[R] negative binomial regression

[ripley@stats.ox.ac.uk]

No modification is required.  The standard way in S to handle offsets is
via the offset() function, and that works in glm.nb.  The offset argument
to R's glm is unnecessary.

See ?Insurance and try
glm.nb(Claims ~ District + Group + Age + offset(log(Holders)),data = 
       Insurance)

(which is not over-dispersed and so gives some warnings).


On Mon, 24 Mar 2003, Ross Nelson wrote:

> I would like to know if it is possible to perform negative binomial 
> regression with rate data (incidence density) using the glm.nb (in 
> MASS) function.
> 
> I used the poisson regression glm call to assess the count of injuries 
> across census tracts.  The glm request was adjusted to handle the data 
> as rates using the offset parameter since the population of census 
> tracts can vary by a factor of three.
> 
> eg.  Call:
> glm(formula = inj ~ lp + rdm, family = poisson(), data = ww,
>      offset = log(pop))
> 
> Deviance Residuals:
>       Min        1Q    Median        3Q       Max
> -17.2779   -2.6034   -0.4519    2.0837   16.9275
> 
> Coefficients:
>              Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.11593    0.01482 -75.290  < 2e-16 ***
> lp2          0.11569    0.01477   7.835 4.70e-15 ***
> lp3          0.02374    0.01763   1.346    0.178
> lp4          0.17777    0.01922   9.248  < 2e-16 ***
> rdm2        -0.08810    0.01747  -5.044 4.57e-07 ***
> rdm3         0.08750    0.01533   5.706 1.15e-08 ***
> rdm4         0.10513    0.01518   6.925 4.35e-12 ***
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
> 
> 
> inj and pop are interval, while lp and rdm are categorical.
> 
> 
> A test of the dispersion indicates that the data is over dispersed, and 
> thus that an alternative distribution should be used.
> 
> I am not sure, however, if or how to modify the glm.nb to handle this 
> situation.
> 
> glm.nb(formula, ...,  init.theta, link = log)
> 
>   

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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