Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors

Abstract

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.

Students’ Motivational Profiles in the Physical Education Context

“…First, it is important to keep in mind that a key limitation of mixture models (including LPA) is the reliance on the assumption that all extracted profiles follow multivariate normal distributions (McLachlan & Peel, 2000). Violation of this assumption, which is impossible to test in practice, could possibly result in the extraction of spurious latent profiles (Bauer & Curran, 2003;Guerra-Peña, & Steinley, 2016;Sen, Cohen, & Kim, 2016). As new methods emerge to test this assumption or to estimate mixture models without relying on this assumption (e.g., , emerging person-centered evidence will likely need to be reassessed.…”

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

“…The authors considered skewness and kurtosis values of 1 on the repeated measures and found that BLRT performed best among likelihood ratio tests and fit indices, except for the BIC and SBIC. Guerra-Peña and Steinley [14] showed that the BLRT performs better than other LRT for both normal and nonnormal repeated measures. Nevertheless, even in normal conditions, type I error rates where 5% or higher, becoming worse as sample size increases (e.g., N = 800) and the ratio of kurtosis to skewness becomes larger (e.g., skewness of 0 and kurtosis of 4).…”

“…Concerning the use of fit indices in the selection of the number of latent classes, the Akaike information criterion (AIC) overestimates the number of latent components even when the repeated measures are normally distributed [26][27][28], and when the data are nonnormal [10][11][12]14]. The Bayesian information criterion (BIC) underestimates the number of groups compared to the "true" model when sample size is small [27,29], overestimates the number of latent classes with nonnormal data and large sample sizes [14], and both the BIC and the sample corrected BIC (SBIC) overestimate the number of latent classes when the model has been misspecified [12] or the data are nonnormal [10][11][12]14]. Moreover, fit indices can distinguish between classes with different trajectories only if they are well separated and as sample size increases [29].…”

“…For this purpose, normal and nonnormal data were simulated and analyzed. Nonnormal conditions of the data not considered previously in the literature are used [10,14,34,35,45,46].…”

“…The normality assumption is of special interest since real world data in social sciences is rarely normal [13]. Moreover, Guerra-Peña and Steinley [14] point out the limitations of using fit indices and LRT to correctly select the number of latent trajectory classes in normal GMM, even when the skewness and/or kurtosis are only present in the covariates and not the repeated measures. In order to deal with this issue, continuous nonnormal skewed distributions have been developed [15] and extended onto GMM [16].…”