On Fri, 26 Oct 2007, Jonas Malmros wrote:
> Hello,
>
> My response variable seems to be distributed according to Student t
> with df=4. I have 320 observations and about 20 variables.
> I am wondering whether there is a way to fit glm with Student t for
> error distribution. Student t is not one of the family choices in glm
> function.
Why should the error distribution be the same as the distribution of the
response variable? It almost certainly is not.
A linear model with t-distributed errors is not a GLM. There are several
ways in R to fit such a model, but you are almost certainly better off
using a general robust linear model, e.g. rlm in package MASS. Looking at
the residuals from such a fit may give you a reasonable idea of plausible
error distributions, if the 'true' model were close to linear in the
explanatory variable provided (and no others).
> How should I proceed to fit glm with Student t?
> I know that Student t is the Inverse Gamma with shape parameter equal
> to degrees of freedom (=4).
That depends on your definition of 'Inverse Gamma', but that at e.g.
http://en.wikipedia.org/wiki/Inverse-gamma_distribution is a distribution
on (0, Inf), unlike the t.
> Would it be correct then to specify Gamma
> family and inverse link in the glm function?
No.
(I think you need to read up about what a GLM is.)
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595