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Heinzl, Felix and Tutz, Gerhard (2012): Clustering in linear mixed models with a group fused lasso penalty. Department of Statistics: Technical Reports, No.123
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Abstract

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear mixed models which are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose an EM algorithm-based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.