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

Wadoux, Alexandre M.J.C.; Heuvelink, Gerard B.M.; Bruin, Sytze De; Brus, Dick J.


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.