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

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Mon, 14 Jul 2008 17:24:24 -0400

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 ?
>

I don't know that text, but I'd guess he's talking about the fact that the expected value of a binomial must lie between 0 and N (or the expected value of X/N, where
X is binomial from N trials, must lie between 0 and 1).

Similarly, the expected value of a gamma or Poisson must be positive, etc.

Duncan Murdoch



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