[R] Goodness of fit for negative binomial model

[Paul Johnson]

On Fri, Mar 20, 2009 at 8:03 PM, t c <mudiver1200 at yahoo.com> wrote:
> Dear r list,
>
> I am using glm.nb in the MASS package to fit negative binomial models to data on manta ray abundance, and AICctab in the bbmle package to compare model IC.  However, I need to test for the goodness of fit of the full model, and have not been able to find a Pearson's Chi Squared statistic in any of the output.  Am I missing it somewhere?  Is there a way to run the test using either chisq.test() or goodfit()?  I would appreciate any suggestions on how to test for goodness of fit in negative binomial models.
>
> Thanks,
>
> Tim Clark

I found myself wondering if the Chi Square you get from anova() is the
Pearson one you want?  (see ?anova.negbin).

Just an example:



> library(MASS)
> example(glm.nb)
> anova(quine.nb3)
Analysis of Deviance Table

Model: Negative Binomial(1.9284), link: log

Response: Days

Terms added sequentially (first to last)


                 Df Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL                               145    272.291
Sex               1    1.705       144    270.586     0.192
Sex:Age           6   30.202       138    240.384 3.599e-05
Sex:Eth           2   20.461       136    219.923 3.606e-05
Sex:Lrn           2    8.459       134    211.465     0.015
Sex:Eth:Lrn       2   18.287       132    193.178 1.069e-04
Sex:Age:Lrn       4    8.649       128    184.529     0.070
Sex:Age:Eth       6    9.503       122    175.025     0.147
Sex:Age:Eth:Lrn   4    7.572       118    167.453     0.109
Warning message:
In anova.negbin(quine.nb3) : tests made without re-estimating 'theta'
>

That warning about re-estimating theta concerns me a bit.

If that's not the correct Pearson statistic, I bet you can get what
you need if you take the Pearson residuals and calculate whatever.  I
am looking at

?residuals.glm

and I note you can get Pearson residuals.  If you have a formula from
a dusty old stats book with the formula, I bet you can get it done.

pj
-- 
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas