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Identifying link functions for gamma glmm

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?