Univariate Autoregressive Structural Equation Models as Mixed-Effects Models

Abstract

Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to estimate them in mixed-effects model software, namely the R package nlme. We also show how nlme can be used to fit extensions of these models, for example, models that do not assume equally spaced time intervals between measurement occasions (i.e., continuous time models). Overall, our expositions show that autoregressive structural equations models and mixed-effects models are closely related. We think that this insight eases researchers to understand the differences between the variants of the autoregressive structural equation model and also allows them to profitably link the two different modeling perspectives.