A hierarchical Ornstein-Uhlenbeck model for continuous repeated measurement data


In this paper, we present a diffusion model for the analysis of continuous-time change in multivariate longitudinal data. The central idea is to model the data from a single person with an Ornstein-Uhlenbeck diffusion process. We extend it hierarchically by allowing the parameters of the diffusion process to vary randomly over different persons. With this approach, both intra and interindividual differences are analyzed simultaneously. Furthermore, the individual difference parameters can be regressed on covariates, thereby providing an explanation of between-person differences. Unstructured and unbalanced data pose no problem for the model to be applied. We demonstrate the method on data from an experience sampling study to investigate changes in the core affect. It can be concluded that different factors from the five factor model of personality are related to features of the trajectories in the core affect space, such as the cross-correlation and variability of the changes.


Oravecz, Z., Tuerlinckx, F., & Vandekerckhove, J. (2009). A hierarchical Ornstein-Uhlenbeck model for continuous repeated measurement data. Psychometrika, 74, 395–418.


    title   = {{A} hierarchical {O}rnstein-{U}hlenbeck model for continuous repeated measurement data},
    author  = {Oravecz, Zita and Tuerlinckx, Francis and Vandekerckhove, Joachim},
    year    = {2009},
    journal = {Psychometrika},
    volume  = {74},
    pages   = {395--418}