Multilevel Autoregressive Models when the Number of Time Points is Small

Abstract

The multilevel autoregressive model disentangles unobserved heterogeneity from state-dependence. Statistically, the random intercept accounts for the dependence of all measurements at different time points on an observed underlying factor, while the lagged dependent predictor allows the outcome to depend on the outcome at the previous time point. In this paper, we consider different implementations of the simplest multilevel autoregressive model, and explore how each of them deals with the endogeneity assumption and the initial conditions problem. We discuss the performance of the no centering approach, the manifest centering approach, and the latent centering approach in the setting where the number of time points is small. We find that some commonly used approaches show bias for the autoregressive parameter. When the outcome at the first time point is considered predetermined, the no centering approach assuming endogeneity performs best.