Estimate the Shape Parameter of the Gamma Distribution in a GLM Fit
Find the maximum likelihood estimate of the shape parameter of
the gamma distribution after fitting a
## S3 method for class 'glm': gamma.shape(object, it.lim = 10, eps.max = .Machine$double.eps^0.25, verbose = FALSE, \dots)
- Fitted model object from a
variance = "mu^2".
- Upper limit on the number of iterations.
- Maximum discrepancy between approximations for the iteration process to continue.
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 square-root 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) Alpha: 538.13 SE: 253.60 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) 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