Covariate measurement error in spatial analysis of count data

Measurement error occurs when variables are not observed precisely. In regression models, covariate measurement error violates the assumption that covariates are fixed and accurately measured, leading to inefficient parameter estimates, inflated variance and underestimated or undetected covariate effects. This study develops methods for spatially correlated data while accounting for measurement error in covariates. We use an extension of the Besag-York-Mollie (BYM2) model, which includes both structured spatial variation and unstructured random variation and is efficient for spatial analysis despite its computational cost. We develop a Bayesian framework of the BYM2 model, with the error-prone covariates adjusted via Berkson and classical measurement error assumptions. Simulation studies show that our model flexibly detects and reduces spatial confounding in the presence of covariates measured with or without error and outperforms methods that ignore measurement error in covariates. We illustrate the application of the proposed methodology using obesity data for 117 health regions across Canada.