Residual Diagnostics for Growth Mixture Models: Examining the Impact of a Preventive Intervention on Multiple Trajectories of Aggressive Behavior

• Activity Number: 51
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section*
• Author(s): Chen-Pin Wang*+
• Affiliation(s): University of South Florida
• Keywords: mixture modeling ; growth modeling ; pseudo class ; latent variable ; multiple imputation ; empirical Bayes

Abstract

This paper presents three graphical methods for diagnosing growth mixture models (GMM; see Muthen and Shedden, 1999; Muthen et al., in press). GMMs are built on a finite mixture of parametric trajectory classes with individuals' scores deviating around the mean of one such curve, where both the class membership and trajectory are allowed to be predicted by covariates. The proposed methods are aimed at detecting misspecification in GMM regarding growth trajectory, covariance structure, and the number of classes. We adopt the pseudo class technique (Bandeen-Roche et al., 1997) to impute class membership for individuals in the sample, and then for each pseudo class, form diagnostic plots based on the empirical Bayes residuals at both level one and level two of the GMM hierarchy. In particular, we suggest using multiple imputation of growth class to enhance the clarity of the diagnostics. These methods are tested with simulation studies involving two classes of linear growths, each having a distinct covariance structure. They are then applied to longitudinal data from a randomized field intervention trial on children's aggressive behavior.