glm.nb { MASS }R Documentation

Fit a Negative Binomial Generalized Linear Model

Description

A modification of the system function < code >glm() to include estimation of the additional parameter, < code >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
formula, data, weights, subset, na.action, start, etastart, mustart, control, method, model, x, y, contrasts, ...

arguments for the < code >glm() function. Note that these exclude < code >family and < code >offset (but < code >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 < code >log, < code >sqrt or < code >identity.

Details

An alternating iteration process is used. For given < code >theta the GLM is fitted using the same process as used by < code >glm(). For fixed means the < code >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 < code >theta are controlled by the < code >maxit parameter of < code >glm.control.)

Setting < code >trace > 0 traces the alternating iteration process. Setting < code >trace > 1 traces the < code >glm fit, and setting < code >trace > 2 traces the estimation of < code >theta.

Value

A fitted model object of class < code >negbin inheriting from < code >glm and < code >lm. The object is like the output of < code >glm but contains three additional components, namely < code >theta for the ML estimate of theta, < code >SE.theta for its approximate standard error (using observed rather than expected information), and < code >twologlik for twice the log-likelihood function.

References

Venables, W. N. and Ripley, B. D. (2002) < em >Modern Applied Statistics with S. Fourth edition. Springer.

See Also

< code >glm, < code >negative.binomial, < code >anova.negbin, < code >summary.negbin, < code >theta.md

There is a < code >simulate method.

Examples
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)

[ Package MASS version 7.3-51.1 Index ]