Is it acceptable to compare the AIC of an OLS linear model to the AIC of a quantile linear model to see which is the better fit?

I only ask as it seems AIC is the only 'goodness of fit' measure available for quantile regression in R.

Much thanks in advance,

Laura ]]>

I am tasked with fitting a linear model with one dependent variable y and one independent variable x.

I am using R for the analysis.

So i fit my model and have three problems. First of all the QQ plot is strongly suggesting non normality in the residuals. Second the variance is heteroskedastic. It is fanning out from left to right. Finally I have a problem with one outlier which has a Cook's distance of 86.

Now I have no reason to delete the outlier and thought fitting a robust linear model would be a good alternative. This does indeed solve the problem caused by my outlier however the other two problems still remain.

Note I am happy to fit either M estimator robust regression or quantile regression based on the median.

My questions are as follows:

1.) I read everywhere that robust regression is robust in the sense that it is robust to outliers. I have seen hints of suggestion that it is also robust to departures from the first two problems i mentioned, is this the case and if so can you point me to a text that verifies this?

2.) If it is not the case, is it OK to apply sandwich estimators to my standard errors to combat the problem caused by non constant variance?

Also note I have tried Boxcox transformations on both of the variables and have had no joy.

Thank you very much for your time in advance!

Laura

I hope the thread's title makes sense to you. I need to perform internal Cross-Validation using k-fold CV (needless to say, to assess how well a model behaves in relation to 'unknown' data).

What I am after is getting the distribution of AUC values across the different folds. So far, I did not found a viable option. I mean, there are some packages that perform different sorts of CV, but no one of them (at the best of my understanding) return what I want.

One that I found quite easy to use if the DAAG package, whose CVbinary() function performs k-folds CV and returns the cross-validation estimate of accuracy. The latter, as far as I understand, is the average of the accuracy across the k-folds (using 0.5 as cutoff point on probabilities).

What I would like to have is something similar, but with the averaged AUCs instead of the averaged accuracy values.

Long story short: do you know of any package that does something like that, or can you provide some help in writing down some piece of code to help me implementing what I am after from scratch?

Thank you for any guidance you will provide.

Best

Gm ]]>