Who is and is not "average"? Random effects selection with spike-and-slab priors

Mixed-effects models are often employed to study individual differences in psychological science. Such analyses commonly entail testing whether between-subjects variability exists and including covariates to explain that variability. We argue that researchers have much to gain by explicitly focusing on the individual in individual differences research. To this end, we propose the spike-and-slab prior distribution for random effect selection in (generalized) mixed-effects models as a means to gain a more nuanced perspective of individual differences. The prior for each random effect is a two-component mixture consisting of a point-mass "spike" centered at zero and a diffuse "slab" capturing nonzero values. Effectively, such an approach allows researchers to answer questions about particular individuals; specifically, "Who is average?", in the sense of deviating from an average effect, such as the population-averaged slope. We begin with an illustrative example, where the spike-and-slab formulation is used to select random intercepts in logistic regression. This demonstrates the utility of the proposed methodology in a simple setting while also highlighting its flexibility in fitting different kinds of models. We then extend the approach to random slopes that capture experimental effects. In two cognitive tasks, we show that despite there being little variability in the slopes, there were many individual differences in performance. In two simulation studies, we assess the ability of the proposed method to correctly identify (non)average individuals without compromising the mixed-effects estimates. We conclude with future directions for the presented methodology. (PsycInfo Database Record (c) 2024 APA, all rights reserved).