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.Comment: Draft version 1.6, 08/08/2020. This paper has not been peer reviewed.
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