Hi,
I have a question regarding finding an appropriate model goodness criterion when a specific transformation is done on the dependent variable (In my case, I have performed Boxcox transformation). If we consider traditional model performance criteria (like AIC, DIC, BIC), their results will be affected by the transformation of the dependent variable, which makes them unrealistic. I am looking for a way to report my model performance when I have done a specific transformation on the dependent variable.
I think that the degree of "unrealisticness" is way higher when analysing a transformed variable instead of the original one.
Why would you want a goodness criterion on a different model? If a transformation is called for (and it often is) then the transformed model is the "right" one and the one you should report and whose fit you should describe. If you are fitting a linear model, you can use any of the standard measures of success--but on the transformed model.
Paul F Velleman The reason that I want to re transform my results is at the end of the day, I want to show that my model can predict the actual dependent variable (not the transformed one). Furthermore, I want to compare my result to some other methods that are used in the literature. They also might have their own method of transformation. So I should find an unbiased goodness metric for my model.
If you use a transformation from the Box/Cox functions (basically, powers and log), the transformation is investable, so you can always take your prediction back to original units. You can even find a CI in the transformed units and invert the bounds on the CI back to original units.
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