Spatial Regression in the Presence of Misaligned data

In this paper, four approaches are presented to the problem of fitting a linear regression model in the presence of spatially misaligned data. These approaches are plug-in method‎, ‎simulation‎, ‎regression calibration and maximum likelihood‎. In the first two approaches‎, ‎with modeling the correlation between the explanatory variable, prediction of explanatory variable is determined at sites corresponding to response variable. Then the model is fitted using the predictions as a covariate in regression model. It is shown that this creates Berkson error and this error leads to bias in estimation of the slope of regression model. To adjust the bias, regression calibration approach is provided. In the maximum likelihood approach, misaligned data is used directly, and the regression model parameters are estimated. In fact, it is not required to predict explanatory variable at sites corresponding to response. Unfortunately, the maximum likelihood estimator properties can not be accurately assessed due to lack of analytical form. In a simulation study, the performance of all these approaches is assessed under several spatial models for explanatory variable. It is observed that regression calibration can significantly reduce the bias of slope of regression line compared to other methods. Moreover, Nominal coverage of confidence interval of slope of regression line is notable by this method.