st: Residuals in Logistic Regression

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

I obviously don't understand how the residual statistics work in logistic 
regression.  I have run a logistic regression of happymar (coded 0, 1) on 
church and female (also both 0, 1) and educ (years of education).  I then 
use predict to get the deviance residuals (I get similar results if I use 
the rstandard or residuals options on predict).  I get the following:

. extremes  dev p happymar church female educ, nolabel high

  +----------------------------------------------------------------+
  | obs:        dev          p   happymar   church   female   educ |
  |----------------------------------------------------------------|
  |  43.   1.170689   .5039612          1        1        0     10 |
  |   2.   1.394511   .3782007          1        0        1     10 |
  |   6.     2.4859   .0858805          0        0        0     11 |
  |  13.     2.4859   .0858805          1        0        0     11 |
  |  36.     2.4859   .0858805          1        0        0     11 |
  +----------------------------------------------------------------+


note: 6 values of -1.331003

What I don't understand is, why does case 6 stand out as an outlier?  The 
observed value of happymar is 0, and the predicted probability of a 1 is 
only .0858805.  So, I would think case 6 is anything but an outlier.  In 
addition, cases 13 and 36 have the same values as 6 on the Xs, but for them 
happymar = 1.  So, I would expect them to be outliers, but I would not 
expect case 6 to be.

Incidentally, if I cheat and run OLS regression instead, case 6 is not 
identified as an outlier.

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