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Re: st: gamma constraints using glm
At 16:24 17/07/02 +0100, Toby Andrew wrote:
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
Could anyone tell me how to constrain a gamma distribution to chi-squared
using GLM in Stata 7.0?
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.
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
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