In analyzing longitudinal data with growth curve models, a critical assumption is that changes in the observed measures reflect construct changes and not changes in the manifestation of the construct over time. However, growth curve models are often fit to a repeated measure constructed as a sum or mean of scale items, making an implicit assumption of constancy of measurement. This practice risks confounding actual construct change with changes in measurement (i.e., differential item functioning [DIF]), threatening the validity of conclusions. An improved method that avoids such confounding is the second-order growth curve (SGC) model. It specifies a measurement model at each occasion of measurement that can be evaluated for invariance over time. The applicability of the SGC model is hindered by key limitations: (a) the SGC model treats time as continuous when modeling construct growth but as discrete when modeling measurement, reducing interpretability and parsimony; (b) the evaluation of DIF becomes increasingly error-prone given multiple timepoints and groups; (c) DIF associated with continuous covariates is difficult to incorporate. Drawing on moderated nonlinear factor analysis, we propose an alternative approach that provides a parsimonious framework for including many time points and DIF from different types of covariates. We implement this model through Bayesian estimation, allowing for incorporation of regularizing priors to facilitate efficient evaluation of DIF. We demonstrate a two-step workflow of measurement evaluation and growth modeling, with an empirical example examining changes in adolescent delinquency over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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在构建测量的潜在变化中建模构建随时间的变化：纵向调节因子分析方法。


在使用增长曲线模型分析纵向数据时，一个关键假设是观察到的测量值的变化反映了构建的变化，而不是构建随时间的表现的变化。然而，增长曲线模型通常适合于构建为规模项目的总和或平均值的重复测量，从而隐含地假设了测量的稳定性。这种做法存在混淆实际结构变化与测量变化（即差异项目功能[DIF]）的风险，从而威胁结论的有效性。避免这种混淆的一种改进方法是二阶增长曲线（SGC）模型。它指定了每次测量时的测量模型，可以评估该模型随时间的不变性。 SGC 模型的适用性受到以下关键限制的阻碍：（a）SGC 模型在建模构建增长时将时间视为连续的，但在建模测量时将时间视为离散的，从而降低了可解释性和简约性； (b) 考虑到多个时间点和组，DIF 的评估变得越来越容易出错； (c) 与连续协变量相关的 DIF 很难合并。利用调节非线性因子分析，我们提出了一种替代方法，该方法提供了一个简洁的框架，用于包含来自不同类型协变量的许多时间点和 DIF。我们通过贝叶斯估计实现该模型，允许合并正则化先验以促进 DIF 的有效评估。我们展示了测量评估和成长建模的两步工作流程，并通过一个实证例子来检验青少年犯罪随时间的变化。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。