Bayesian estimation of GEE models I'm facing a problem where I want to model a GEE with a tweedie distribution but it's not implemented in any R package that I found.
I know that GEEs and linear mixture models (LMM) are somehow related but I'm not an expert. It's very easy to define an LMM in Bayesian terms and carry out parameter estimation in rStan for example.
Is there a way to do this for GEEs as well? I'm interested in an example as well.
 A: As far as I know, this is not possible. GEE uses estimating equations for the various moments. The benefit of this approach is that you don't have to write down a likelihood and make the assumptions therein, however this also makes it limited in terms of using Bayesian methods that require specification of a likelihood. Here is a link https://ete-online.biomedcentral.com/articles/10.1186/s12982-015-0030-y
A: I agree with Zach's answer, GEE is inherently a frequentist technique. There are Bayesian analogs to estimating equations (see also the last chapter of Small and Wang's book), but it's not exactly the same thing. The only property of the Tweedie family that is needed by GEE is the power law relationship between mean and variance. So, in principle there is no reason you couldn't fit a GEE that is consistent with a Tweedie outcome. For example, there is a function called geeglm in the R package geepack that accepts GLM family objects. You could pass in the tweedie family from the statmod package.
