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

Area of Science:

• Psychological Science
• Statistical Modeling

Background:

• Mixed-effects models are increasingly used in psychological research.
• Traditionally, homogeneous variance is treated as an assumption to be met, overlooking its analytical potential.

Purpose of the Study:

• To propose a shift in perspective, viewing within-person variance modeling as an opportunity for deeper psychological insights.
• To introduce and apply the mixed-effects location scale model for simultaneous analysis of mean and variance structures.

Main Methods:

• Utilizing mixed-effects location scale models to estimate submodels for both the mean (location) and within-person variance (scale).
• Developing a Bayesian hypothesis test for correlations between mean and variance in random effects distributions.
• Applying the framework to reaction time data from cognitive inhibition tasks.

Main Results:

• Individual differences in within-person variance were more pronounced than in the mean structure.
• Complex structural relationships between mean and variance were identified.
• Paradoxical within-person effects were observed, such as slower and less variable responses in some individuals, contradicting typical mean-variance associations.

Conclusions:

• Within-person variance holds significant information about psychological processes, challenging the view of it as solely 'noise'.
• The mixed-effects location scale model provides a powerful tool for exploring these complex mean-variance relationships.
• Future research can leverage this methodology for both theoretical and methodological advancements in psychological science.