# gamma.shape

##### 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 `Gamma`

generalized
linear model.

- Keywords
- models

##### Usage

```
# S3 method for glm
gamma.shape(object, it.lim = 10,
eps.max = .Machine$double.eps^0.25, verbose = FALSE, …)
```

##### Arguments

- 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.

##### 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

the maximum likelihood estimate

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

##### References

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

##### See Also

##### Examples

```
# 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
# }
```

*Documentation reproduced from package MASS, version 7.3-51.1, License: GPL-2 | GPL-3*