Liu, ZhedongVan Niekerk, JanetRue, Håvard2025-11-042025-11-042025-07-04Liu, Z., Van Niekerk, J., Rue, H. 2025, 'Leave-group-out cross-validation for latent Gaussian models', SORT-Statistics and Operations Research Transactions, vol. 49, no. 1, pp. 121-146, doi : 10.57645/20.8080.02.25.1696-2281 (print)2013-8830 (online)10.57645/20.8080.02.25http://hdl.handle.net/2263/105104Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations, LOOCV has since been extended to other cases such as hierarchical models. However, it focuses rimarily on short-range prediction and may not fully capture long-range prediction scenarios. For structured hierarchical models, particularly those involving multiple random effects, the concepts of short- and long-range predictions become less clear, which can complicate the interpretation of LOOCV results. In this paper, we propose a complementary cross-validation framework specifically tailored for longer-range prediction in latent Gaussian models, including those with structured random effects. Our approach differs from LOOCV by excluding a carefully constructed set from the training set, which better emulates longer-range prediction conditions. Furthermore, we achieve computational efficiency by adjusting the full joint posterior for this modified cross-validation, thus eliminating the need for model refitting. This method is implemented in the R-INLA package (www.r-inla.org) and can be adapted to a variety of inferential frameworks.en© Institut d'Estadistica de Catalunya.Bayesian cross-validationLatent Gaussian modelsR-INLALeave-one-out cross-validation (LOOCV)Article