Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models

Crossed random effects models (CREMs) are particularly useful in longitudinal data applications because they allow researchers to account for the impact of dynamic group membership on individual outcomes. However, no research has determined what data conditions need to be met to sufficiently identify these models, especially the group effects, in a longitudinal context. This is a significant gap in the current literature as future applications to real data may need to consider these conditions to yield accurate and precise model parameter estimates, specifically for the group effects on individual outcomes. Furthermore, there are no existing CREMs that can model intrinsically nonlinear growth. The goals of this study are to develop a Bayesian piecewise CREM to model intrinsically nonlinear growth and evaluate what data conditions are necessary to empirically identify both intrinsically linear and nonlinear longitudinal CREMs. This study includes an applied example that utilizes the piecewise CREM with real data and three simulation studies to assess the data conditions necessary to estimate linear, quadratic, and piecewise CREMs. Results show that the number of repeated measurements collected on groups impacts the ability to recover the group effects. Additionally, functional form complexity impacted data collection requirements for estimating longitudinal CREMs.