Estimate the Shape Parameter of the Gamma Distribution in a GLM Fit

Usage

gamma.shape.glm(fm, it.lim=10, 
		eps.max=sqrt(.Machine$single.eps), verbose=F)

Arguments

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

Description

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

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.

Value

List of two components called alpha and SE giving the maximum likelihood estimate and approximate standard error respectively. The latter is the square-root of the reciprocal of the observed information.

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)

                
Alpha: 538.13
   SE: 253.60

> gm <- glm(Days ~ Age*Eth*Sex*Lrn, 
		quasi(link=log, variance=mu^2), quine)
> gamma.shape(gm, verbose=T)
Initial estimate: 2.496504 
Iter.  1  Alpha: 1.52639010555267 
Iter.  2  Alpha: 1.76127471069498 
Iter.  3  Alpha: 1.80662722216594 
Iter.  4  Alpha: 1.80790983354237 
Iter.  5  Alpha: 1.80791080638548 

                 
Alpha: 1.80791
   SE: 0.19522
> summary(gm, dispersion = gamma.dispersion(gm))  # better summary
    ....


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