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I have a situation where I need to compare the ability of two different--but correlated--measures to predict survival. In order to remove the overlapping variance between the two predictors (and therefore analyze only their independent contributions), I would normally regress one predictor onto the other with ordinary least squares (OLS), save the residuals, and conduct the survival analysis with those residuals. (And then do the same with the second measure.)
Question 1: I have seen this done now and then, but I can't find a reference to substantiate that interpretation of the residuals. Any leads would be greatly appreciated.
My problem is that the residuals are highly heteroscedastic. So, I used WEIGHT ESTIMATION, saved the weights, and entered the weights into the "WLS Weight:" box in LINEAR REGRESSION. SPSS dutifully produced my new residuals.
Question 2: Do I treat interpret these WLS residuals exactly like I did the OLS residuals? Or do I first need to un-transform them? (Un-transforming the residuals consists of multiplying them by the square root of their weight. I know that it is necessary to do so in order to graph them, but I don't know if it is necessary to un-transform them for my final purposes.) Again, any leads would be greatly appreciated.
- James Cantor
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