The linear mixed model and the hierarchical Ornstein-Uhlenbeck model: some equivalences and differences

We focus on comparing different modelling approaches for intensive longitudinal designs. Two methods are scrutinized, namely the widely used linear mixed model (LMM) and the relatively unexplored Ornstein-Uhlenbeck (OU) process based state-space model. On the one hand, we show that given certain conditions they result in equivalent outcomes. On the other hand, we consider it important to emphasize that their perspectives are different and that one framework might better address certain types of research questions than the other. We show that, compared to a LMM, an OU process based approach can cope with modelling inter-individual differences in aspects that are more substantively interesting. However, the estimation of the LMM is faster and the model is more straightforward to implement. The models are illustrated through an experience sampling study.