Statistical Modelling 13 (1) (2013), 41–67
Clustering in linear mixed models with approximate Dirichlet process mixtures using EM algorithm
Felix Heinz
Department of Statistics,
Ludwig-Maximillians-University Munic
Munich,
Germany
e-mail: feliz.heinzl@stat.uni-muenchen.de
Gerhard Tutz
Department of Statistics,
Ludwig-Maximillians-University Munich
Munich,
Germany
Abstract:
In linear mixed models the assumption of normally distributed random effects is often inappropriate and unnecessary restrictive. The proposed approximate Dirichlet process mixture assumes a hierarchical Gaussian mixture that is based on the truncated version of the stick breaking presentation of the Dirichlet process. In addition to the weakening of distributional assumptions the specification allows to identify clusters of observations with a similar random effects structure. An Expectation-Maximization algorithm is given that solves the estimation problem and that, in certain respects, may exhibit
advantages over Markov chain Monte Carlo approaches when modeling with Dirichlet processes. The method is evaluated in a simulation study and applied to the dynamics of unemployment in Germany as well as lung function growth data.
Keywords:
approximate Dirichlet process mixture; EM algorithm; likelihood inference; linear mixed models; stick breaking
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