Beneath the Surface: Unearthing Within-Person Variability and Mean Relations with Bayesian Mixed Models

Mixed-effects models are becoming common in psychological science. Although they have many desirable features, there is still untapped potential that has not yet been fully realized. It is customary to view homogeneous variance as an assumption to satisfy. We argue to move beyond that perspective, and to view modeling within-person variance (``noise'') as an opportunity to gain a richer understanding of psychological processes. This can provide important insights into behavioral (in)stability. The technique to do so is based on the mixed-effects location scale model. The formulation can simultaneously estimate mixed-effects sub-models to both the mean (location) and within-person variance (scale) for clustered data common to psychology. We develop a framework that goes beyond assessing the sub-models in isolation of one another, and allows for testing structural relations between the mean and within-person variance with the Bayes factor. We first present a motivating example, which makes clear how the model can characterize mean--variance relations. We then apply the method to reaction times gathered from two cognitive inference tasks. We find there are more individual differences in the within-person variance than the mean structure, as well as a complex web of structural mean--variance relations in the random effects. This stands in contrast to the dominant view of within-person variance--i.e., measurement ``error'' or ``noise.'' The results also point towards paradoxical within-person, as opposed to between-person, effects. That is, in both tasks, several people had \emph{slower} and \emph{less} variable incongruent responses. This contradicts the typical pattern, wherein \emph{larger} means are expected to be \emph{more} variable. We conclude with future directions. These span from methodological to theoretical inquires that can be answered with the presented methodology.