The Performance of Multilevel Growth Mixture Models With Between-Group Mixture for Identifying Between-Group Latent Classes

• In Event: Recent Developments in Multiple-Group, Multilevel, and Longitudinal Mixture Modeling

Abstract

Multilevel growth mixture models with between-group mixture (MGMM-B; Palardy &Vermunt, 2010) are a recently developed modeling technique that can be used to classify individuals in terms of their distinct growth patterns as well as classifying groups they are nested in based on the average within-group growth trajectories. The MGMM-B provides researchers with new and innovative insights on complex research questions at the cluster level. However, the use of MGMM to capture cluster effects and accurately identify organization-level latent classes has not yet been systematically investigated. Palardy and Vermunt (2010) raised two critical issues regarding MGMM specification: The first one is the inclusion of random effects at a higher-level, which could increase model analytic complexity and impact the interpretation of the results given the latent classes and random effects compete to account for the heterogeneity of growth trajectories. The second issue is how to use covariates in MGMM, which could change the distribution of random effects and thereby alter the number of classes that are identified. Ignoring or incorrectly modeling covariates effects may impact class enumeration and within-class parameter estimates.

Purpose statement
This study will address the following research questions:
1) Under which conditions model selection indices and statistics can effectively identify the between-group classes in MGMM-B?
2) What is the effect of omission, total or partial inclusion of covariates, and misspecification of covariate effects on between-group class enumeration in MGMM-B?
Methods
A Monte Carlo simulation study was employed to answer the research questions stated above. To examine the effects of covariate specification on MGMM-B class enumeration, two scenarios with different population models are considered: Scenario 1: a MGMM-B model with a between-group covariate predicting latent class membership only; Scenario 2: a MGMM-B model with a between-group covariate predicting both latent class membership and growth factors. In each scenario, we compare the efficacy of multiple model selection indices for class enumeration for the following manipulated conditions: number of clusters, cluster size, ICC, covariate effect, class separation and analysis models with different covariate specification, as shown in Table 1. Manipulated conditions and their levels were defined based on a review of empirical and methodology literature about GMM and multilevel mixture modeling (e.g., Tofighi & Enders, 2008; Hu, Leite & Gao, 2017; Diallo, Morin &Lu, 2017; Chen et al., 2017 Lukočienė & Vermunt, 2009; Park & Yu 2017; Li & Harring, 2016).
For each simulated dataset, we will fit MGMM-B without covariates and with covariates. Class enumeration will be examined using multiple model selection indices and likelihood ratio tests. We will compare two versions of BIC and CAIC: BIC-W and CAIC-W defined N using the total sample size, and BIC-B and CAIC-B considered N as the number of group. We will also evaluate the Akaike Information Criterion (AIC), the Vuong-Mendell-Rubin Likelihood Ratio Test (VMR) and the Bootstrapped Likelihood Ratio Test (BLR).

Authors

• Yu Su, University of Florida

• Walter L. Leite, University of Florida