The Forgotten Semantics of Regression Modeling in Geography

Abstract

This article is concerned with the semantics associated with the statistical analysis of spatial data. It takes the simplest case of the prediction of variable y as a function of covariate(s) x, in which predicted y is always an approximation of y and only ever a function of x, thus, inheriting many of the spatial characteristics of x, and illustrates several core issues using “synthetic” remote sensing and “real” soils case studies. The outputs of regression models and, therefore, the meaning of predicted y, are shown to vary due to (1) choices about data: the specification of x (which covariates to include), the support of x (measurement scales and granularity), the measurement of x and the error of x, and (2) choices about the model including its functional form and the method of model identification. Some of these issues are more widely recognized than others. Thus, the study provides definition to the multiple ways in which regression prediction and inference are affected by data and model choices. The article invites researchers to pause and consider the semantic meaning of predicted y, which is often nothing more than a scaled version of covariate(s) x, and argues that it is naïve to ignore this.