Impact of Misspecifications of the Latent Variance–Covariance and Residual Matrices on the Class Enumeration Accuracy of Growth Mixture Models

Abstract

This series of simulation studies was designed to assess the impact of misspecifications of the latent variance–covariance matrix (i.e., ) and residual structure (i.e., ) on the accuracy of growth mixture models (GMMs) to identify the true number of latent classes present in the data. Study 1 relied on a homogenous (1-class) population model. Study 2 relied on a population model in which the latent variance–covariance matrix is constrained to be 0 Study 3 relied on a population model in which the latent variance–covariance matrix was specified as invariant across classes Finally, Study 4 relied on a more realistic specification of the latent variance–covariance matrix as different across classes In each of these studies, we assessed the class enumeration accuracy of GMMs as a function of different types of estimated model (6 models corresponding to the 3 types of population models used to simulate the data and involving the free estimation of the residual structure across latent classes or not) and 4 design conditions (within-class residual matrix, sample size, mixing ratio, class separation). Overall, our results show the advantage of relying on models involving the free estimation of the and matrices within all latent classes. However, based on the observation that inadmissible solutions occur more frequently in these models than in more parsimonious models, we propose a more comprehensive sequential strategy to the estimation of GMM.

Keywords:

• accuracy
• class enumeration
• growth mixture
• latent class growth analysis
• latent variance–covariance
• misspecification
• residual

Notes

¹ Inadmissible solutions include nonconvergent solutions and improper solutions. Following the standard practice in mixture modeling simulation studies (e.g., Bauer & Curran, 2003; McLachlan & Peel, 2000) a replication was labeled nonconvergent when that replication failed to converge on a solution with any of the sets of the starting values that were used. A convergent solution was labeled improper when it included out-of-bound parameter estimates (i.e., negative variances, correlations greater than 1 or smaller than –1). Because inadmissible solutions are rarely interpreted (Chen, Bollen, Paxton, Curran, & Kirby, 2001) they were excluded from the results reported here.