Clustering in Additive Mixed Models with Approximate Dirichlet Process Mixtures using the EM Algorithm

Heinzl, Felix and Tutz, Gerhard (14. February 2013): Clustering in Additive Mixed Models with Approximate Dirichlet Process Mixtures using the EM Algorithm. Department of Statistics: Technical Reports, No.138

Abstract

We consider additive mixed models for longitudinal data with a nonlinear time trend. As random effects distribution an approximate Dirichlet process mixture is proposed that is based on the truncated version of the stick breaking presentation of the Dirichlet process and provides a Gaussian mixture with a data driven choice of the number of mixture components. The main advantage of the specification is its ability to identify clusters of subjects with a similar random effects structure. For the estimation of the trend curve the mixed model representation of penalized splines is used. AnExpectation-Maximization algorithm is given that solves the estimation problem and that exhibits advantages over Markov chain Monte Carlo approaches, which are typically used when modeling with Dirichlet processes. The method is evaluated in a simulation study and applied to body mass index profiles of children.

• Item Type: Paper
• Form of publication: Preprint
• Keywords: Additive mixed models; Dirichlet process mixture; EM algorithm; penalized splines; stick breaking
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Subjects: 500 Science > 510 Mathematics
• Language: English