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.

中文翻译：

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地理建模中被遗忘的语义

本文关注与空间数据统计分析相关的语义。这需要变量的预测的最简单的情况ÿ作为协变量（多个）的函数X，其中预测ÿ总是近似ÿ和只有永远函数 X，从而，继承很多的空间特性X，并使用“合成”遥感和“真实”土壤案例研究说明了几个核心问题。回归模型的输出以及预测y的含义由于（1）关于数据的选择而发生变化：x的规格（包括协变量），对x的支持。X（测量尺度和粒度），测量X和的误差X，和（2）关于该模型包括其功能形式和的模型识别的方法的选择。其中一些问题比其他问题得到更广泛的认识。因此，该研究为通过数据和模型选择影响回归预测和推断的多种方式提供了定义。本文邀请研究人员暂停并考虑预测y的语义，后者通常不过是协变量x的缩放版本，并认为忽略这一点是幼稚的。