Subject: How to detect and characterize overfitting in spatiotemporal models using cross-validation?

[Gabriel Vinicius Vian]

Dear R-INLA community,

I am currently working on a spatiotemporal disease mapping model for dengue fever incidence in the state of São Paulo, Brazil. We are analyzing 15 years of monthly count data across all municipalities in the state.

Our model uses a Zero-Inflated Negative Binomial (zeroinflatednbinomial1). The linear predictor includes an autoregressive component (log-lagged cases), a spatial structured effect (besag), cyclic seasonal effects (rw2), delayed non-linear climate effects (using DLNMs), and several socioeconomic covariates. We are also using PC priors for the hyperparameters.

To perform model selection and avoid relying only on WAIC/DIC, I implemented a Leave-One-Year-Out cross-validation.  

My main question is: how can I rigorously detect and characterize "overfitting" in this specific INLA context?

Are there specific "red flags" in INLA that I should monito, such as the the behavior of the PIT values:?

Any insights, rules of thumb, or literature recommendations on identifying overfitting in complex INLA models would be greatly appreciated.

Thank you in advance for your time and help!

Best regards,

Gabriel Vian