Residual diagnostics for growth mixture models: examining the impact of a preventive intervention on multiple trajectories of aggressive behavior.

Journal of the American Statistical Association, September, 2005 by Bandeen-Roche, Karen; Brown, C. Hendricks; Wang, Chen-Pin

Growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population. In this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes, growth trajectory means, and covariance structures. For each model misspecification, we propose a different type of empirical Bayes residual to quantify the departure. Our procedure begins by imputing multiple independent sets of growth classes for the sample. Then, from these so-called "pseudoclass" draws, we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class. Our proposals draw on the property that each single set of pseudoclass adjusted residuals is...

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