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

[James Rudge]

Dear Vince,

Great, it seems to be working well! Thanks so much.

James

Date: Fri, 18 Dec 2015 12:29:41 -0500
Subject: Re: [R-sig-ME] priors for fixed-effect covariates using bglmer - centering the t-distribution?
From: vjd4 at nyu.edu
To: james_980 at hotmail.com
CC: r-sig-mixed-models at r-project.org

I can't remember why I didn't add prior means for fixed effects - I think it had to do with not breaking the profiling scheme of lme4 and the ability to roughly achieve the same thing through linear transformations of the covariates.
Regardless, I just added them to t priors in the source repository on Github (https://github.com/vdorie/blme). It works as you might expect, where the the specifying function takes a "mean" argument of length 1, 2, or the number of fixed effects, where if it length 2 the first term applies just to the intercept and the second is used for all the slopes.
Let me know if you end up using it and encountering any trouble. Before I submit to CRAN I would have to think some more about the case of normal priors and do some additional testing.
Vince
On Fri, Dec 18, 2015 at 4:15 AM, James Rudge <james_980 at hotmail.com> wrote:
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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