Beneath the surface: Unearthing within-person variability and mean relations with Bayesian mixed models

Donald R. Williams*, Joris Mulder, Jeffrey N Rouder, Philip Rast

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


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.
Original languageEnglish
JournalPsychological Methods
Publication statusAccepted/In press - 2021


  • Bayesian
  • Behavioral (in)consistency
  • Mean-variance relations
  • Mixed-effects location scale model
  • Within-person variance

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