Bayesian Multivariate Mixed-Effects Location Scale Modeling of Longitudinal Relations Among Affective Traits, States, and Physical Activity.

Intensive longitudinal studies and experience sampling methods are becoming more common in psychology. While they provide a unique opportunity to ask novel questions about within-person processes relating to personality, there is a lack of methods specifically built to characterize the interplay between traits and states. We thus introduce a Bayesian multivariate mixed-effects location scale model (M-MELSM). The formulation can simultaneously model both personality traits (the location) and states (the scale) for multivariate data common to personality research. Variables can be included to predict either (or both) the traits and states, in addition to estimating random effects therein. This provides correlations between location and scale random effects, both across and within each outcome, which allows for characterizing relations between any number of personality traits and the corresponding states. We take a fully Bayesian approach, not only to make estimation possible, but also because it provides the necessary information for use in psychological applications such as hypothesis testing. To illustrate the model we use data from 194 individuals that provided daily ratings of negative and positive affect, as well as their physical activity in the form of step counts over 100 consecutive days. We describe the fitted model, where we emphasize, with visualization, the richness of information provided by the M-MELSM. We demonstrate Bayesian hypothesis testing for the correlations between the random effects. We conclude by discussing limitations of the MELSM in general and extensions to the M-MELSM specifically for personality research.