Interpreting Interaction Effects in Generalized Linear Models of Nonlinear Probabilities and Counts
2021/02/01 by Connor J. McCabe, Connor McCabe, Max A. Halvorson +3 · 97 citations
Mathematics · Psychology · #Advanced Causal Inference Techniques #Computer science #Econometrics #Generalized additive model #Generalized linear mixed model #Generalized linear model #Interaction #Linear model #Marginal model #Mathematics #Mental Health Research Topics #Nonlinear system #Regression analysis #Statistical Methods and Bayesian Inference #Statistics #Variable (mathematics) #Variables
paper · open access · doi:10.1080/00273171.2020.1868966
published in Multivariate Behavioral Research 57(2-3), 243-263 (Taylor & Francis)
openalex publication_date 2021/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Abstract
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.
Citations
Cited by
- Self‐Injurious Thoughts and Behaviors From Pregnancy to Postpartum: Risk Factors and Clinical Implications
- A Tutorial on Analyzing Ecological Momentary Assessment Data in Psychological Research With Bayesian (Generalized) Mixed-Effects Models
- Anything Goes: Statistical Interactions Without Substantive Theory
- Alcohol and Cannabis Use Predicted by Affect-Urgency Interactions in Everyday Life
- Registered Report: A Replication Examining Occupational Experience and Performance on the Water-Level Task
- Exploring the Physical Properties, Hydrogen Storage Capacity and Thermal Barrier Performance of LaMg2H7: A First-Principles Investigation
- Crime propensity and lifestyle risk: The interplay of personal morality and self-control ability in determining the significance of criminogenic exposure
- Are online norms‐based alcohol interventions efficacious for college students with higher social anxiety?
- Examining the moment‐to‐moment association between drinking and problems: The moderating role of emotional functioning
- Alcohol use disorder as a moderator of the relationship between posttraumatic stress disorder and suicidality among military personnel
- The Drinking Dashboard for alcohol‐induced blackout: A randomized pilot trial
- Making sense of some odd ratios: A tutorial and improvements to present practices in reporting and visualizing quantities of interest for binary and count outcome models.
- Making sense of some odd ratios: A tutorial and improvements to present practices in reporting and visualizing quantities of interest for binary and count outcome models. [europepmc]
- Complementarity in daily marijuana and alcohol among emerging adults. [europepmc]
- Early Adolescent Substance Use Before and During the COVID-19 Pandemic: A Longitudinal Survey in the ABCD Study Cohort. [europepmc]
- Fluctuation in the sense of belongingness during college moderates within-person associations between perceived injunctive norms and subsequent drinking. [europepmc]
- Approach motivation and loneliness: Individual differences and parasympathetic activity. [europepmc]
- Who disengages from emotion and when? An EMA study of how urgency and distress intolerance relate to daily emotion regulation. [europepmc]
- Twin study of caffeine use, ADHD, and disrupted sleep in ABCD youth. [europepmc]
- The association between student loan debt and perceived socioeconomic status and problematic drinking and mental health symptoms: A preliminary investigation. [europepmc]
- Kinematic priming of action predictions. [europepmc]
- Chronic Pain, Hopelessness, and Suicide Risk Among Adult Medical Inpatients. [europepmc]
- A pilot study of the acceptability, efficacy, and iatrogenic effects of a brief dynamic norms intervention for reducing young adult alcohol use. [europepmc]
- Longitudinal examination of alcohol use motives, item-level protective behavioral strategies, and alcohol-related consequences. [europepmc]
- Association of healthy lifestyle score with control of hypertension among treated and untreated hypertensive patients: a large cross-sectional study. [europepmc]
- Family ties: examining family functioning and alcohol use among American Indian youth. [europepmc]
- Elite career expectations of adolescents: Popularity, gender differences, and social divides. [europepmc]
- Interactions between latent variables in count regression models. [europepmc]
- Reactive and Proactive Aggression in Daily Life: An Exploratory Experience-Sampling Method Study. [europepmc]
- Cumulative Risk and Cumulative Protection: Relative Contributions to Predicting Substance Use, Antisocial Behaviour and Mental Health Across Development. [europepmc]
- A Tutorial on Analyzing Ecological Momentary Assessment Data in Psychological Research With Bayesian (Generalized) Mixed-Effects Models. [europepmc]
- Effects of very low nicotine cigarettes, e-cigarettes, and nicotine patches on daily own-cigarette abstinence in a randomized controlled switching trial. [europepmc]
- The Drinking Dashboard for alcohol-induced blackout: A randomized pilot trial. [europepmc]
- Hypothesis-Driven Research on Multiple Stressors: An Analytical Framework for Stressor Interactions. [europepmc]
- Impact of insurance type on outpatient mental health treatment of US adults. [europepmc]
- Incentives and delivery modality as moderators of a web-based personalized normative feedback intervention for heavy-drinking college students. [europepmc]
- Machine learning and Mendelian randomization identify key lifestyle factors in coronary heart disease: A NHANES-Based study. [europepmc]
Related