Longitudinal research is often interested in identifying correlates of heterogeneity in change. This paper compares three approaches for doing so: the mixed‐effects model (latent growth curve model), the growth mixture model, and structural equation model trees. Each method is described, with special focus given to how each structures heterogeneity, attributes that heterogeneity to covariates, and the kinds of research questions each can be used to address. Each approach is used to analyze data from the National Longitudinal Survey of Youth to understand the similarities and differences between methods in the context of empirical data. Specifically, changes in weight across adolescence are examined, as well as how differences in these change patterns can be explained by sex, race, and mother's education. Recommendations are provided for how to select which approach is most appropriate for analyzing one's own data.

中文翻译：

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确定变化异质性相关性的三种方法的比较

纵向研究通常对确定变化异质性的相关性感兴趣。本文比较了三种方法：混合效应模型（潜在增长曲线模型）、增长混合模型和结构方程模型树。描述了每种方法，特别关注每种方法如何构建异质性，将异质性归因于协变量，以及每种方法可用于解决的研究问题类型。每种方法都用于分析来自全国青年纵向调查的数据，以了解经验数据背景下方法之间的异同。具体来说，研究了整个青春期的体重变化，以及如何通过性别、种族和母亲的教育来解释这些变化模式的差异。