[R-sig-ME] priors for fixed-effect covariates using bglmer - centering the t-distribution?

[James Rudge]

I'm trying to fit a mixed effects model with a pig Disease as the binary outcome, Water.Source as a categorical fixed effects predictor, and Herd as random effects.
However I have quasi-complete separation of the outcome, with no disease events in some categories of Water.Source, so a GLMM model will not converge.

So I'm now trying to define a weak prior for the fixed effects using bglmer, as suggested by Ben Bolker in this helpful post: http://stats.stackexchange.com/questions/132677/binomial-glmm-with-a-categorical-variable-with-full-successes

For choosing the prior for the fixed effects, I'd like to follow this reference:
José Cortiñas Abrahantes and Marc Aerts (2012) A solution to separation for clustered binary data Statistical Modelling 12(1):3–27  doi: 10.1177/1471082X1001200102 

They propose using a Cauchy (t1) distribution, centered around  the value of the beta coefficient (call it beta.f) estimated using Firth's penalized maximum likelihood method for the variable in question (i.e. ignoring the random effects), with scale equal to 2 times the variance (call it var.f) also estimated from the Firth logistic regression model.

So I have the following for my model so far, which scales the t-distribution by 2*var.f, how can I also center it around beta.f?

bglmer(Disease~Water.Source+(1|Herd), data=pigdat,
                  family=binomial,
                  fixef.prior=t(df=1, scale=2*var.f))

Thanks in advance!
 		 	   		  
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