Martínez Huertas, José ÁngelFerrer, Emilio2025-12-092025-12-092025-12-08Martínez-Huertas, J. Á., & Ferrer, E. (2025). A multilevel Ornstein–Uhlenbeck process with individual- and variable-specific estimates as random effects. British Journal of Mathematical and Statistical Psychology, 00, 1–16. https://doi.org/10.1111/bmsp.700192044-8317https://doi.org/10.1111/bmsp.70019https://hdl.handle.net/20.500.14468/31053The registered version of this article, first published in British Journal of Mathematical and Statistical Psychology, is available online at the publisher's website: Wiley; The British Psychological Society, https://doi.org/10.1111/bmsp.70019La versión registrada de este artículo, publicado por primera vez en British Journal of Mathematical and Statistical Psychology, está disponible en línea en el sitio web del editor: Wiley; The British Psychological Society, https://doi.org/10.1111/bmsp.70019In the present study, we extend a stochastic differential equation (SDE) model, the Ornstein–Uhlenbeck (OU) process, to the simultaneous analysis of time series of multiple variables by means of random effects for individuals and variables using a Bayesian framework. This SDE model is a stationary Gauss-Markov process that varies over time around its mean. Our extension allows us to estimate the variability of different parameters of the process, such as the mean (μ) or the drift parameter (φ), across individuals and variables of the system by means of marginalized posterior distributions. We illustrate the estimations and the interpretability of the parameters of this multilevel OU process in an empirical study of affect dynamics where multiple individuals were measured on different variables at multiple time points. We also conducted a simulation study to evaluate whether the model can recover the population parameters generating the OU process. Our results support the use of this model to obtain both the general parameters (common to all individuals and variables) and the variable-specific point estimates (random effects). We conclude that this multilevel OU process with individual- and variable-specific estimates as random effects can be a useful approach to analyse time series for multiple variables simultaneously.eninfo:eu-repo/semantics/openAccess6107.01 Metodología6302.02 Psicología socialartículoOU processstochastic differential equationsmultilevelrandom effectsmultivariate time seriesaffect dynamics