From J.T.Kent@leeds.ac.uk  Fri Nov 16 10:35:13 2001
From: J.T.Kent@leeds.ac.uk (J.T.Kent@leeds.ac.uk)
Date: Fri, 16 Nov 2001 11:35:13 +0100 (MET)
Subject: [Rd] pearson residuals in glm for binomial response (PR#1175)
Message-ID: <200111161035.LAA27495@pubhealth.ku.dk>

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.

Thank you.

Professor John T. Kent         tel (direct)   (44) 113-233-5103
Department of Statistics       tel(secretary) (44) 113-233-5101
University of Leeds            fax            (44) 113-233-5090
Leeds LS2 9JT, England         e-mail: J.T.Kent@leeds.ac.uk

Input:

x_1:4 # regressor variable
y_c(2,6,7,8) # response binomial counts
n_rep(10,4) # number of binomial trials
ym_cbind(y,n-y) # response variable as a matrix
glm1_glm(ym~x,binomial) # fit a generalized linear model
f_fitted(glm1)
rp1_(y-n*f)/sqrt(n*f*(1-f)) # direct calculation of pearson residuals
rp2_residuals(glm1,type="pearson") # should be pearson residuals
rd_residuals(glm1) # deviance residuals
cbind(rp1,rp2,rd) # note second column is wrong, in this case by factor of 10

Output:

             rp1          rp2          rd
[1,] -0.56502992 -0.056500696 -0.58467936
[2,]  0.73739407  0.073739452  0.73886417
[3,]  0.05266796  0.005266533  0.05279174
[4,] -0.38314283 -0.038307944 -0.37010220
> 

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[Rd] pearson residuals in glm for binomial response (PR#1175)
J.T.Kent@leeds.ac.uk