University of California, San Diego.
University of Washington.
Multivariate Behav Res. 2022 Mar-May;57(2-3):243-263. doi: 10.1080/00273171.2020.1868966. Epub 2021 Feb 1.
Psychology research frequently involves the study of probabilities and counts. These are typically analyzed using generalized linear models (GLMs), which can produce these quantities via nonlinear transformation of model parameters. Interactions are central within many research applications of these models. To date, typical practice in evaluating interactions for probabilities or counts extends directly from linear approaches, in which evidence of an interaction effect is supported by using the product term coefficient between variables of interest. However, unlike linear models, interaction effects in GLMs describing probabilities and counts are not equal to product terms between predictor variables. Instead, interactions may be functions of the predictors of a model, requiring nontraditional approaches for interpreting these effects accurately. Here, we define interactions as change in a marginal effect of one variable as a function of change in another variable, and describe the use of partial derivatives and discrete differences for quantifying these effects. Using guidelines and simulated examples, we then use these approaches to describe how interaction effects should be estimated and interpreted for GLMs on probability and count scales. We conclude with an example using the Adolescent Brain Cognitive Development Study demonstrating how to correctly evaluate interaction effects in a logistic model.
心理学研究经常涉及概率和计数的研究。这些通常使用广义线性模型 (GLM) 进行分析，通过对模型参数的非线性变换可以得到这些数量。这些模型在许多研究应用中，交互作用是核心。迄今为止，评估概率或计数的交互作用的典型方法直接从线性方法扩展而来，其中通过对感兴趣变量之间的乘积项系数，支持交互作用效应的证据。然而，与线性模型不同，描述概率和计数的 GLM 中的交互作用不等于预测变量之间的乘积项。相反，交互作用可能是模型预测变量的函数，需要采用非传统的方法来准确解释这些效应。在这里，我们将交互作用定义为一个变量的边际效应随另一个变量变化而变化的函数，并描述了使用偏导数和离散差来量化这些效应的方法。然后，我们使用指南和模拟示例，使用这些方法描述如何估计和解释概率和计数尺度上的 GLM 的交互作用效应。最后，我们使用青少年大脑认知发展研究的一个例子来说明如何在逻辑模型中正确评估交互作用效应。
