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

Abstract

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). (PsycINFO Database Record

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“…As Muthén (2001) suggests, the relative strength of LMR and BIC is not sufficiently well-understood though several recent studies do caution that LMR does not always function as a reliable indicator for deciding optimal solution (Diallo, Morin, & Lu, 2016a; 2016b). Accordingly, the decision on the number of classes should not be based solely on statistical measures but also on theoretical justification and interpretability.…”

“…Fourth, given that the growth mixture modeling analysis procedure used in this study is newly developed, it is quite common that different modeling-fitting indices or statistical tests may not support the same decision as indicated in many studies (e.g., Diallo, Morin, & Lu, 2016b; Marsh et al, 2009). While there are no agreed-upon criteria for facilitating decisions about the number of classes in growth mixture modeling, future research should investigate whether our findings can be replicated across multiple studies (Nylund et al, 2007).…”

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“…All model fit indicators are reported here for clarity, though only the CAIC, BIC, ABIC, and BLRT were used to decide upon the optimal number of classes. Simulation work (Diallo et al, 2016) suggests that the ABIC and BLRT are preferred when entropy is lower (closer to .50), and the BIC and CAIC preferred when entropy levels are higher (closer to .90). Sample size is another important consideration for selecting the final model, because with a sufficiently large sample size the observed indicators may carry on suggesting the addition of more classes without reaching a minimum .…”

“…Finally, entropy is an indicator of model precision with regard to classifying individuals into their most likely classes. Scores range from 0 to 1 with a higher value representing greater accuracy (Diallo, Morin, & Lu, 2016).…”

“…Simulation work has found four statistical indicators (CAIC, BIC, ABIC, and BLRT) to be most informative in identifying the correct number of classes (Nylund, Asparouhov, & Muth en, 2007;Peugh & Fan, 2013;Tofighi & Enders, 2008). Conversely, the AIC, LMR, and aLMR are suboptimal for informing decisions regarding the number of classes because they tend to support the extraction of the incorrect number of classes (Diallo et al, 2016;Nylund et al, 2007;Peugh & Fan, 2013). All model fit indicators are reported here for clarity, though only the CAIC, BIC, ABIC, and BLRT were used to decide upon the optimal number of classes.…”