Facilitating Growth Mixture Model Convergence in Preventive Interventions

Abstract

Growth mixture models (GMMs) are applied to intervention studies with repeated measures to explore heterogeneity in the intervention effect. However, traditional GMMs are known to be difficult to estimate, especially at sample sizes common in single-center interventions. Common strategies to coerce GMMs to converge involve post hoc adjustments to the model, particularly constraining covariance parameters to equality across classes. Methodological studies have shown that although convergence is improved with post hoc adjustments, they embed additional tenuous assumptions into the model that can adversely impact key aspects of the model such as number of classes extracted and the estimated growth trajectories in each class. To facilitate convergence without post hoc adjustments, this paper reviews the recent literature on covariance pattern mixture models, which approach GMMs from a marginal modeling tradition rather than the random effect modeling tradition used by traditional GMMs. We discuss how the marginal modeling tradition can avoid complexities in estimation encountered by GMMs that feature random effects, and we use data from a lifestyle intervention for increasing insulin sensitivity (a risk factor for type 2 diabetes) among 90 Latino adolescents with obesity to demonstrate our point. Specifically, GMMs featuring random effects-even with post hoc adjustments-fail to converge due to estimation errors, whereas covariance pattern mixture models following the marginal model tradition encounter no issues with estimation while maintaining the ability to answer all the research questions.

Keywords: Covariance pattern mixture model; Group based trajectory modeling; Growth mixture modeling; Insulin sensativity; Pediatric diabetes; Small sample.

Fig. 1

Plot of empirical insulin sensitivity data over time for full data (N = 90; top panel) and the data with potential outliers removed (N = 85; bottom panel)

Fig. 2

Plot of class-specific growth trajectories for 3-class solution of CPGMM from full data (N = 90; top panel) and from the data with outliers removed (N = 85; bottom panel)

Fig. 3

Class-specific growth trajectories plotted against the empirical data of people assigned to each class for full data (N = 90; top panel) and data with outliers removed (N = 85; bottom panel)