  We propose a multiple imputation method to deal with incomplete categorical
data. This method imputes the missing entries using the principal components
method dedicated to categorical data: multiple correspondence analysis (MCA).
The uncertainty concerning the parameters of the imputation model is reflected
using a non-parametric bootstrap. Multiple imputation using MCA (MIMCA)
requires estimating a small number of parameters due to the dimensionality
reduction property of MCA. It allows the user to impute a large range of data
sets. In particular, a high number of categories per variable, a high number of
variables or a small the number of individuals are not an issue for MIMCA.
Through a simulation study based on real data sets, the method is assessed and
compared to the reference methods (multiple imputation using the loglinear
model, multiple imputation by logistic regressions) as well to the latest works
on the topic (multiple imputation by random forests or by the Dirichlet process
mixture of products of multinomial distributions model). The proposed method
shows good performances in terms of bias and coverage for an analysis model
such as a main effects logistic regression model. In addition, MIMCA has the
great advantage that it is substantially less time consuming on data sets of
high dimensions than the other multiple imputation methods.
