Class Enumeration and Parameter Recovery of Growth Mixture Modeling and Second-Order Growth Mixture Modeling in the Presence of Measurement Noninvariance between Latent Classes.

Eun Sook Kim,Yan Wang

doi:10.3389/fpsyg.2017.01499

Abstract

Population heterogeneity in growth trajectories can be detected with growth mixture modeling (GMM). It is common that researchers compute composite scores of repeated measures and use them as multiple indicators of growth factors (baseline performance and growth) assuming measurement invariance between latent classes. Considering that the assumption of measurement invariance does not always hold, we investigate the impact of measurement noninvariance on class enumeration and parameter recovery in GMM through a Monte Carlo simulation study (Study 1). In Study 2, we examine the class enumeration and parameter recovery of the second-order growth mixture modeling (SOGMM) that incorporates measurement models at the first order level. Thus, SOGMM estimates growth trajectory parameters with reliable sources of variance, that is, common factor variance of repeated measures and allows heterogeneity in measurement parameters between latent classes. The class enumeration rates are examined with information criteria such as AIC, BIC, sample-size adjusted BIC, and hierarchical BIC under various simulation conditions. The results of Study 1 showed that the parameter estimates of baseline performance and growth factor means were biased to the degree of measurement noninvariance even when the correct number of latent classes was extracted. In Study 2, the class enumeration accuracy of SOGMM depended on information criteria, class separation, and sample size. The estimates of baseline performance and growth factor mean differences between classes were generally unbiased but the size of measurement noninvariance was underestimated. Overall, SOGMM is advantageous in that it yields unbiased estimates of growth trajectory parameters and more accurate class enumeration compared to GMM by incorporating measurement models.

Highlights

In educational and psychological research the change or growth in temporal outcomes is one of the major research questions (e.g., Muthén et al, 2000; Li et al, 2001; Miner and Clarke-Stewart, 2008)
Because the impact of measurement noninvariance on the performance of growth mixture modeling (GMM) was of focal interest in this study, the following factors were fixed as a constant for simplicity of discussions: two latent classes, four occasions, six items that load on a single factor at each occasion, and two noninvariant items, which were commonly adopted in previous simulation studies (e.g., Nylund et al, 2007; Chen et al, 2010; Kim and Willson, 2014a)
When there was measurement noninvariance between unknown groups, we investigated the impact of the ignored noninvariance on the performance of GMM, the accuracy of class enumeration and the parameter recovery

Summary

Introduction

In educational and psychological research the change or growth in temporal outcomes (e.g., alcohol use, depression, antisocial behavior, reading skills over time) is one of the major research questions (e.g., Muthén et al, 2000; Li et al, 2001; Miner and Clarke-Stewart, 2008). One of the major assumptions of GMM is measurement invariance of longitudinal outcomes across latent classes that emerge from the data (Grimm and Ram, 2009). It is not known how the violation of the measurement invariance assumption impacts the performance of GMM. This study investigated the behaviors of GMM under the violation of measurement invariance across latent classes. We proposed the second-order growth mixture modeling (SOGMM) that allows modeling and testing measurement invariance explicitly across latent classes in the growth mixture analysis

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