School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada.
Department of Statistics, University of Haifa, Haifa, Israel.
Br J Math Stat Psychol. 2023 Feb;76(1):1-19. doi: 10.1111/bmsp.12285. Epub 2022 Sep 8.
In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631).
在许多心理学研究中，特别是那些通过经验采样进行的研究中，对每个参与者的心理状态进行了多次重复测量。这种设计允许回归模型将两个变量之间的关联分为个体间和个体内，或特质和状态成分。但这些模型通常是为连续变量设计的，而心理状态变量通常是在有序量表上进行测量的。在本文中，我们开发了一种模型，用于将一个有序变量对另一个变量的个体间和个体内效应进行分解。与标准有序回归一样，我们的模型假设了一个连续的潜在反应，其值决定了观察到的反应。我们允许潜在的反应与特质和状态变量非线性相关，但施加了一个新颖的惩罚，该惩罚将潜在尺度上的拟合向线性模型收缩。一项模拟研究表明，这种惩罚方法在找到过于严格的线性模型和过度拟合的非线性模型之间的中间立场是有效的。该方法通过对 Baumeister 等人（2020 年，《人格与社会心理学公报》，46，1631）的经验采样研究数据的应用进行了说明。
