Regarding glm.nb and the theta parametre.

[AlexMillando]

Hi folks,

I have been doing a negative binomial regression model using the following code (note that MASS package is used for glm.nb)
set.seed(1234)
(y <- rnbinom(100, mu = 3.2, size= 3.2 / 7))
fit.what <- glm.nb(y~1)
summary(fit.what)
exp(fit.what$coefficients)

My mu-estimate here comes out as 3.48. (the exponential of the intercept).

The data was taken randomly (with set seed) from a distribution with mu at 3.2 so yeah it makes sense for it to be this close. BUT
When i try and find the maximum likelihood function it appears to be peaking at a mu value of around 3.13, which to me doesn't make much sense. Why aren't these to mu's the same. I would assume the GLM.NB is using the maximum likelihood estimator on a log-scale?¨

Here is the loglikelihoodfunction

LL <- function(my)
{
R=dnbinom(y,mu=my,size=my/7)
sum(log(R))
}
logLike <- Vectorize(LL)
LL(3.13425)
par(mfrow=c(1,1))
curve(logLike,from=2,to=4,xname="my")

[technocrat]

Hi, could you edit to make the code copy able, please, as reproducible example, called a reprex?

I know it's not all that long, but peeps are much more likely to take a look if they can just cut and paste.