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 Bakk and Kuha (2017), 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.
翻译:实验性研究人员通常有兴趣调查基准共变模型在发现样本异质和将样本分解成更同质的组别时产生的影响,但结构方程模型(SEM)框架的大量研究通常在结构方程模型(SEM)框架的异质和可能的原因方面以模糊的假设开始,这表明(1) 确定和具体确定一个适当的共变模型并非直截了当,(2) 探索过程可能是计算密集型的,因为SEM框架中的一个模型通常很复杂,候选共变变量库通常在广泛采用SEM框架的心理和教育领域非常庞大。在Bakk和Kuha(2017年)之后,这一文章提出了一个两步增长混合模型(GMMM),该模型从研究非线性轨迹和基线特征的潜在类别之间的关系。我们的模拟研究表明,拟议的模型能够将非线性变化模式组合在一起,并且准确地估计利息参数,同时展示适当的信任间隔范围。考虑到候选的共变异源库通常巨大且高度相关联。在BEM框架(2017年)之后,本研究报告还提出了一个两步发展混合混合的混合模型模型模型模型模型,该模型用来研究非线性分析非线性地分析非线性、我们探索性地利用GMFIFIFIFIFAL方法。