I'm trying to get some model averaged effect sizes from a set of candidate models, all of them assuming a Gamma error distribution, according to the theory given by the book from Burnham and Anderson (2002).

For the calculation I'm using the function modavg from the R package AICcmodavg by Marc J. Mazerolle. In the help pages of the modavg function it says:

if gamma GLM is used, the dispersion parameter should be specified here to apply the same value to each model.

This seems somewhat counterintuitive, as applying the same dispersion to all candidate models would result in a "non-MLE" situation. I did not find any literature addressing this issue.

Can you confirm Mazerolles restriction to one equal dispersion estimate and/or suggest some literature on that?

Burnham, K. P., Anderson, D. R., 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd Edition. Springer-Verlag.


Or, to ask in a different way:

When averaging parameter estimates and standard errors - Is there a reason that for GLMs with Gaussian family you should take the different estimated dispersions, whereas for Gamma family you should take only one single dispersion?



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