linear model family
- Produces a generalized linear model family object with any power variance function and
any power link. Includes the Gaussian, Poisson, gamma and inverse-Gaussian families as
- tweedie(var.power = 0, link.power = 1-var.power)
- OPTIONAL ARGUMENTS
||index of power variance function
||index of power link function. link.power=0 produces a log-link. Defaults to
the canonical link, which is 1-var.power.
- 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.
- This function provides access to a range of generalized linear model response
distributions which are not otherwise provided by S-Plus, or any other package for that
matter. It is also useful for accessing distribution/link combinations which are
perversely disallowed by S-Plus, such as Inverse-Gaussion/Log or Gamma/Identity.
Let mi = E( yi)
be the expectation of the ith response. We assume that
miq = xiTb, var( yi) = f mip
where xi is a vector of covariates and b is a vector of regression cofficients, for some f, p and q. This family is specified by var.power
= p and link.power = q. A value of zero for q is interpreted
as log(mi) = xiTb.
The variance power p characterizes the distribution of the
responses y. The following are some special cases:
||Compound Poisson, non-negative with mass at zero
||Stable, with support on the positive reals
The name Tweedie has been associated with this family by Jørgensen in
honour of M. C. K. Tweedie.
- Tweedie, M. C. K. (1984). An index which distinguishes between some important
exponential families. In Statistics: Applications and New Directions. Proceedings of
the Indian Statistical Institute Golden Jubilee International Conference. (Eds. J. K.
Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.
- Jørgensen, B. (1987). Exponential dispersion models. J. R. Statist. Soc. B, 49,
- Smyth, G. K. (1996). Regression modelling of quantity data with exact zeroes. Proceedings
of the Second Australia-Japan Workshop on Stochastic Models in Engineering, Technology and
Management. Technology Management Centre, University of Queensland, 572-580. (postscript file)
- Jørgensen, B. (1997). Theory of Dispersion Models, Chapman and Hall, London.
- Smyth, G. K., and Verbyla, A. P., (1999). Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics 10, 695-709.
- SEE ALSO
- Tweedie Distributions, qres, Poison-gamma Distribution, inverse-Gaussian
- # Fit a poisson generalized linear model with identity link
# Fit an inverse-Gaussion glm with log-link
Copyright © 1996-2003. Last modified:
24 December 2002