mice {mice}R Documentation

Multivariate Imputation by Chained Equations (MICE)

Description

Generates Multivariate Imputations by Chained Equations (MICE)

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)], 
    post = vector("character", length = ncol(data)), 
    defaultMethod = c("pmm","logreg","polyreg","polr"),
    maxit = 5, 
    diagnostics = TRUE, 
    printFlag = TRUE,
    seed = NA,
    imputationMethod = NULL,
    defaultImputationMethod = 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 the defaultMethod 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 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.

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.

post

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 "".

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. If FALSE, only the imputed data are saved. The default is TRUE.

printFlag

If TRUE, mice will print history on console. Use print=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.

...

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.

Built-in elementary imputation methods are:

pmm

Predictive mean matching (numeric)

norm

Bayesian linear regression (numeric)

norm.nob

Linear regression ignoring model error (numeric)

mean

Unconditional mean imputation (numeric)

2l.norm

Two-level normal imputation (numeric)

logreg

Logistic regression (factor, 2 levels)

polyreg

Polytomous logistic regression (factor, >= 2 levels)

polr

Proportional odds model (ordered, >=2 levels)

lda

Linear discriminant analysis (factor, >= 2 categories)

sample

Random sample from the observed values (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.

Value

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

call

The call that created the object

data

A copy of the incomplete data set

m

The number of imputations

nmis

An array of length ncol(data) containing the number of missing observations per column

imp

A list of ncol(data) components with the generated multiple imputations. Each part of the list is a nmis[j] by m matrix of imputed values for variable data[,j]. The component equals NULL for columns without missing data.

method

A vector of strings of length ncol(data) specifying the elementary imputation method per column

predictorMatrix

A square matrix of size ncol(data) containing 0/1 data specifying the predictor set

visitSequence

The sequence in which columns are visited

post

A vector of strings of length ncol(data) with commands for post-processing

seed

The seed value of the solution

iteration

Last Gibbs sampling iteration number

lastSeedValue

The most recent seed value

chainMean

An array containing the mean of the generated multiple imputations. The array can be used for monitoring convergence. Factors are replaced by their numerical representation using as.integer(). Note that observed data are not present in this mean.

chainVar

An array with similar structure of chainMean, containing the variances of the imputed values.

pad

A list containing various settings of the padded imputation model, i.e. the imputation model after creating dummy variables. Normally, this list is only useful for error checking. List members are pad$data (data padded with columns for factors), pad$predictorMatrix (predictor matrix for the padded data), pad$method (imputation methods applied to the padded data), the vector pad$visitSequence (the visit sequence applied to the padded data), pad$post (post-processing commands for padded data) and categories (a matrix containing descriptive information about the padding operation).

loggedEvents

A matrix with six 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: 1. A variable that contains missing values, that is not imputed and that is used as a predictor is removed, 2. a constant variable is removed, and 3. a collinear variable is removed. During iteration, the program does the following actions: 1. one or more variables that are linearly dependent are removed (for categorical data, a 'variable' corresponds to a dummy variable), and 2. proportional odds regression imputation that does not converge and is replaced by polyreg. Column it is the iteration number at which the record was added, im is the imputation number, co is the column number in the data, dep is the name of the name of the dependent variable, meth is the imputation method used, and out is a (possibly long) character vector with the names of the altered or removed predictors.

Author(s)

Stef van Buuren (stef.vanbuuren@tno.nl), Karin Groothuis-Oudshoorn (c.g.m.oudshoorn@utwente.nl) (2000-2010) with contributions of Roel de Jong, Jason Turner, John Fox, Frank E. Harrell, and Peter Malewski.

References

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., 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. http://www.stefvanbuuren.nl/publications/FCS in multivariate imputation - JSCS 2006.pdf

Van Buuren, S. (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16, 3, 219–242. http://www.stefvanbuuren.nl/publications/MI by FCS - SMMR 2007.pdf

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. http://www.stefvanbuuren.nl/publications/Multiple imputation - Stat Med 1999.pdf

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

complete, mids, with.mids, set.seed

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")) 

[Package mice version 2.11 Index]