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

Usage

gamma.shape.glm(fm, it.lim=10, 
		eps.max=.Machine$double.eps^0.25, verbose=FALSE)

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 TRUE, 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

data(quine)
gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn, 
		quasi(link=log, variance=mu^2), quine, start=rep(0,32))
gamma.shape(gm, verbose=TRUE)

Initial estimate: 1.0603 
Iter.  1  Alpha: 1.23840774338543 
Iter.  2  Alpha: 1.27699745778205 
Iter.  3  Alpha: 1.27834332265501 
Iter.  4  Alpha: 1.27834485787226 
               
Alpha: 1.27834
   SE: 0.13452

summary(gm, dispersion = gamma.dispersion(gm))  # better summary
    ....


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