The re-estimated version is the principled one -- the other is a
computational shortcut.
However, what you model might choose depends on why you are doing model
selection, and also if there is a subject-specific reason to consider the
terms in this order.
And if you look in MASS (the book) you will see a similar example and
discussion of how to treat it. It uses dropterm(), which is likely to be
preferable to either of these approaches.
On Mon, 7 Apr 2008, Nelson, Gary (FWE) wrote:
Hi All,
I am using the glm.nb function from the MASS package (current version)
to fit and compare GLMs with negative binomial error distributions. My
question is: what is the appropriate method to use in the anova function
to compare models? If only one fitted object like
m-glm.nb(number-p+sal+temp,data=data)
is specified in the anova function (anova(m)), a fixed theta is used to
generate the analysis of deviance:
Analysis of Deviance Table
Model: Negative Binomial(0.2345), link: log
Response: number
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev P(|Chi|)
NULL117122.707
p 1 11.327 116111.380 0.001
sal12.286 115109.094 0.131
tem11.979 114107.115 0.159
ph 12.567 113104.549 0.109
Warning message:
In anova.negbin(m) : tests made without re-estimating 'theta'
If multiple fitted objects like
m1-glm.nb(number~1,data=data)
m2-glm.nb(number~p,data=data)
m3-glm.nb(number~p+sal,data=data)
m4-glm.nb(number~p+sal+temp,data=data)
is specified (anova(m1,m2,m3,4)), the theta is assumed re-estimated in
each case to calculate the likelihood ratio tests:
Likelihood ratio tests of Negative Binomial Models
Response: number
Model theta Resid. df2 x log-lik. Testdf LR
stat. Pr(Chi)
1 1 0.1892056 117 -527.7463
2 p 0.2153105 116 -517.9349 1 vs 2 1
9.811382 0.001734351
3p + sal 0.2214626 115 -515.7942 2 vs 3 1
2.140706 0.143435894
4 p + sal + tem 0.2261900 114 -513.8846 3 vs 4 1
1.909643 0.167002884
5 p + sal + tem + ph 0.2344827 113 -511.3633 4 vs 5 1
2.521237 0.112322429
The conclusions are the same, but I'd like to know if one method is
favored over the other.
Thanks,
Gary Nelson.
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Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
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