Find the maximum likelihood estimate of the shape parameter of
the gamma distribution after fitting a `Gamma`

generalized
linear model.

```
# S3 method for 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.

List of two components

the maximum likelihood estimate

the approximate standard error, the square-root of the reciprocal of the observed information.

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.

Venables, W. N. and Ripley, B. D. (2002)
*Modern Applied Statistics with S.* Fourth edition. Springer.

# NOT RUN { 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) 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) summary(gm, dispersion = gamma.dispersion(gm)) # better summary # }

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