Gamma Model: Identity Link?

[Paul May]

Hello,

Is there any way for R-inla to provide an identity link for Gamma GLMMs? I understand the issues with this (need to insure linear predictor \eta > 0), but that log transformation is awful strong.

In my particular application, I have repeat observation for each realization of the linear predictor

y_ij ~ Gamma(g^{-1}(\eta_j), scale);   i =1 , ... , n_j

so I can get a decent approximation of \mu_j = g^{-1}(\eta_j) with the sample mean \bar{y}_j. These look plausibly normally distributed, and a log transformation introduces a significant left tail.

Thanks,

Paul