Spatiotemporal forecasting models with and without a confounded covariate

The aim of this paper is to analyze the prediction accuracy of multivariate spatiotemporal forecasting models with a confounded covariate versus univariate models without covariates for discrete (count and binary) and continuous response variables by means of theoretical considerations and Monte Carlo simulation. For the simulation, we propose a Bayesian latent Gaussian Markov random fields framework for three types of generalized additive prediction models: (i) a multivariate model with a spatiotemporally confounded covariate only, denoted in the rest of the paper as the multivariate model; (ii) a univariate model with spatiotemporal random effects and their interaction only; (iii) and a full multivariate model consisting of the combination of (i) and (ii), that is, a univariate model combined with a multivariate model. One simulation result is that for all three kinds of response variables, the univariate and the full multivariate model uniformly dominate the multivariate model in terms of prediction accuracy measured by the mean-squared prediction error (MSPE). A second finding is that for discrete variables the univariate model uniformly dominates the full multivariate model. A third result is that for continuous response variables the full multivariate model dominates the univariate model in the case of low confoundedness of the covariate. For high confoundedness, the reverse holds. The results provide important guidelines for practitioners.