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. 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 as an opportunity to gain a richer understanding of psychological processes. The technique to do so is based on the mixed-effects location scale model that can simultaneously estimate mixed-effects submodels to both the mean (location) and within-person variance (scale). We develop a framework that goes beyond assessing the submodels in isolation of one another and introduce a novel Bayesian hypothesis test for mean—variance correlations in the distribution of random effects. 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 (RTs) gathered from 2 cognitive inhibition 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. This stands in contrast to the dominant view of within-person variance (i.e., “noise”). The results also point toward paradoxical within-person, as opposed to between-person, effects: several people had slower and less variable incongruent responses. This contradicts the typical pattern, wherein larger means tend to be associated with more variability. We conclude with future directions, spanning from methodological to theoretical inquires, that can be answered with the presented methodology.

Impact Statement
Translational Abstract: Mixed-effects models are becoming common in psychological science. Although researchers typically focus on explaining the dependent variable, characterizing individual differences in within-person variance can provide valuable insights into behavioral consistency. The technique to do so is based on an extension to the mixed-effect model that can simultaneously predict both the mean and within-person variance. We introduce Bayesian methodology to test the covariance among individual difference parameters that capture mean and within-person variance relations. This is motivated by theoretical models that predict larger means will be associated with more variability. Our approach allows for confirmatory hypothesis testing of this proposed relation in the distribution of random effects. Hence, researchers can begin to test the interplay between an experimental effect on the mean and within-person variability in their repeated measurements. We apply our method to RTs gathered from two cognitive inhibition 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. We also uncovered strikingly large correlations between the experimental effect on the mean and within-person variability. Substantively this novel finding suggests that cognitive inhibition has important and highly interrelated signatures on both RT and RT consistency. The method is implemented in the user-friendly R package hypMuVar.