Spatial Confounding in Multivariate Areal Data Analysis

Abstract: We investigate spatial confounding in the presence of multivariate disease dependence. In the "analysis model perspective" of spatial confounding, adding a spatially dependent random effect can lead to significant variance inflation of the posterior distribution of the fixed effects. The "data generation perspective" views covariates as stochastic and correlated with an unobserved spatial confounder, leading to inferior statistical inference over multiple realizations. While multiple methods have been proposed for adjusting statistical models to mitigate spatial confounding in estimating regression coefficients, results on interactions between spatial confounding and multivariate dependence are very limited. We contribute to this domain by investigating spatial confounding from the analysis and data generation perspectives in a Bayesian coregionalized areal regression model. We derive novel results that distinguish variance inflation due to spatial confounding from inflation based on multicollinearity between predictors and provide insights into the estimation efficiency of a spatial estimator under a spatially confounded data generation model. We demonstrate favorable performance of spatial analysis compared to a non-spatial model in our simulation experiments even in the presence of spatial confounding and a misspecified spatial structure. In this regard, we align with several other authors in the defense of traditional hierarchical spatial models (Gilbert et al., 2025; Khan and Berrett, 2023; Zimmerman and Ver Hoef, 2022) and extend this defense to multivariate areal models. We analyze county-level data from the US on obesity / diabetes prevalence and diabetes-related cancer mortality, comparing the results with and without spatial random effects.