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DESCRIPTION

Produces a generalized linear model family object. The Digamma distribution is the distribution of the unit deviance for a gamma generalized linear model.

 

USAGE

Digamma(link = "log")

 

OPTIONAL ARGUMENTS

link

link function. See quasi in the S-Plus help for specification of this argument.

VALUE

A family object, which is a list of functions and expressions used by glm and gam in their iteratively reweighted least-squares algorithms. See family.object in the S-Plus help for details.

 

DETAILS

This family is useful for generalized linear dispersion modelling. The Digamma distribution is closed related to the Chisquare. For small means it is nearly chiquare on 1 df. For large means it is nearly chisquare on 1df.

The Digamma distribution is so named because it is dual to the gamma distribution in the above sense, and because the digamma function appears in it's mean function.

 

REFERENCES

Smyth, G. K. (1989). Generalized linear models with varying dispersion. J. R. Statist. Soc. B, 51, 47-61.

 

SEE ALSO

Double Generalized Linear Models

 

EXAMPLES

# Fit a Digamma generalized linear model with identity link
glm(y~x,family=Digamma(link="identity"))

# Fit an Digamma glm with power link
glm(y~x,family=Digamma(link=power(1.5))

# Test for log-linear dispersion trend in gamma regression
out.gam <- glm(y~x,family="Gamma(link="log"))
d <- residuals(out.gam)^2
out.dig <- glm(d~x,family="Digamma(link="log"))
summary(out.dig,dispersion=2)

Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004