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RE: st: Residuals in Logistic Regression

From   Richard Williams <[email protected]>
To   [email protected]
Subject   RE: st: Residuals in Logistic Regression
Date   Fri, 09 Apr 2004 20:37:31 -0500

At 08:00 PM 4/9/2004 -0500, David Airey wrote:
What's the relationship between fit and deviance residuals? How do you get the same parameter estimates and models without getting the same residuals? Just asking out loud before going to look it up myself.

I think you'll need to look it up, because I can't explain it very well! After reading pp. 315-316 of Reference Manual G-M, I sort of understand it, but I'd have to read H & L to really get it. Like I said in my first message, what Stata does seems very counter-intuitive to me, but it does have its reasons.

One thing to realize is that residuals are handled differently in regress than in logistic. In regress, -predict resid, resid- would give you Observed Y - Yhat. But, in logistic, -predict resid, resid- gives you "the Pearson residual adjusted for the number sharing the same covariate pattern." Other Logistic regression residual stats are also adjusted for the covariate pattern. So, there is this covariate pattern adjustment bit that does not have an analog in OLS regression. If you don't like it, one workaround would seem to be adding and subtracting very small numbers to cases so that no two covariate patterns were exactly identical (Or, I suppose, you could just program the calculations yourself - perhaps somebody has done it already.)

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