Clustering with missing data: which imputation model for which cluster analysis method?

TL;DR

This paper examines the compatibility of different multiple imputation methods with clustering techniques for continuous data, emphasizing the importance of model congruence and proposing a new FCS method for complex distributions.

Contribution

It introduces a new FCS multiple imputation method with theoretical properties similar to JM-GL and extends it for complex distributions, improving clustering accuracy.

Findings

Imputation models that consider data clustering improve partition accuracy.

JM-GL and JM-DP are suitable for Gaussian mixture distributed data.

FCS methods outperform JM methods on complex data distributions.

Abstract

Multiple imputation (MI) is a popular method for dealing with missing values. One main advantage of MI is to separate the imputation phase and the analysis one. However, both are related since they are based on distribution assumptions that have to be consistent. This point is well known as congeniality. In this paper, we discuss congeniality for clustering on continuous data. First, we theoretically highlight how two joint modeling (JM) MI methods (JM-GL and JM-DP) are congenial with various clustering methods. Then, we propose a new fully conditional specification (FCS) MI method with the same theoretical properties as JM-GL. Finally, we extend this FCS MI method to account for more complex distributions. Based on an extensive simulation study, all MI methods are compared for various cluster analysis methods (k-means, k-medoids, mixture model, hierarchical clustering). This study highlights the partition accuracy is improved when the imputation model accounts for clustered individuals. From this point of view, standard MI methods ignoring such a structure should be avoided. JM-GL and JM-DP should be recommended when data are distributed according to a gaussian mixture model, while FCS methods outperform JM ones on more complex data.