Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, BC, V6T1Z4, Canada.
Behav Res Methods. 2024 Apr;56(4):3023-3057. doi: 10.3758/s13428-023-02238-7. Epub 2023 Nov 22.
In psychology and other fields, data often have a cross-classified structure, whereby observations are nested within multiple types of non-hierarchical clusters (e.g., repeated measures cross-classified by persons and stimuli). This paper discusses ways that, in cross-classified multilevel models, slopes of lower-level predictors can implicitly reflect an ambiguous blend of multiple effects (for instance, a purely observation-level effect as well as a unique between-cluster effect for each type of cluster). The possibility of conflating multiple effects of lower-level predictors is well recognized for non-cross-classified multilevel models, but has not been fully discussed or clarified for cross-classified contexts. Consequently, in published cross-classified modeling applications, this possibility is almost always ignored, and researchers routinely specify models that conflate multiple effects. In this paper, we show why this common practice can be problematic, and show how to disaggregate level-specific effects in cross-classified models. We provide a novel suite of options that include fully cluster-mean-centered, partially cluster-mean-centered, and contextual effect models, each of which provides a unique interpretation of model parameters. We further clarify how to avoid both fixed and random conflation, the latter of which is widely misunderstood even in non-cross-classified models. We provide simulation results showing the possible deleterious impact of such conflation in cross-classified models, and walk through pedagogical examples to illustrate the disaggregation of level-specific effects. We conclude by considering additional model complexities that can arise with cross-classification, providing guidance for researchers in choosing among model specifications, and describing newly available software to aid researchers who wish to disaggregate effects in practice.
在心理学和其他领域，数据通常具有交叉分类结构，即观察结果嵌套在多种非层次聚类中（例如，按人 员和刺激重复测量交叉分类）。本文讨论了在交叉分类多层次模型中，较低层次预测器的斜率如何隐含地反映多种效 应的模糊混合（例如，纯粹的观察水平效应以及每种类型聚类的独特的聚类间效应）。对于非交叉分类多层次 模型，已经充分认识到混淆较低层次预测器的多个效应的可能性，但对于交叉分类情况尚未进行充分讨论或澄清。 因此，在已发表的交叉分类建模应用中，这种可能性几乎总是被忽略，并且研究人员通常指定混淆多个效应的模型。 在本文中，我们展示了为什么这种常见做法可能存在问题，并展示了如何在交叉分类模型中分解特定于水平的效应。 我们提供了一套新颖的选项，包括完全聚类均值中心化、部分聚类均值中心化和上下文效应模型，每个模型都提供了 模型参数的独特解释。我们进一步澄清了如何避免固定和随机混淆，即使在非交叉分类模型中，后者也被广泛误解。 我们提供了模拟结果，显示了这种混淆在交叉分类模型中可能产生的有害影响，并通过教学示例说明如何分解特定于 水平的效应。最后，我们考虑了与交叉分类相关的其他模型复杂性，为研究人员在模型规范之间的选择提供了指导，并 描述了新的可用软件，以帮助希望在实践中分解效应的研究人员。
