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Re: st: OLS assumptions not met: transformation, gls, or glm as solutions?


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: OLS assumptions not met: transformation, gls, or glm as solutions?
Date   Tue, 18 Dec 2012 20:02:40 +0100

On Tue, Dec 18, 2012 at 7:24 PM, Laura R. wrote:
> I thought generalized linear models (this is what I meant with glm)
> support different distributions of the dependent variable y, not the
> residuals.

You are right, it is a model for the conditional distribution of y and
not the residuals. This means that the marginal distribution for the
dependent variable can deviate considerably from the unconditional
distribution that gave your model its name. See:
<http://www.maartenbuis.nl/software/margdistfit.html>. This is not a
problem, but you do need to take that into account when you diagnose
your problem.

Only in special cases (e.g. the normal/Gaussian distribution) does the
distribution of the residuals correspond to the unconditional
distribution.

> My dependent variable and the residuals are both right
> skewed, so maybe glm with inverse gaussian would be good.

Maybe, but I should not get carried away like that. I can very well
imagine that it is better in your case to stick to simple linear
regression with robust standard errors. I realise that this
contradicts some other advise you have been given. This is a sign that
you have come at a point where the decision has to be based on the
specifics of your study, which means that we can no longer help you.

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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