[R-sig-ME] A mixed effect regression tool based on bayesian priors like bayesglm

[Angelo D'Ambrosio]

I use extensively Gelman's bayesglm for the every day use due to the great
stability of the estimates especially in the case of separation.

I needed an equivalent of empirical bayesian regularization for glm mixed
effect models. These models are strongly influenced by extreme conditions
(like conditional probabilities of zero and separation) and like usual
logistic regression model they fail in these cases.

I found the blme package that does exactly what I need, solving the
separation problem. Now the problem is to set it up in order to be work
exactly as bayesglm, in order to achieve consistency in my analysis.
Reading Gelman paper on bayesglm() I understood I should use a t
distribution with 1 df (eg. Cauchy) and 2.5 scale, rescaling inputs:

    bglmer(Out ~ arm::rescale(Pred) + (1 | PatientID), family = binomial,
Data.events, fixef.prior = t(df = 1, scale = 2.5))

Is it correct? My doubt is what to do with the cov.prior parameter; should
I leave it as default (wishart) or should I put it to NULL? Also in
Gelman's paper it is said that the intercept should have the same prior
distribution but with scale 10, and I don't know how to specify a different
prior for it.

Also, I'm starting to think that bayesglm doesn't rescale the inputs
directly but scales the prior distribution according to the inputs. Am I
right?

Can you help me with this?

Thanks

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