Class enumeration false positive in skew-t family of continuous growth mixture models

Abstract

Growth Mixture Modeling (GMM) has gained great popularity in the last decades as a methodology for longitudinal data analysis. The usual assumption of normally distributed repeated measures has been shown as problematic in real-life data applications. Namely, performing normal GMM on data that is even slightly skewed can lead to an over selection of the number of latent classes. In order to ameliorate this unwanted result, GMM based on the skew t family of continuous distributions has been proposed. This family of distributions includes the normal, skew normal, t, and skew t. This simulation study aims to determine the efficiency of selecting the "true" number of latent groups in GMM based on the skew t family of continuous distributions, using fit indices and likelihood ratio tests. Results show that the skew t GMM was the only model considered that showed fit indices and LRT false positive rates under the 0.05 cutoff value across sample sizes and for normal, and skewed and kurtic data. Simulation results are corroborated by a real educational data application example. These findings favor the development of practical guides of the benefits and risks of using the GMM based on this family of distributions.

A Monte Carlo evaluation of growth mixture modeling

“…This suggests that under conditions that are common in psychopathology research, GMM may impose structure rather than identifying existing latent subgroups. These findings suggest that recent efforts to develop GMM in ways that reduce effects of nonnormality, such as those using skew t family distributions (Guerra-Peña et al, 2020; Muthén & Asparouhov, 2015), should continue.…”

“…Even then, however, a similar distribution drawn from the same population may yield similar findings (Hoeksma & Kelderman, 2006). Although newer approaches to GMM that use the skew t family of distributions show promise toward addressing over-extraction from nonnormal data (Guerra-Peña, García-Batista, Depaoli, & Garrido, 2020; Muthén & Asparouhov, 2015), their use is limited to date. Here, we focus on GMM as typically applied in the literature (see above).…”

“…It provides a summary measure of the probability of membership for each individual for the class to which the individual most likely belongs (Connell & Frye, 2006). Given limitations of GMM and inconsistencies in the literature described above, and given relatively few simulation studies to date (Bauer & Curran, 2003a; Chen, Kwok, Luo, & Willson, 2010; Grimm, Ram, Shiyko, & Lo, 2014; Guerra-Peña et al, 2020; Hoeksma & Kelderman, 2006; Kim, 2012; Nylund et al, Peugh & Fan, 2012), we performed a Monte Carlo evaluation to determine when GMM captures latent structure effectively, and when it might not. We evaluate GMM as it is typically applied in psychopathology research, using more simulations than reported to date.…”

Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

“…In Depaoli et al (2019), the class enumeration was greatly influenced by the degree of latent class separation when the underlying population consisted of heterogenous subgroups. In Guerra-Peña et al (2020), the growth mixture modeling with skewed-t successfully maintained the Type 1 error rate when the underlying population was homogeneous but had a skewed or kurtic distribution.…”

“…The performance of the model comparison criteria varied, but they appeared to be influenced by a number of factors, especially the complexity of trajectory shapes and the magnitude of separations of latent classes. Depaoli et al (2019) and Guerra-Peña et al (2020) used Student's t, skewedt, and skewed-normal distributions on latent factors and explored class enumeration when data satisfied or violated the normality assumption. In Depaoli et al (2019), the class enumeration was greatly influenced by the degree of latent class separation when the underlying population consisted of heterogenous subgroups.…”