[R] statistics question about a statement in julian faraway's "extending the linear model with R" text

Peter Dalgaard p.dalgaard at biostat.ku.dk
Mon Jul 14 23:35:53 CEST 2008

markleeds at verizon.net wrote:
> In Julian Faraway's text on pgs 117-119, he gives a very nice, pretty 
> simple description of how a glm can be thought of as linear model
> with non constant variance. I just didn't understand one of his 
> statements  on the top of 118. To quote :
> "We can use a similar idea to fit a GLM. Roughly speaking, we want to 
> regress g(y) on X with weights inversely proportional
> to var(g(y). However, g(y) might not make sense in some cases - for 
> example in the binomial GLM. So we linearize g(y)
> as follows: Let eta = g(mu) and mu = E(Y). Now do a one step 
> expanation , blah, blah, blah.
> Could someone explain ( briefly is fine ) what he means by g(y) might 
> not make sense in some cases - for example in the binomial
> GLM ?
Note that he does say "roughly speaking". The intention is presumably 
that if y is a vector of proportions and g is the logit function, 
proportions can be zero or one, but then their logits would be minus or 
plus infinity. (However, that's not the only thing that goes wrong; the 
model for g(E(Y)) is linear, the expression for E(g(y)) in general is not.)

   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

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