[Paper Review] Hybridizing two-step growth mixture model and exploratory factor analysis to examine heterogeneity in nonlinear trajectories

Jin Liu, Robert A. Perera+3 more|arXiv (Cornell University)|Nov 22, 2019

Mental Health Research Topics4 citations

TL;DR

This paper proposes a hybrid two-step method combining growth mixture modeling (GMM) and exploratory factor analysis (EFA) to identify nonlinear trajectory classes in longitudinal data and uncover their relationships with baseline covariates. By applying EFA to reduce high-dimensional, correlated covariates before GMM, the approach improves computational efficiency and model accuracy in detecting heterogeneous growth patterns in educational and psychological research.

ABSTRACT

Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the structural equation modeling (SEM) framework usually start with vague hypotheses in terms of heterogeneity and possible reasons. It suggests that (1) the determination and specification of a proper model with covariates is not straightforward, and (2) the exploration process may be computational intensive given that a model in the SEM framework is usually complicated and the pool of candidate covariates is usually huge in the psychological and educational domain where the SEM framework is widely employed. Following \citet{Bakk2017two}, this article presents a two-step growth mixture model (GMM) that examines the relationship between latent classes of nonlinear trajectories and baseline characteristics. Our simulation studies demonstrate that the proposed model is capable of clustering the nonlinear change patterns, and estimating the parameters of interest unbiasedly, precisely, as well as exhibiting appropriate confidence interval coverage. Considering the pool of candidate covariates is usually huge and highly correlated, this study also proposes implementing exploratory factor analysis (EFA) to reduce the dimension of covariate space. We illustrate how to use the hybrid method, the two-step GMM and EFA, to efficiently explore the heterogeneity of nonlinear trajectories of longitudinal mathematics achievement data.

Motivation & Objective

• To address the challenge of identifying heterogeneous nonlinear growth trajectories in longitudinal data when baseline covariates are numerous and highly correlated.
• To improve model specification and reduce computational burden in structural equation modeling (SEM) frameworks where model selection is complex and hypothesis-driven assumptions are often vague.
• To develop a systematic, data-driven method for exploring covariate effects on latent trajectory classes without relying on pre-specified models.
• To enhance the accuracy and precision of parameter estimation in growth mixture models under realistic conditions of high-dimensional covariate spaces.
• To demonstrate the utility of the hybrid method in real-world educational data, particularly in longitudinal mathematics achievement studies.

Proposed method

• Applying a two-step approach: first, conducting exploratory factor analysis (EFA) on a large pool of baseline covariates to reduce dimensionality and extract underlying latent factors.
• Using the extracted EFA factors as predictors in a two-step growth mixture model (GMM) to identify distinct nonlinear trajectory classes.
• In the first step, EFA is used to transform a high-dimensional, correlated set of covariates into a smaller set of uncorrelated latent factors that capture the main sources of variation.
• In the second step, the GMM is estimated using the EFA-derived factors as covariates to predict class membership and model nonlinear growth patterns.
• The method ensures that model specification is data-driven and computationally efficient, avoiding the need to test all possible combinations of covariates.
• The approach is validated through simulation studies to assess parameter recovery, class enumeration accuracy, and confidence interval coverage.

Experimental results

Research questions

• RQ1 Can the hybrid two-step GMM-EFA method effectively identify distinct nonlinear trajectory classes in longitudinal data with high-dimensional covariates?
• RQ2 How well does the EFA step reduce dimensionality while preserving the predictive power of baseline covariates for class membership?
• RQ3 To what extent does the proposed method produce unbiased and precise parameter estimates in the presence of correlated and numerous covariates?
• RQ4 Does the method maintain appropriate confidence interval coverage for estimated parameters under realistic sample sizes and trajectory complexities?
• RQ5 How does the hybrid approach compare to traditional SEM-based methods in terms of computational efficiency and model fit when exploring heterogeneity in longitudinal educational data?

Key findings

• The proposed two-step GMM-EFA method successfully clusters nonlinear change patterns in longitudinal data with high accuracy.
• Parameter estimates for both trajectory growth parameters and covariate effects were found to be unbiased and precise in the simulation studies.
• The method demonstrated appropriate confidence interval coverage, indicating reliable inference for estimated parameters.
• Exploratory factor analysis effectively reduced the dimensionality of the covariate space, improving computational efficiency without sacrificing model fit or detection power.
• The hybrid approach outperformed traditional SEM-based methods in terms of computational feasibility when dealing with large, correlated covariate pools.
• The method was successfully applied to real longitudinal mathematics achievement data, revealing meaningful trajectory classes linked to baseline factors.