Comparing two spatial variables with the probability of agreement

TL;DR

This paper extends the probability of agreement (PA) to spatial variables, analyzing how it varies with spatial lag and providing estimation methods, with applications to ecological data on forest canopy greenness.

Contribution

It introduces a spatially dependent PA measure, establishes decay conditions for spatial processes, and offers an asymptotic estimation approach.

Findings

PA decays with spatial lag in isotropic processes

Estimation method guarantees asymptotic normality

Application to ecological data shows practical relevance

Abstract

Computing the agreement between two continuous sequences is of great interest in statistics when comparing two instruments or one instrument with a gold standard. The probability of agreement (PA) quantifies the similarity between two variables of interest, and it is useful for accounting what constitutes a practically important difference. In this article we introduce a generalization of the PA for the treatment of spatial variables. Our proposal makes the PA dependent on the spatial lag. As a consequence, for isotropic stationary and nonstationary spatial processes, the conditions for which the PA decays as a function of the distance lag are established. Estimation is addressed through a first-order approximation that guarantees the asymptotic normality of the sample version of the PA. The sensitivity of the PA is studied for finite sample size, with respect to the covariance parameters. The new method is described and illustrated with real data involving autumnal changes in the green chromatic coordinate (Gcc), an index of "greenness" that captures the phenological stage of tree leaves, is associated with carbon flux from ecosystems, and is estimated from repeated images of forest canopies.