# [Rd] Pearson residuals (PR#1123)

**Peter Dalgaard BSA
**
p.dalgaard@biostat.ku.dk

*10 Oct 2001 13:13:41 +0200*

carmen@mcs.st-and.ac.uk writes:
>* I think there is a problem when computing Pearson residuals, in that they seem
*>* to be computed at the raw residuals divided by the square root of the
*>* corresponding diagonal element of the weight matrix W evaluated at the last step
*>* of the iterative model fitting procedure (IWLS), instead of dividing by the
*>* square root of the model variance. Here's an example of the weird effects it
*>* produces:
*>*
*>* > me <- c(1:100)/2
*>* > y <- rpois(100,me)
*>* > yglm <- glm(y~me-1, family=poisson(link="identity"))
*>* > plot(fitted(yglm), residuals(yglm,type="response"))
*>*
*>* plots the raw residuals... but
*>*
*>* > plot(fitted(yglm), residuals(yglm,type="pearson"))
*>*
*>* plots the raw residuals MULTIPLIED by sqrt(fitted(yglm))... because it
*>* computes the Pearson residuals dividing by the square root of the diagonal
*>* element of the weight matrix W (at the end of the iterative fitting process)
*>* rather than dividing by the sqrt of variance.
*
Um, right... At the very least, there's a "/" that should have been
"*". But do we also divide by the dispersion (when it is estimated)? I
forget what the definition says.
--
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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