Spatial leave‐one‐out cross‐validation for variable selection in the presence of spatial autocorrelation

Abstract

Aim Processes and variables measured in ecology are almost always spatially autocorrelated, potentially leading to the choice of overly complex models when performing variable selection. One way to solve this problem is to account for residual spatial autocorrelation ( RSA ) for each subset of variables considered and then use a classical model selection criterion such as the A kaike information criterion ( AIC ). However, this method can be laborious and it raises other concerns such as which spatial model to use or how to compare different spatial models. To improve the accuracy of variable selection in ecology, this study evaluates an alternative method based on a spatial cross‐validation procedure. Such a procedure is usually used for model evaluation but can also provide interesting outcomes for variable selection in the presence of spatial autocorrelation. Innovation We propose to use a special case of spatial cross‐validation, spatial leave‐one‐out ( SLOO ), giving a criterion equivalent to the AIC in the absence of spatial autocorrelation. SLOO only computes non‐spatial models and uses a threshold distance (equal to the range of RSA ) to keep each point left out spatially independent from the others. We first provide some simulations to evaluate how SLOO performs compared with AIC . We then assess the robustness of SLOO on a large‐scale dataset. R software codes are provided for generalized linear models. Main conclusions The AIC was relevant for variable selection in the presence of RSA if the independent variables considered were not spatially autocorrelated. It otherwise failed because highly spatially autocorrelated variables were more often selected than others. Conversely, SLOO had similar performances whether the variables were themselves spatially autocorrelated or not. It was particularly useful when the range of RSA was small, which is a common property of spatial tools. SLOO appears to be a promising solution for selecting relevant variables from most ecological spatial datasets.

Bibliographic Information