Bendler Jasper, Reinecke Jost
Faculty of Law, University of Münster, Bispinghof 24/25, 48143, Münster, Germany.
Faculty of Sociology, University of Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany.
Behav Res Methods. 2025 Mar 10;57(4):112. doi: 10.3758/s13428-025-02624-3.
Moderation effects in longitudinal structural equation models are often analysed using latent variable product terms, which can be complex and difficult to estimate, especially in large models with many panel waves. An alternative approach for categorical moderation variables is the simpler technique of multiple-group comparisons. This method allows for straightforward model specification and precise differentiation of effects in complex models. This tutorial demonstrates multiple-group comparisons using examples based on developmental trajectories of juvenile delinquency. These trajectories are modelled via a latent growth curve approach, treating the variables as count data and applying Bayesian estimation using the software Mplus. The results are processed using the R programming language. This method addresses challenges associated with maximum likelihood estimation, particularly for latent growth models with count variables and additional exogenous latent variables. The analysis examines group differences by gender and school type in the trajectories of an unconditional growth model. It also examines the effect of legal norm acceptance on these trajectories using a conditional growth model. The moderating effects of gender and school type on these effects are analysed separately. The results reveal group differences of gender and school type for the unconditional growth model, while the conditional growth model highlights a moderating effect of school type on the relationship between legal norm acceptance and growth trajectories.
纵向结构方程模型中的调节效应通常使用潜在变量乘积项进行分析，这可能很复杂且难以估计，尤其是在具有多个面板波的大型模型中。对于分类调节变量，另一种方法是更简单的多组比较技术。这种方法允许在复杂模型中进行直接的模型设定和精确的效应区分。本教程使用基于青少年犯罪发展轨迹的示例演示多组比较。这些轨迹通过潜在增长曲线方法进行建模，将变量视为计数数据，并使用Mplus软件应用贝叶斯估计。结果使用R编程语言进行处理。该方法解决了与最大似然估计相关的挑战，特别是对于具有计数变量和额外外生潜在变量的潜在增长模型。分析考察了无条件增长模型轨迹中按性别和学校类型划分的组间差异。它还使用条件增长模型考察了法律规范接受对这些轨迹的影响。分别分析了性别和学校类型对这些效应的调节作用。结果揭示了无条件增长模型中性别和学校类型的组间差异，而条件增长模型则突出了学校类型对法律规范接受与增长轨迹之间关系的调节作用。
