I have two linear regression models on the same data, but where the response variable has been transformed using respectively the BoxCox transformation and the logit transformation. Therefore, I cannot use AIC or other maximum likelihood based criteria for model selection.
Instead, I'm trying to select the "best" model using other criteria. I've come up with the 3 criteria below:
- Parsimony (simpler models should preferred over complex models)
- Adherence to theoretical assumptions (examining if residuals are iid using residual analysis)
- Empirical performance (MAE/MSE using leave-one-out cross-validation)
I am unsure how to rank these 3 criteria, which makes it hard for me to determine which of the two models I should use. In what situations should I rank one criteria higher than the other two and would you recommend a general ranking?