ABSTRACT

Multilevel regression mixtures involving both discrete latent classes and continuous random effects are an increasingly popular approach for accommodating nested data structures. However, their application has outpaced the development of effect size measures to aid model interpretation. In response, we provide a general framework of R-squared measures for multilevel regression mixtures with random effects as well as either classes only at level-1 (L1MIX), or classes only at level-2 (L2MIX), or classes at both levels (L1L2MIX). This work extends and unites a previous suite of R-squared measures for multilevel mixtures with latent classes but no random effects (Rights & Sterba, 2018) and a suite of R-squared measures for multilevel models with random effects but no latent classes (Rights & Sterba, 2019).The general framework provided here includes total and class-specific measures that each allow the researcher to distinguish among distinct sources of explained variance in the fitted model. We provide software for implementing these measures and provide two illustrative empirical examples.

摘要

涉及离散潜在类和连续随机效应的多级回归混合是一种越来越流行的适应嵌套数据结构的方法。然而，它们的应用已经超过了帮助模型解释的效应量测量的发展。作为回应，我们为具有随机效应的多级回归混合以及仅在级别 1 的类 (L1MIX) 或仅在级别 2 的类 (L2MIX) 或两个级别的类提供了 R 平方度量的通用框架（L1L2MIX）。这项工作扩展并统一了以前的一套 R 平方度量，用于具有潜在类别但没有随机效应的多级混合 (Rights & Sterba, 2018)，以及一套针对具有随机效应但没有潜在类别的多级模型的 R 平方度量 (Rights和斯特巴，2019）。这里提供的一般框架包括总体和特定类别的措施，每个措施都允许研究人员区分拟合模型中解释方差的不同来源。我们提供了用于实施这些措施的软件，并提供了两个说明性的经验示例。