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

Chen Pin Wang, C. Hendricks Brown, Karen Bandeen-Roche

Research output: Contribution to journalArticle

110 Citations (Scopus)

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. These are then applied to longitudinal data from a randomized field trial that tests whether children's trajectories of aggressive behavior could be modified during elementary and middle school. Our diagnostics lead to a solution involving a mixture of three growth classes. When comparing the diagnostics obtained from multiple pseudoclasses with those from multiple imputations, we show the computational advantage of the former and obtain a criterion for determining the minimum number of pseudoclass draws.

Original languageEnglish
Pages (from-to)1054-1076
Number of pages23
JournalJournal of the American Statistical Association
Volume100
Issue number471
DOIs
StatePublished - Sep 1 2005

Fingerprint

Growth Model
Mixture Model
Diagnostics
Trajectory
Covariance Structure
Diagnostic Plot
Mixture Modeling
Growth Curve
Multiple Imputation
Model Misspecification
Empirical Bayes
Misspecification
Empirical Distribution
Longitudinal Data
Independent Set
Quantify
Class
Mixture model
Simulation Study

Keywords

  • Empirical Bayes
  • Growth mixture modeling
  • Latent variables
  • Marginal maximum likelihood
  • Preventive intervention
  • Pseudoclass

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Residual diagnostics for growth mixture models : Examining the impact of a preventive intervention on multiple trajectories of aggressive behavior. / Wang, Chen Pin; Brown, C. Hendricks; Bandeen-Roche, Karen.

In: Journal of the American Statistical Association, Vol. 100, No. 471, 01.09.2005, p. 1054-1076.

Research output: Contribution to journalArticle

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