Spatial cross-validation is not the right way to evaluate map accuracy

Abstract

For decades scientists have produced maps of biological, ecological and environmental variables. These studies commonly evaluate the map accuracy through cross-validation with the data used for calibrating the underlying mapping model. Recent studies, however, have argued that cross-validation statistics of most mapping studies are optimistically biased. They attribute these overoptimistic results to a supposed serious methodological flaw in standard cross-validation methods, namely that these methods ignore spatial autocorrelation in the data. They argue that spatial cross-validation should be used instead, and contend that standard cross-validation methods are inherently invalid in a geospatial context because of the autocorrelation present in most spatial data. Here we argue that these studies propagate a widespread misconception of statistical validation of maps. We explain that unbiased estimates of map accuracy indices can be obtained by probability sampling and design-based inference and illustrate this with a numerical experiment on large-scale above-ground biomass mapping. In our experiment, standard cross-validation (i.e., ignoring autocorrelation) led to smaller bias than spatial cross-validation. Standard cross-validation was deficient in case of a strongly clustered dataset that had large differences in sampling density, but less so than spatial cross-validation. We conclude that spatial cross-validation methods have no theoretical underpinning and should not be used for assessing map accuracy, while standard cross-validation is deficient in case of clustered data. Model-free, design-unbiased and valid accuracy assessment is achieved with probability sampling and design-based inference. It is valid without the need to explicitly incorporate or adjust for spatial autocorrelation and perfectly suited for the validation of large scale biological, ecological and environmental maps.