A unified Gaussian copula methodology for spatial regression analysis

Spatially referenced data arise in many fields, including imaging, ecology, public health, and marketing. Although principled smoothing or interpolation is paramount for many practitioners, regression, too, can be an important (or even the only or most important) goal of a spatial analysis. When doing spatial regression it is crucial to accommodate spatial variation in the response variable that cannot be explained by the spatially patterned explanatory variables included in the model. Failure to model both sources of spatial dependence—regression and extra-regression, if you will—can lead to erroneous inference for the regression coefficients. In this article I highlight an under-appreciated spatial regression model, namely, the spatial Gaussian copula regression model (SGCRM), and describe said model’s advantages. Then I develop an intuitive, unified, and computationally efficient approach to inference for the SGCRM. I demonstrate the efficacy of the proposed methodology by way of an extensive simulation study along with analyses of a well-known dataset from disease mapping.