Modeling within-level latent interaction effects in multilevel vector-autoregressive models.

The study of time-dependent within-person dynamics has gained popularity in recent years through the use of multilevel (latent) time-series models. However, due to the complexity of the models, model applications are usually limited with respect to the inclusion of time-varying moderating factors on the longitudinal within-person relations between variables. That is, in common applications of multilevel time-series models, the within-person dynamics of constructs over time are regarded as being insensitive to changes in other time-varying factors or changes in contexts. We illustrate an extension of multilevel latent time-series models that incorporate latent interaction effects at the dynamic within-person level. We build on previous work that incorporated time-varying observed or latent moderator variables for the dynamic parameters in vector autoregressive models and provide a tutorial for the application of the models, implemented and estimated using Bayesian estimation via Markov chain Monte Carlo techniques. The models are illustrated by two empirical applications that investigate the temporal dynamics of negative affect, rumination, and mindful attention. The performance of different models with varying complexity is investigated via several simulation studies to provide recommendations regarding the models' applicability for applied researchers. Required sample sizes range between at least 25 time points for around 50 persons in the simplest fixed-effects models and at least 100 time points for at least 100 persons in random-effects factor models, depending on the expected effect sizes of the dynamic parameters.