A modification of the system function glm() to include
estimation of the additional parameter, theta, for a
Negative Binomial generalized linear model.
Usage
glm.nb(formula, data, weights, subset, na.action,
start = NULL, etastart, mustart,
control = glm.control(...), method = "glm.fit",
model = TRUE, x = FALSE, y = TRUE, contrasts = NULL, ...,
init.theta, link = log)
arguments for the glm() function.
Note that these exclude family and offset
(but offset() can be used).
init.theta
Optional initial value for the theta parameter. If omitted a moment
estimator after an initial fit using a Poisson GLM is used.
link
The link function. Currently must be one of log, sqrt
or identity.
Value
A fitted model object of class negbin inheriting from glm
and lm. The object is like the output of glm but contains
three additional components, namely theta for the ML estimate of
theta, SE.theta for its approximate standard error (using
observed rather than expected information), and twologlik for
twice the log-likelihood function.
Details
An alternating iteration process is used. For given theta the GLM
is fitted using the same process as used by glm(). For fixed means
the theta parameter is estimated using score and information
iterations. The two are alternated until convergence of both. (The
number of alternations and the number of iterations when estimating
theta are controlled by the maxit parameter of
glm.control.) Setting trace > 0 traces the alternating iteration
process. Setting trace > 1 traces the glm fit, and
setting trace > 2 traces the estimation of theta.
References
Venables, W. N. and Ripley, B. D. (2002)
Modern Applied Statistics with S. Fourth edition. Springer.