mice (version 2.30)

mice: Multivariate Imputation by Chained Equations (MICE)


Generates Multivariate Imputations by Chained Equations (MICE)


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, ...)



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 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 the defaultMethod argument. Columns that need not be imputed have the empty method ''. See details for more information.


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 of predictorMatrix must be zero. The default for predictorMatrix is that all other columns are used as predictors (sometimes called massive imputation). Note: For two-level imputation codes '2' and '-2' are also allowed.


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.


A vector of strings with length ncol(data), specifying formulae. Each string is parsed and executed within the sampler() 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 in predictors.


A vector of strings with length ncol(data), specifying expressions. Each string is parsed and executed within the sampler() function to postprocess imputed values. The default is to do nothing, indicated by a vector of empty strings ''.


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)


A scalar giving the number of iterations. The default is 5.


A Boolean flag. If TRUE, diagnostic information will be appended to the value of the function. If FALSE, only the imputed data are saved. The default is TRUE.


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.


Same as method argument. Included for backwards compatibility.


Same as defaultMethod argument. Included for backwards compatibility.


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 the m Gibbs sampling streams from the same imputations.


Named arguments that are passed down to the elementary imputation functions.


Returns an S3 object of class mids (multiply imputed data set)


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.

Built-in elementary imputation methods are:


Predictive mean matching (any)


Bayesian linear regression (numeric)


Linear regression ignoring model error (numeric)


Linear regression using bootstrap (numeric)


Linear regression, predicted values (numeric)


Unconditional mean imputation (numeric)


Two-level normal imputation (numeric)


Two-level normal imputation using pan (numeric)


Imputation at level-2 of the class mean (numeric)


Imputation at level-2 by Bayesian linear regression (numeric)


Imputation at level-2 by Predictive mean matching (any)


Imputation of quadratic terms (numeric)


Logistic regression (factor, 2 levels)


Logistic regression with bootstrap


Polytomous logistic regression (factor, >= 2 levels)


Proportional odds model (ordered, >=2 levels)


Linear discriminant analysis (factor, >= 2 categories)


Classification and regression trees (any)


Random forest imputations (any)


Random indicator method for nonignorable data (numeric)


Random sample from the observed values (any)


Experimental: Fast predictive mean matching using C++ (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 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 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.


Van Buuren, S., Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. 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., 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.

See Also

mids, with.mids, set.seed, complete


Run this code

# do default multiple imputation on a numeric matrix
imp <- mice(nhanes)

# list the actual imputations for BMI

# first completed data matrix

# imputation on mixed data with a different method per column

mice(nhanes2, meth=c('sample','pmm','logreg','norm'))

# }

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