[Rd] pearson residuals in glm for binomial response (PR#1175)

[Peter Dalgaard BSA]

J.T.Kent@leeds.ac.uk writes:

> R version 1.3.0
> OS: SunOS 5.7, but I think the same problem occurs with Windows
> 
> An incorrect formula seems to be used to calculate the pearson residuals
> for a generalized linear model with a binomial response.  Here is a
> simple program which gives (a) the pearson residuals calculated directly,
> (b) the pearson residuals from glm, and (c) the deviance residuals from 
> glm.  The first and last columns are quite close.  The middle differs from 
> the first by a factor of n (n=10 here).  This problem did not occur with
> an earlier version of R I tried, version 0.64.2.

I almost said that your version is old and that you forgot to check
the bug repository for prior reports (PR#1123 was also on Pearson
residuals). However, the problem persists in the development version.

The issue is that we have (in 1.4.0pre)

 pearson = (y - mu)/sqrt(wts * (object$family$variance)(mu))

However, the y and mu that we use are divided by n:

> glm1$prior.weights
[1] 10 10 10 10
> glm1$fitted.values
[1] 0.2802480 0.4834715 0.6923131 0.8439674
> glm1$family$variance(glm1$fitted.values)
[1] 0.2017091 0.2497268 0.2130157 0.1316864
> glm1$y
[1] 0.2 0.6 0.7 0.8

I've stuck my foot in it with this stuff before, but should the
denominator not be sqrt(object$family$variance(mu)/wts) ?? (If the
weights are large, the variance should be smaller, not larger).

Could someone please ram a wooden stake through this one and prevent
it from haunting us again?

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907
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