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

Abstract

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 measurements over time are modeled in terms of three person-specific parameters: a baseline level, intra-individual variation around the baseline and regulatory mechanisms adjusting towards baseline. Variation due to measurement error is separated from meaningful intra-individual vari- can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated in the same step. 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.

Revisiting the neuroticism – performance link: A dynamic approach to individual differences

“…Person‐specific estimates for neuroticism baseline, variability and attractor strength were obtained using the Bayesian Hierarchical Ornstein‐Uhlenbeck model (BHOUM; Oravecz, Tuerlinckx, & Vandekerckhove, ). The BHOUM model is based on stochastic differential equations and captures the trajectory of personality states over time through a measurement equation (Equation ) and a transition equation (Equation ):…”

At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the COGITO Study

“…Researchers have been applying this approach using Bayesian software like JAGS (Plummer, 2003) and WinBUGS (Spiegelhalter, Thomas, Best, & Lunn, 2003; e.g., Wang, Hamaker, & Bergman, 2012), but there are also specialized programs that were developed for this purpose. These include the Bayesian Ornstein-Uhlenbeck Model (BOUM) toolbox package (Oravecz, Tuerlinckx, & Vandekerckhove, 2016), the R-package mlVAR (Epskamp, Deserno, & Bringmann, 2017), and the R-package ctsem (Driver, Oud, & Voelkle, 2017), which in turn uses either OpenMx (Boker et al, 2011) or Stan (Stan Development Team, 2017).…”

Single-Subject Research in Psychiatry: Facts and Fictions

“…Furthermore, while person-mean centering is useful for disaggregating between-and within-person effects of the predictors, with respect to other model features within-and between-person variance is more difficult to separate (for example, the error covariance matrix) (97,98). Recently, new models like Dynamic Structural Equation Modeling (99), or Bayesian Dynamic Modeling (96,100,101) do offer increased possibilities to adequately model other model features within a multilevel framework. However, with increased model complexity, for example with multiple interactions, feedback loops, or non-linear effects, the problem of disaggregating within-and between-person variance in multilevel models becomes quite difficult.…”