gamma.shape {MASS}  R Documentation 
Find the maximum likelihood estimate of the shape parameter of
the gamma distribution after fitting a Gamma
generalized
linear model.
## S3 method for class 'glm': gamma.shape(object, it.lim = 10, eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)
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. 
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.
List of two components
alpha 
the maximum likelihood estimate 
SE 
the approximate standard error, the squareroot of the reciprocal of the observed information. 
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
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) ## Not run: Alpha: 538.13 SE: 253.60 ## End(Not run) 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) ## Not run: 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 ## End(Not run) summary(gm, dispersion = gamma.dispersion(gm)) # better summary