# Is AIC a valid criterion for the selection of variance structures in GLS?

In generalized least squares, I’ve specified a weights function that accounts for heterogeneity in residual variance that exist along the range of a covariate. The validation graphs (residuals plotted against covariate values) clearly shows that this adjustment gets rid of the heteroscedasticity, yet the AIC of this model is higher than the uncorrected model.

So my question is, when the model is incorrectly specified and the assumptions are violated, can the calculated likelihood (and therefore the AIC) be trusted? Would it not be better to use a more parametrized variance structure despite the higher AIC estimate?

However it is fair to wonder if the AIC penalty is too high for your particular case. Keep also in mind that heteroskedasticity problem in a well specified OLS is simply one of efficiency: it makes the convergence to true $\beta$ slower which might not be an issue in your case.