The impact of total and partial inclusion or exclusion of active and inactive time invariant covariates in growth mixture models

This article evaluates the impact of partial or total covariate inclusion or exclusion on the class enumeration performance of growth mixture models (GMMs). Study 1 examines the effect of including an inactive covariate when the population model is specified without covariates. Study 2 examines the case in which the population model is specified with 2 covariates influencing only the class membership. Study 3 examines a population model including 2 covariates influencing the class membership and the growth factors. In all studies, we contrast the accuracy of various indicators to correctly identify the number of latent classes as a function of different design conditions (sample size, mixing ratio, invariance or noninvariance of the variance-covariance matrix, class separation, and correlations between the covariates in Studies 2 and 3) and covariate specification (exclusion, partial or total inclusion as influencing class membership, partial or total inclusion as influencing class membership, and the growth factors in a class-invariant or class-varying manner). The accuracy of the indicators shows important variation across studies, indicators, design conditions, and specification of the covariates effects. However, the results suggest that the GMM class enumeration process should be conducted without covariates, and should rely mostly on the Bayesian information criterion (BIC) and consistent Akaike information criterion (CAIC) as the most reliable indicators under conditions of high class separation (as indicated by higher entropy), versus the sample size adjusted BIC or CAIC (SBIC, SCAIC) and bootstrapped likelihood ratio test (BLRT) under conditions of low class separation (indicated by lower entropy).