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, 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, ...)
```

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 `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.

predictorMatrix

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.

where

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.

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 `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.

visitSequence

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).

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.
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.

blots

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`

.

post

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.

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
`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.

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.

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 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.

Returns an S3 object of class `mids`

(multiply imputed data set)

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).
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.

The mice package contains functions to

Inspect the missing data pattern

Impute the missing data

*m*times, resulting in*m*completed data setsDiagnose 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 |

`quadratic` |
numeric | Imputation of quadratic terms |

`ri` |
numeric | Random indicator for nonignorable data |

`logreg` |
binary | Logistic regression |

`logreg.boot` |
binary | Logistic regression with bootstrap |

`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 |

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',…{})`

.

*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.

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.
https://www.jstatsoft.org/v45/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.

```
# NOT RUN {
# 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'))
# }
```

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