Difference between glm, family(nbinomial 1) link(log) and nbreg ?

[Dan Su]

Hi experts,

I want to use negative binomial regression and was wondering what's the difference between "glm, family(nbinomial 1) link(log)" and "nbreg" ? Thank you!

[Clyde Schechter]

In the PDF manuals that come with your Stata installation, in the -glm- chapter of the [R] volume, you could have found this:

Some family() and link() combinations result in models already fit by Stata. These are
family() link() Options Equivalent Stata command
gaussian identity nothing j irls j irls vce(oim) regress
gaussian identity t(var) vce(hac nwest #) newey, t(var) lag(#) (see note 1)
vfactor(#v)
binomial cloglog nothing j irls vce(oim) cloglog (see note 2)
binomial probit nothing j irls vce(oim) probit (see note 2)
binomial logit nothing j irls j irls vce(oim) logit or logistic (see note 3)
poisson log nothing j irls j irls vce(oim) poisson (see note 3)
nbinomial log nothing j irls vce(oim) nbreg (see note 4)
gamma log scale(1) streg, dist(exp) nohr (see note 5)

and

4. Family negative binomial, log-link models—also known as negative binomial regression
models—are used for data with an overdispersed Poisson distribution. Although glm can be
used to fit such models, using Stata’s maximum likelihood nbreg command is probably better. In
the GLM approach, you specify family(nbinomial #k) and then search for a #k that results in
the deviance-based dispersion being 1. You can also specify family(nbinomial ml) to estimate
#k via maximum likelihood, which will report the same value returned from nbreg. However,
nbreg also reports a confidence interval for it; see [R] nbreg and Rogers (1993). Of course, glm
allows links other than log, and for those links, including the canonical nbinomial link, you will
need to use glm.

which completely answers your question.

Sorry, I can't seem to get the table from the manual to align nicely in the Forum editor. Neither quote blocks nor code blocks achieves that.

[Dan Su]

Hi experts,

I want to use negative binomial regression and was wondering what's the difference between "glm, family(nbinomial 1) link(log)" and "nbreg" ? Thank you!

Hi Clyde, thanks so much! It seems nbreg is more recommended than glm, but when I use the nbreg, there are too many iterations and stata keep running, but glm is fine without causing any errors. And I found I got same coef by using both but different CI.