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Standard techniques such as leave-one-out cross-validation (LOOCV) might notbe suitable for evaluating the predictive performance of models incorporatingstructured random effects. In such cases, the correlation between the trainingand test sets could have a notable impact on the model's prediction error. Toovercome this issue, an automatic group construction procedure forleave-group-out cross validation (LGOCV) has recently emerged as a valuabletool for enhancing predictive performance measurement in structured models. Thepurpose of this paper is (i) to compare LOOCV and LGOCV within structuredmodels, emphasizing model selection and predictive performance, and (ii) toprovide real data applications in spatial statistics using complex structuredmodels fitted with INLA, showcasing the utility of the automatic LGOCV method.First, we briefly review the key aspects of the recently proposed LGOCV methodfor automatic group construction in latent Gaussian models. We also demonstratethe effectiveness of this method for selecting the model with the highestpredictive performance by simulating extrapolation tasks in both temporal andspatial data analyses. Finally, we provide insights into the effectiveness ofthe LGOCV method in modelling complex structured data, encompassingspatio-temporal multivariate count data, spatial compositional data, andspatio-temporal geospatial data.

Automatic cross-validation in structured models: Is it time to leave out leave-one-out?