[R-sig-ME] Identifying link functions for gamma glmm

[Rolf Turner]

On Fri, 19 Nov 2021 13:38:14 -0700
Tahsin Ferdous <tahsinferdousuofc using gmail.com> wrote:

> I am running a generalized linear mixed model with a gamma family.
> How can I understand which link function I should use (log link,
> identity link, or inverse link)? I tried to plot observed vs fitted
> values plots. But they look similar? Should I look at AIC? If I fit a
> gamma glm, should I also look at AIC to know which link function I
> should use in my model?
> 
> If I fit gamma GEE . should I look at QIC for choosing the appropriate
> model with link function?

I used a cross-validation approach, in a somewhat similar context.  I
tried both leave-one-out and k-fold cross-validation, with moderate
success.  The complete story is complicated, and has an unsatisfactory
ending (I wound up getting answers that the client did not like!) so
I shall not go into any more detail.

OTOH if your plots "look similar", perhaps it doesn't really matter.
Can you think of a criterion for deciding whether it *does* matter?

cheers,

Rolf Turner

-- 
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276