Modeling Heterogeneity in Temporal Dynamics: Extending Latent State-Trait Autoregressive and Cross-lagged Panel Models to Mixture Distribution Models

Longitudinal models suited for the analysis of panel data, such as cross-lagged panel or autoregressive latent-state trait models, assume population homogeneity with respect to the temporal dynamics of the variables under investigation. This assumption is likely to be too restrictive in a myriad of research areas. We propose an extension of autoregressive and cross-lagged latent state-trait models to mixture distribution models. The models allow researchers to model unobserved person heterogeneity and qualitative differences in longitudinal dynamics based on comparatively few observations per person, while taking into account temporal dependencies between observations as well as measurement error in the variables. The models are extended to include categorical covariates, to investigate the distribution of encountered latent classes across observed groups. The potential of the models is illustrated with an application to self-esteem and affect data in patients with borderline personality disorder, an anxiety disorder, and healthy control participants. Requirements for the models' applicability are investigated in an extensive simulation study and recommendations for model applications are derived.