It depends completely on the statistics of the system to be modelled. For a linear Gaussian multivariate model there is no problem since least square methods provide the accuracy of the model internally. For non-Gaussian models, especially for time varying models or stable statistical distributions it is much more difficult.

Dear John, I'm not acquainted with the modelling "typology" YET. I have just recently approached to this subject, so, pardon me If I make some mistakes here. The situation is: I'm fitting models (Kd, Langmuir and Freundlich) to sorption isotherms and assessing the "goodness of fit" by both ordinary linear regression criteria (R and R^2) and Kullback-Liebler based criteria (AIC and AICc). In some cases, the "traditional" criteria indicates that the fitting was good enough, but AICc points the other way, even indicating that the model gives no support to the experimental data. The opposite also occurs. Is it possible somehow that the R and R^2 are indicating the descriptive power of the model and the AICc is indicating the predictive power of the model? It seems reasonable because R and R^2 take into account the experimental data alone, whereas the AICc considers also the predictions of the model to the dependent variable (sorption) from parameters estimated by linear regression. Unfortunately I have no theoretical basis to evaluate nor criticize that YET. What do you think?