  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.
