st: outliers v skew

["Campo, Marc" <MCampo@mercy.edu>]

We have developed a least squares regression model with a three level categorical predictor (and about 3 covariates) and an outcome (SF-12) that is skewed.  The sf-12 scores are skewed - negatively - in each group of the primary predictor.  This can be unavoidable if your mean score is above national norms.  The residuals are similarly skewed (in each predictor category) but slightly less so.  

The skew results from a series of outliers in each group, almost all of which are negative.   Without the outliers, the residual distributions are 
somewhat normal.   We have a large sample (about 1,445) and I would 
say there are about 25-30 observations with standardized residuals 
between -3 and -5.5.   With the exception of a couple of the cases 
most of these don't seem to cause much havoc.  They are interesting 
and may deserve to influence the coefficients.  Hard to tell - even 
from a clinical perspective. 

So, is this a question of non normality or an outlier problem or 
both.......both robust and median regression results in coefficients that are about 1 less than standard regression for one level of the dummy coded predictor, and similar for the other.  (there is also an age interaction so we report across 3 levels of age).  Transformations of the DV don't seem to add much. Looking at a variety of transformations  only the cubic seemed to make things even close to normal.   Transformations would also make this difficult to interpret.   



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