MIMCA: Multiple imputation for categorical variables with multiple correspondence analysis

TL;DR

MIMCA is a new multiple imputation method for incomplete categorical data that uses multiple correspondence analysis and bootstrap to efficiently handle high-dimensional data with many categories.

Contribution

The paper introduces MIMCA, a novel imputation approach leveraging MCA and bootstrap, which is computationally efficient and effective for high-dimensional categorical datasets.

Findings

MIMCA performs well in bias and coverage compared to existing methods.

It is less time-consuming on high-dimensional data.

MIMCA handles many categories and variables without issues.

Abstract

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.