[R] glm.nb versus glm estimation of theta.

[Bill.Venables at csiro.au]

Whoa!  Just hang on a minute.

theta is NOT the dispersion parameter.   Under the NB model, the variance of an observation is mu+mu^2/theta, so that's how theta enters the picture.  The smaller theta is the larger the variance.

glm(..., family = negative.binomial(theta = <something>), ...)  

will NOT estimate theta.  It will estimate a dispersion parameter, and if you get your <something> wrong, it could be a silly estimate.  One would hope the estimate of the dispersion parameter would be close to unity.

With your data try

mod2 <- glm(count ~ year + season + time + depth,
  family = negative.binomial(theta=mod$theta),link = "log",
  data = dat, control = glm.control(maxit=100, trace=T))

You should get the same estimates as you got with the negative binomial model (though standard errors, &c, will differ because you have cheated on that), and your dispersion parameter should be close to (though not necessarily equal to) unity.
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of hesicaia [dboyce at dal.ca]
Sent: 14 August 2009 04:31
To: r-help at r-project.org
Subject: [R]  glm.nb versus glm estimation of theta.

Hello,

I have a question regarding estimation of the dispersion parameter (theta)
for generalized linear models with the negative binomial error structure. As
I understand, there are two main methods to fit glm's using the nb error
structure in R: glm.nb() or glm() with the negative.binomial(theta) family.
Both functions are implemented through the MASS library. Fitting the model
using these two functions to the same data produces much different results
for me in terms of estimated theta and the coefficients, and I am not sure
why.

the following model:
mod<-glm.nb(count ~ year + season + time + depth,
link="log",data=dat,control=glm.control(maxit=100,trace=T))
estimates theta as 0.0109

while the following model:
mod2<-glm(count ~ year + season + time + depth,
family=negative.binomial(theta=100),link="log",data=dat,control=glm.control(maxit=100,trace=T))
will not accept 0.0109 as theta and instead estimates it as 1271 (these are
fisheries catch data and so are very overdispersed).

Fitting a quasipoisson model also yields a large dispersion parameter
(1300). The models also produce different coefficients and P-values, which
is disconcerting.

What am I doing wrong here? I've read through the help sections
(?negative.binomial,?glm.nb, and ?glm) but did not find any answers.

Any help and/or input is greatly appreciated!
Daniel.
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