Clustering with missing data: which imputation model for which cluster analysis method?
Résumé
Multiple imputation (MI) is a popular method for dealing with missing values. One main advantage of MI is to dissociate 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 talk, we discuss congeniality of imputation models and clustering on continuous data. First, we theoretically highlight how two joint modelling (JM) MI methods, using either general location model (JM-GL) or Dirichlet process mixture (JM-DP), could be 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 from normal distribution 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 always 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 data involving more complex distributions.