MASS (version 7.3-57)

gamma.shape: Estimate the Shape Parameter of the Gamma Distribution in a GLM Fit

Description

Find the maximum likelihood estimate of the shape parameter of the gamma distribution after fitting a Gamma generalized linear model.

Usage

# S3 method for glm
gamma.shape(object, it.lim = 10,
            eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)

Value

List of two components

alpha

the maximum likelihood estimate

SE

the approximate standard error, the square-root of the reciprocal of the observed information.

Arguments

object

Fitted model object from a Gamma family or quasi family with variance = "mu^2".

it.lim

Upper limit on the number of iterations.

eps.max

Maximum discrepancy between approximations for the iteration process to continue.

verbose

If TRUE, causes successive iterations to be printed out. The initial estimate is taken from the deviance.

...

further arguments passed to or from other methods.

Details

A glm fit for a Gamma family correctly calculates the maximum likelihood estimate of the mean parameters but provides only a crude estimate of the dispersion parameter. This function takes the results of the glm fit and solves the maximum likelihood equation for the reciprocal of the dispersion parameter, which is usually called the shape (or exponent) parameter.

References

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

See Also

gamma.dispersion

Examples

clotting <- data.frame(
    u = c(5,10,15,20,30,40,60,80,100),
    lot1 = c(118,58,42,35,27,25,21,19,18),
    lot2 = c(69,35,26,21,18,16,13,12,12))
clot1 <- glm(lot1 ~ log(u), data = clotting, family = Gamma)
gamma.shape(clot1)

gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn,
          quasi(link=log, variance="mu^2"), quine,
          start = c(3, rep(0,31)))
gamma.shape(gm, verbose = TRUE)
summary(gm, dispersion = gamma.dispersion(gm))  # better summary