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

Kiero Guerra-Peña,Sarah Depaoli,Zoilo Emilio García-Batista,Luis Eduardo Garrido,Alan D Hutson

doi:10.1371/journal.pone.0231525

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.

Highlights

Growth Mixture Modeling (GMM) has gained great popularity in the social sciences as a group of longitudinal data modeling techniques for the selection of the number of latent trajectory classes, and the estimation of the specific relation between these classes and level 1 or level 2 covariates [1,2,3,4,5]
In the same way as fit indices were presented in the left-hand side of these same tables, these tables show the proportion of times likelihood ratios test (LRT) selected the model with the “false” 2-class solution within the particular skew t family GMM, and across distributions of the simulated data and sample sizes
VLMR-LRT and LMR-adjusted LRT type I error rates are presented for all members of the skew t family GMM

Summary

Introduction

Growth Mixture Modeling (GMM) has gained great popularity in the social sciences as a group of longitudinal data modeling techniques for the selection of the number of latent trajectory classes, and the estimation of the specific relation between these classes and level 1 or level 2 covariates [1,2,3,4,5]. These trajectories, or growth curves, could be interpreted as substantively different groups of patients suffering from major depression according to their response to antidepressants [6], adolescents’ developmental trajectories of Anxiety [7], groups with quantitatively different alcohol use trajectories [8], or different clinical groups of alcohol abuse patients [9].

Objectives

Methods

Results

Conclusion