |
lasso.norm | numeric | Lasso linear regression |
lasso.select.norm | numeric | Lasso select + linear regression |
quadratic | numeric | Imputation of quadratic terms |
ri | numeric | Random indicator for nonignorable data |
logreg | binary | Logistic regression |
logreg.boot | binary | Logistic regression with bootstrap |
lasso.logreg | binary | Lasso logistic regression |
lasso.select.logreg | binary | Lasso select + logistic regression |
polr | ordered | Proportional odds model |
polyreg | unordered | Polytomous logistic regression |
lda | unordered | Linear discriminant analysis |
2l.norm | numeric | Level-1 normal heteroscedastic |
2l.lmer | numeric | Level-1 normal homoscedastic, lmer |
2l.pan | numeric | Level-1 normal homoscedastic, pan |
2l.bin | binary | Level-1 logistic, glmer |
2lonly.mean | numeric | Level-2 class mean |
2lonly.norm | numeric | Level-2 class normal |
2lonly.pmm | any | Level-2 class predictive mean matching |
These corresponding functions are coded in the mice library under
names mice.impute.method, where method is a string with the
name of the univariate imputation method name, for example norm. The
method argument specifies the methods to be used. For the j'th
column, mice() calls the first occurrence 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',...{}).
Skipping imputation: The user may skip imputation of a column by
setting its entry to the empty method: "". For complete columns without
missing data mice will automatically set the empty method. Setting t
he empty method does not produce imputations for the column, so any missing
cells remain NA. If column A contains NA's and is used as
predictor in the imputation model for column B, then mice produces no
imputations for the rows in B where A is missing. The imputed data
for B may thus contain NA's. The remedy is to remove column A from
the imputation model for the other columns in the data. This can be done
by setting the entire column for variable A in the predictorMatrix
equal to zero.
Passive imputation: mice() supports a special built-in 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 univariate 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 deterministic
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 univariate 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.
#'A new argument ls.meth can be parsed to the lower level
.norm.draw to specify the method for generating the least squares
estimates and any subsequently derived estimates. Argument ls.meth
takes one of three inputs: "qr" for QR-decomposition, "svd" for
singular value decomposition and "ridge" for ridge regression.
ls.meth defaults to ls.meth = "qr".
Auxiliary predictors in formulas specification:
For a given block, the formulas specification takes precedence over
the corresponding row in the predictMatrix argument. This
precedence is, however, restricted to the subset of variables
specified in the terms of the block formula. Any
variables not specified by formulas are imputed
according to the predictMatrix specification. Variables with
non-zero type values in the predictMatrix will
be added as main effects to the formulas, which will
act as supplementary covariates in the imputation model. It is possible
to turn off this behavior by specifying the
argument auxiliary = FALSE.
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., Brand, J.P.L., Groothuis-Oudshoorn 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., Groothuis-Oudshoorn, K. (2011). mice:
Multivariate Imputation by Chained Equations in R. Journal of
Statistical Software, 45(3), 1--67. tools:::Rd_expr_doi("10.18637/jss.v045.i03")
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Van Buuren, S., Groothuis-Oudshoorn, K. (2011). mice:
Multivariate Imputation by Chained Equations in R. Journal of
Statistical Software, 45(3), 1-67.
tools:::Rd_expr_doi("10.18637/jss.v045.i03")
Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.
Van Buuren, S., Brand, J.P.L., Groothuis-Oudshoorn 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. (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16, 3, 219--242.
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.
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.
mice, with.mids,
pool, complete, ampute
mids, with.mids,
set.seed, complete
# do default multiple imputation on a numeric matrix
imp <- mice(nhanes)
imp
# list the actual imputations for BMI
imp$imp$bmi
# first completed data matrix
complete(imp)
# imputation on mixed data with a different method per column
mice(nhanes2, meth = c("sample", "pmm", "logreg", "norm"))
if (FALSE) {
# example where we fit the imputation model on the train data
# and apply the model to impute the test data
set.seed(123)
ignore <- sample(c(TRUE, FALSE), size = 25, replace = TRUE, prob = c(0.3, 0.7))
# scenario 1: train and test in the same dataset
imp <- mice(nhanes2, m = 2, ignore = ignore, print = FALSE, seed = 22112)
imp.test1 <- filter(imp, ignore)
imp.test1$data
complete(imp.test1, 1)
complete(imp.test1, 2)
# scenario 2: train and test in separate datasets
traindata <- nhanes2[!ignore, ]
testdata <- nhanes2[ignore, ]
imp.train <- mice(traindata, m = 2, print = FALSE, seed = 22112)
imp.test2 <- mice.mids(imp.train, newdata = testdata)
complete(imp.test2, 1)
complete(imp.test2, 2)
}
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