Bias correction of bounded location errors in binary data

Abstract

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially-referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide bias-corrected coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within non-overlapping polygons of any geometry. The COS accommodates spatial and non-spatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the location of the observations are unknown, but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data which ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.