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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 analysisone. However, both are related since they are based on distribution assumptionsthat 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-GLand JM-DP) are congenial with various clustering methods. Then, we propose anew fully conditional specification (FCS) MI method with the same theoreticalproperties as JM-GL. Finally, we extend this FCS MI method to account for morecomplex distributions. Based on an extensive simulation study, all MI methodsare compared for various cluster analysis methods (k-means, k-medoids, mixturemodel, hierarchical clustering).  This study highlights the partition accuracy is improved when the imputationmodel accounts for clustered individuals. From this point of view, standard MImethods ignoring such a structure should be avoided. JM-GL and JM-DP should berecommended when data are distributed according to a gaussian mixture model,while FCS methods outperform JM ones on more complex data.

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