[R] negative binomial regression
Ross Nelson
rnelson at cariboo.bc.ca
Mon Mar 24 20:40:45 CET 2003
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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