[R] accuracy of GLM dispersion parameters

[Gavin Simpson]

On Tue, 2010-11-30 at 08:54 -0800, Timothy_Handley at nps.gov wrote:
> >From Ben Bolker:
> >  I would trust the gamma.dispersion() result more, although I
> >agree that the difference is worrisome.  The way to look at this
> >further would be to profile the dispersion parameter.  As I recall
> >there isn't such a built in option in MASS (profile.glm only
> >profiles the coefficients), but you may be able to do it
> >*approximately* like this:
> >
> >library(bbmle)
> >m1 <- mle2(precip_sbi ~ dgamma(shape=a,scale=mu/a),
> >   parameters=list(mu~precip_oxx+precip_oxx_sq),
> >   data=w.combo, start=list(mu=0.1,a=2))
> >p1 <- profile(m1)
> >plot(p1)
> 
> Ben: Thanks for the suggestion. I ran the code you sent, and according to
> the graphical profile, the 99% confidence interval for shape is [.4, .7],
> corresponding to a 99% interval for the dispersion parameter of [1.4, 2.5].
> So your profile tool agrees with gamma.dispersion().
> 
> I now feel more somewhat more comfortable about gamma.dispersion(), but I'm
> still worried by the difference between summary() and gamma.dispersion().
> While I have a basic understanding of GLM's, I don't understand why the
> reported value for dispersion would be 'crude'. Note that the word 'crude'
> comes from help(gamma.shape) {MASS}.
> 
> If you or anyone else could help me further understand this issue, I'd
> greatly appreciate it.

Tim,

MASS is support software for Venables' and Ripley's 'Modern Applied
Statistics with S'. So I would normally suggest you consult that book
for details. However, the authors cover this (Gamma GLM) in their online
complements to the book, the pdf of which can be located here:

http://www.stats.ox.ac.uk/pub/MASS4/VR4stat.pdf

There are several pages on the topic under discussion here.

HTH

G

> 
> Tim Handley
> Research Assistant
> Channel Islands National Park
> (Will be working from both CHIS and SAMO)
> CHIS Phone: 805-658-5759 (Tue, Wed, Thu)
> SAMO Phone: 805-370-2300 x2412(Mon, Fri)
> 
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