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Trajectory Modeling of Longitudinal Binary Data: Application of the EM Algorithm for Mixture Models
Authors:Man-Kee M Chu  John J Koval
Institution:1. Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Ontario, Canadamchu5@uwo.ca;3. Department of Epidemiology and Biostatistics, The University of Western Ontario, London, Ontario, Canada
Abstract:A developmental trajectory describes the course of behavior over time. Identifying multiple trajectories within an overall developmental process permits a focus on subgroups of particular interest. We introduce a framework for identifying trajectories by using the Expectation-Maximization (EM) algorithm to fit semiparametric mixtures of logistic distributions to longitudinal binary data. For performance comparison, we consider full maximization algorithms (PROC TRAJ in SAS), standard EM, and two other EM-based algorithms for speeding up convergence. Simulation shows that EM methods produce more accurate parameter estimates. The EM methodology is illustrated with a longitudinal dataset involving adolescents smoking behaviors.
Keywords:Binary data  Expectation-maximization algorithm  Longitudinal trajectories  Mixture models
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