Use of auxiliary data in semi-parametric spatial regression with nonignorable missing responses

We propose a method for reducing the error of the prediction of a quantity of interest when the outcome has missing values that are suspected to be nonignorable and the data are correlated in space. We develop a maximum likelihood approach for the parameter estimation of semi-parametric regressions in a mixed model framework. We apply the proposed method to phytoplankton data collected at fixed stations in the Chesapeake Bay, for which chlorophyll data coming from remote sensing are available. A simulation study is also performed. The availability of a variable correlated to the response allows us to achieve a substantial reduction of the prediction error of the expected value of the smoother, without having to specify a nonignorable model.