RE: st: Residuals in Logistic Regression

[Richard Williams <Richard.A.Williams.5@nd.edu>]

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.
>
> -Dave
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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