Growth mixture modeling

Analysis with non-Gaussian random effects

Authored by: Muthén Bengt , Asparouhov Tihomir

Longitudinal Data Analysis

Print publication date:  August  2008
Online publication date:  August  2008

Print ISBN: 9781584886587
eBook ISBN: 9781420011579
Adobe ISBN:


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This chapter gives an overview of non-Gaussian random-effects modeling in the context of finite-mixture growth modeling developed in Muthén and Shedden (1999), Muthén (2001a, 2001b, 2004), and Muthén et al. (2002), and extended to cluster samples and cluster-level mixtures in Asparouhov and Muthén (2008). Growth mixture modeling represents unobserved heterogeneity between the subjects in their development using both random effects (e.g., Laird and Ware, 1982) and finite mixtures (e.g., McLachlan and Peel, 2000). This allows different sets of parameter values for mixture components corresponding to different unobserved subgroups of individuals, capturing latent trajectory classes with different growth curve shapes. This chapter discusses examples motivating modeling with such trajectory classes. A general latent-variable modeling framework is presented together with its maximum likelihood estimation. Examples from criminology, mental health, and education are analyzed. The choice of a normal or a non-parametric distribution for the random effects is discussed and investigated using a simulation study. The discussion will refer to growth mixture modeling techniques as implemented in the Mplus program (Muthén and Muthén, 19982007) and input scripts for the analyses are available at

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