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
....