Collinearity issues in autoregressive models with time-varying serially dependent covariates

Abstract

Autoregressive models are becoming an increasingly popular tool in psychological science, and are typically used to assess the temporal dynamics of a univariate process. Their popularity has led researchers to extend the basic autoregressive model to include theoretically relevant time-varying covariates, such as experimental stimuli or contextual factors in observational studies. Including covariates in an autoregressive model can however hamper estimation of such models due to predictor collinearity. As we show in this paper, predictor collinearity in AR(1) models with time-varying covariates can emerge as a function of the serial dependence within the variables involved. We provide an analytic study of the collinearity issue and a simulation study to showcase that it generalizes across different types of time-varying covariates. Implications for study design, the use of time as a predictor, and related model variants are discussed.