When using bal.tab() with multiply imputed data, the output will be different from the case with a single data set. Multiply imputed data can be used with all bal.tab() methods, and the mimids and wimids methods for MatchThem objects automatically incorporate multiply imputed data. This page outlines the outputs and options available with multiply imputed data.

There are two main components of the output of bal.tab() with multiply imputed data: the within-imputation balance summaries and the across-imputation balance summary. The within-imputation balance summaries display balance for units within each imputed data set separately. In general, this will not be very useful because interest rarely lies in the qualities of any individual imputed data set.

The across-imputation balance summary pools information across the within-imputation balance summaries to simplify balance assessment. It provides the average, smallest, and largest balance statistic for each covariate across all imputations. This allows you to see how bad the worst imbalance is and what balance looks like on average across the imputations. The summary behaves differently depending on whether abs is specified as TRUE or FALSE. When abs = TRUE, the across-imputation balance summary will display the mean absolute balance statistics and the maximum absolute balance statistics. When abs = FALSE, the across-imputation balance summary will display the minimum, mean, and maximum of the balance statistic in its original form.

## Arguments

There are four arguments for each bal.tab() method that can handle multiply imputed data: imp, which.imp, imp.summary, and imp.fun.

imp

A vector of imputation membership. This can be factor, character, or numeric vector. This argument is required to let bal.tab() know that the data is multiply imputed unless MatchThem objects are used. If a data argument is specified, this can also be the name of a variable in data that contains imputation membership. If the data argument is a mids object, the output of a call to mice(), imp does not need to be specified and will automatically be extracted from the mids object.

which.imp

This is a display option that does not affect computation. If .all, all imputations in imp will be displayed. If .none (the default), no imputations will be displayed. Otherwise, can be a vector of imputation indices for which to display balance.

imp.summary

This is a display option that does not affect computation. If TRUE, the balance summary across imputations will be displayed. The default is TRUE, and if which.imp is .none, it will automatically be set to TRUE.

imp.fun

This is a display option that does not affect computation. Can be "min", "mean", or "max" and corresponds to which function is used in the across-imputation summary to combine results across imputations. For example, if imp.fun = "mean" the mean balance statistic across imputations will be displayed. The default when abs = FALSE in the bal.tab() call is to display all three. The default when abs = FALSE in the bal.tab() call is to display just the mean and max balance statistic.

## Value

The output is a bal.tab.imp object, which inherits from bal.tab. It has the following elements:

Imputation.Balance

For each imputation, a regular bal.tab object containing a balance table, a sample size summary, and other balance assessment tools, depending on which options are specified.

Balance.Across.Imputations

The balance summary across imputations. This will include the combination of each balance statistic for each covariate across all imputations according to the value of imp.fun.

Observations

A table of sample sizes or effective sample sizes averaged across imputations before and after adjustment.

As with other methods, multiple weights can be specified, and values for all weights will appear in all tables.

## Author

Noah Greifer

bal.tab(), bal.tab.data.frame(), print.bal.tab()