Re: st: gamma constraints using glm

[Roger Newson <roger.newson@kcl.ac.uk>]

At 16:24 17/07/02 +0100, Toby Andrew wrote:
> Dear Statalist,
>
> Could anyone tell me how to constrain a gamma distribution to chi-squared 
> using GLM in Stata 7.0?
You don't specify why you wish to do this. However, a chi-squared 
distribution with k degrees of freedom is simply a gamma distribution with 
inverse squared coefficient of variation k/2 and scale parameter 1/2, or, 
equivalently, with mean k and variance of 2k. If you don't want to 
constrain k to be an integer, then you are effectively using the Poisson 
variance function variance=phi*mu, fixing phi=2. If you want to constrain k 
to be an integer, then you are getting outside the framework of generalized 
linear models.

You don't say what link you are using. However, if you use

glm y x1-xn, family(poisson) scale(2) link(whatever_you_want_to_use)

and ignore any message about non-integer y-values, then you will be fitting 
maximum quasi-likelihood estimates with the correct link and variance 
function for a chi-squared distribution. In generalized linear models, the 
-family- option specifies a variance function, ie a function for deriving 
the variance from the mean and a single parameter phi, and the -link- 
option specifies a function defining the mean as a function of sum(x_j*beta_j).

I hope this helps.

Roger


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
  or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk

Opinions expressed are those of the author, not the institution.

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/