I am running negative binomial regression on SPSS$-29.$ When i use model performance metrics $($AIC$,$ Deviance and Log Likelihood$)$ i realize that they are similar $($e$.$g$.9\mathrm{.}0$ and $8\mathrm{.}8$ for example$)$ for main $($train$)$ dataset with about $200$ events and the dataset used for external validation $($test$),$ which also had $200$ events. However, when i did $5-$fold cross validation, the AIC, Deviance and Log Likelihood for each fold made up of $40$ events is half $($e$.$g$.4\mathrm{.}4$ and $4\mathrm{.}8$ for example$)$ of main dataset and external validation dataset both with $200$ events.

Questions $($main data is for training and external validation data is for testing$)$:

$(1)$ is this overfitting although sample sizes differ?