Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model

In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measures over time are modeled in terms of three person-specific parameters: a baseline level, intraindividual variation around the baseline, and regulatory mechanisms adjusting toward baseline. Variation due to measurement error is separated from meaningful intraindividual variation. The proposed model allows for the simultaneous analysis of longitudinal measurements of two linked variables (bivariate longitudinal modeling) and captures their relationship via two person-specific parameters. Relationships between explanatory variables and model parameters can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated simultaneously. Mathematical details of the approach, including a description of the core process model—the Ornstein-Uhlenbeck model—are provided. We also describe a user friendly, freely accessible software program that provides a straightforward graphical interface to carry out parameter estimation and inference. The proposed approach is illustrated by analyzing data collected via self-reports on affective states.