A Methodological Note: An Introduction to Autoregressive Models

The autoregressive model is a useful tool to analyze longitudinal data. It is particularly suitable for gerontological research as autoregressive models can be used to establish the causal relationship within a single variable over time as well as the causal ordering between two or more variables (e.g., physical health and psychological well-being) over time through bivariate autoregressive cross-lagged or contemporaneous models. Specifically, bivariate autoregressive models can explore the cross-lagged effects between two variables over time to determine the proper causal ordering between these variables. The advantage of analyzing cross-lagged effects is to test for the strength of prediction between two variables controlling for each variable's previous time score as well as the autoregressive component of the model. Bivariate autoregressive contemporaneous models can also be used to determine causal ordering within the same time point when compared to cross-lagged effects. Since the technique uses structural equation modeling, models are also adjusted for measurement error. This paper will present an introduction to setting up models and a step-by-step approach to analyzing univariate simplex autoregressive models, bivariate autoregressive cross-lagged models, and bivariate autoregressive contemporaneous models.