We would like to thank Dr. Tamara Wall for her thoughtful comments on previous versions of this manuscript.Data used in the preparation of this article were obtained from the Adolescent Brain Cognitive Development (ABCD) Study (https://abcdstudy.org), held in the NIMH Data Archive (NDA). This is a multisite, longitudinal study designed to recruit more than 10,000 children age 9-10 and follow them over 10 years into early adulthood.
AbstractPsychology studies frequently involve the analysis of binary and count dependent variables. These are typically conducted using generalized linear models (GLMs) that specify non-linear relations between predictors and outcomes. Interactions are central within many research applications of these models. To date, typical practice in evaluating interaction effects in GLMs extends directly from linear approaches, in which the product term coefficient between variables of interest are used to provide evidence of an interaction effect. However, unlike linear models, interaction effects in GLMs are not equal to product terms between predictor variables and are instead a function of all predictors of a model. Here, we applied a partial derivative and finite difference framework to propose solutions for computing and conducting hypothesis testing on interaction effects in binary and count GLMs. We provided concrete guidelines and simulated examples to describe how interaction effects should be estimated and interpreted when GLMs are employed. We further illustrated via simulation how using the product term coefficient as an estimator of the interaction can result in bias and inefficiency of the interaction parameter. We concluded with an example using the Adolescent Brain Cognitive Development Study demonstrating how to correctly evaluate interaction effects in a logistic model.
Interaction
INTERACTIONS IN GLMS 4Estimating and interpreting interaction effects in generalized linear models of binary and count data 1 Journals were selected to represent various sub-disciplines of psychology, and included Developmental Addictive Behaviors. Databases included PsychInfo and PsychArticles. Boolean search conditions were "KW (interaction OR moderation) OR TX (interacted OR interaction OR moderated OR moderation) AND TX (logistic OR probit OR poisson OR ordinal OR negative binomial) AND TX regression", yielding 1,812 unique publications. Selected articles failed to meet criteria if search terms resulted in false-positives (e.g., moderation was mentioned in-text but was not examined directly in analyses).