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Re: st: rreg vs qreg regression


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: rreg vs qreg regression
Date   Thu, 28 Aug 2003 18:51:02 +0100

Ricardo Ovaldia

> After unsuccessfully trying to normalize
> (transform)some very skew clinical data, I decided to
> use -rreg- to fit a robust regression model.
> Everything look good until I decided to use a -qreg-
> for median regression on these same data. To my
> surprise, the two methods produced very different
> results. Covariates significant in one model were not
> in the other, and vice-versa. Also the p-values from
> -qreg- were in general smaller than those from -rreg-.
> I now have to decide which results to believe. 

> Could someone please tell me how I should proceed in
> determining which results are more consistent with my
> data? That is, when should I use -rreg- and when is
> -qreg- more appropriate?   

Some partial thoughts follow. I make 4 points, but 
others could in principle make at least 40, because
this all raises a bundle of highly interrelated issues. 

1. You shouldn't believe either if you can't believe both. 
That is, if your results differ, and incomprehensibly,
you need to understand why, rather than try to identify 
which method is better. I doubt there is a general 
prescription for when one method is preferable. I like 
-qreg- a lot because the principle is so easy to explain, 
whereas -rreg- looks like a bizarre mixture of spells, but 
that's purely taste. 

2. You don't say wherein the extreme skewness lies. 
However, if it is in the response, a simple point, but 
one often overlooked, is that the key assumptions are about 
the conditional distribution of the response given the 
predictors, not the unconditional distribution of the 
response. 

3. It could be that your difficulties lie also in 
fitting a too complicated model. 

4. Plot the results! You can do all sorts of plots
such as residual vs fitted, etc., etc., irrespective
of the number of predictors. Sometimes they make it 
clear which model is lousier. 

Nick 
n.j.cox@durham.ac.uk 
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