I have a simple model with 3 free parameters to fit, and wanted to try estimating those parameters via grid search. I was wondering -- what is the convention for selecting the best model in this case? I'm thinking it shouldn't be too complicated since the number of parameters are the same, so can I just use R^2? If not, would I need to select the parameters based on smallest MSE from some type of cross validation?
I suppose I don't have intuition about what to expect from cross validation when I have the same model structure, with different parameter estimates and correspondingly R^2 values. Assuming overfitting isn't an issue, would the model with the best R^2 always so better in cross validation?