Residual Diagnostics for Growth Mixture Models

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Abstract
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 asymptotically normal with known mean and (co)variance when the underlying model is correct. These methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures....