Spatial regression with covariate measurement error: A semi-parametric approach

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially-defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modelling because of the presence of spatial correlation among the observations. We propose a semi-parametric regression approach to obtain bias corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.