  Standard techniques such as leave-one-out cross-validation (LOOCV) might not
be suitable for evaluating the predictive performance of models incorporating
structured random effects. In such cases, the correlation between the training
and test sets could have a notable impact on the model's prediction error. To
overcome this issue, an automatic group construction procedure for
leave-group-out cross validation (LGOCV) has recently emerged as a valuable
tool for enhancing predictive performance measurement in structured models. The
purpose of this paper is (i) to compare LOOCV and LGOCV within structured
models, emphasizing model selection and predictive performance, and (ii) to
provide real data applications in spatial statistics using complex structured
models fitted with INLA, showcasing the utility of the automatic LGOCV method.
First, we briefly review the key aspects of the recently proposed LGOCV method
for automatic group construction in latent Gaussian models. We also demonstrate
the effectiveness of this method for selecting the model with the highest
predictive performance by simulating extrapolation tasks in both temporal and
spatial data analyses. Finally, we provide insights into the effectiveness of
the LGOCV method in modelling complex structured data, encompassing
spatio-temporal multivariate count data, spatial compositional data, and
spatio-temporal geospatial data.
