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and what one wants to maximize (e.g. parsimony, predictive ability, reliability, interpretability...).

https://blog.minitab.com/en/how-to-choose-the-best-regression-model

With kind regards

Karabiner

Best model selection is based in context knowledge. If a person was deviating from that practice, using 3 data splits would be the standard. Train: where you fit all candidate models. Validate: see which model is best on holdout set. Train: where you fit the best model and acquire final estimates.

But now I have some models with differents variables and an other data. I used AIC too, to find the best model with this data.

But how compare and find the best data between the model where the data = A and the one where the data = B

Can you pool the data or do they contain non-overlapping sets of variables?

These are sub-samples at different points in time, I need to assess for each sample whether the variables that are significant are the same regardless of sample and time or not.

It may be that the models of the two different sub-samples have different variables.

But what criterion should be used to choose the "best" model (see if the model with subsample A is better than the model with sample B?)