[R] negative binomial regression

[Ross Nelson]

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)

  
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