  In geostatistics, it is common to model spatially distributed phenomena
through an underlying stationary and isotropic spatial process. However, these
assumptions are often untenable in practice because of the influence of local
effects in the correlation structure. Therefore, it has been of prolonged
interest in the literature to provide flexible and effective ways to model
nonstationarity in the spatial effects. Arguably, due to the local nature of
the problem, we might envision that the correlation structure would be highly
dependent on local characteristics of the domain of study, namely, the
latitude, longitude and altitude of the observation sites, as well as other
locally defined covariate information. In this work, we provide a flexible and
computationally feasible way for allowing the correlation structure of the
underlying processes to depend on local covariate information. We discuss the
properties of the induced covariance functions and methods to assess its
dependence on local covariate information. The proposed method is used to
analyze daily ozone in the southeast United States.
