Model Specification in Mixed-Effects Models: A Focus on Random Effects

Mixed-effect regression models are powerful tools for researchers in a myriad of fields. Part of the appeal of mixed-effect models is their great flexibility, but that flexibility comes at the cost of complexity and if users are not careful in how their model is specified, they could be making faulty inferences from their data. As others have argued, we think there is a great deal of confusion around appropriate random effects to be included in a model given the study design, with researchers generally being better at specifying the fixed effects of a model which map onto to their research hypotheses. To that end, we present an instructive framework for evaluating the random effects of a model in three different situations: (1) longitudinal designs; (2) factorial repeated measures; and (3) when dealing with multiple sources of variance. We provide worked examples with open-access code and data in an online repository. This framework will be helpful for students and researchers who are new to mixed effect models, and to reviewers who may have to evaluate a novel model as part of their review. Ultimately, it is difficult to specify "the" appropriate random-effects structure for a mixed model, but by giving users tools to think more deeply about their random effects, we can improve the validity of statistical conclusions in many areas of research.