glm.nb
A modification of the system function glm()
to include
estimation of the additional parameter, theta
, for a
Negative Binomial generalized linear model.
 Keywords
 models, regression
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
 formula, data, weights, subset, na.action, start, etastart, mustart, control, method, model, x, y, contrasts, …

arguments for the
glm()
function. Note that these excludefamily
andoffset
(butoffset()
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
oridentity
.
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
.
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 loglikelihood function.
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
See Also
glm
, negative.binomial
,
anova.negbin
, summary.negbin
,
theta.md
There is a simulate
method.
Examples
library(MASS)
quine.nb1 < glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)
quine.nb2 < update(quine.nb1, . ~ . + Sex:Age:Lrn)
quine.nb3 < update(quine.nb2, Days ~ .^4)
anova(quine.nb1, quine.nb2, quine.nb3)