ABSTRACT
This chapter considers the extension of ordinary least squares known as generalized least squares (GLS), which can properly account for spatial correlation among the observations. The presentation begins with some theory and methodology, followed by two illustrative toy examples that contrast GLS-based and OLS-based results. Then, the important class of spatial mixed linear models, to which GLS is applied, is introduced. Next is presented a careful study of spatial confounding, a phenomenon in which the covariance structure is purported to interfere, in some sense, with estimation of the mean structure. After that, structures of the covariance matrix that can be exploited to carry out the necessary computations for GLS estimation are considered. The chapter concludes with a brief introduction to empirical GLS, which is the form of GLS applicable to the general spatial linear model in which covariance parameters are estimated.
