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Regularized Finite Mixture Models for Probability Trajectories

Published online by Cambridge University Press:  01 January 2025

Kerby Shedden  and
Robert A. Zucker
Kerby Shedden*
Affiliation:
Department of Statistics, University of Michigan
Robert A. Zucker
Affiliation:
Departments of Psychiatry and Psychology, University of Michigan
*
Requests for reprints should be sent to Kerby Shedden, Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1107, USA. E-mail: [email protected]
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Abstract

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse.

Keywords

finite mixture modelsgrowth mixture modelslatent class analysisfunctional data analysispenalized likelihoodlongitudinal data analysistrajectory analysis
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 625 - 646
Copyright
Copyright © 2008 The Psychometric Society

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Footnotes

This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.

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