Hi all,

I'm using MCMCglmm to fit a two-level binary response model. Following
"CourseNotes.pdf" (and various postings on R-SIG-ME), I'm using a parameter
expanded prior:

prior.exp = list(R = list(V = 1, fix = 1), G = list(G1 = list(V = 1, nu =
> 1, alpha.mu = 0, alpha.V = 1000)))


And based on section 8.08 in the course notes, I'm also using a rescaled
residual variance, setting R = list(V = 10, fix = 1). This improves the
chain mixing dramatically, and so seems like a good idea. For example,
using the parameter expanded prior, with V = 1, and running for 2000
iterations:

            post.mean l-95% CI u-95% CI eff.samp  pMCMC

(Intercept)    0.7216   0.3406   1.1267   1643.7  0.001 ***

w2            -1.3178  -1.3897  -1.2357    117.5 <5e-04 ***

w3            -1.3120  -1.3814  -1.2414    144.7 <5e-04 ***


Whereas with V = 10:

            post.mean l-95% CI u-95% CI eff.samp  pMCMC

(Intercept)    1.3262   0.6586   1.9349   1819.3 <5e-04 ***

w2            -2.4290  -2.5791  -2.3001    580.9 <5e-04 ***

w3            -2.4310  -2.5631  -2.3062    560.9 <5e-04 ***

My question, then, is how do I rescale the posteriors so that the results
when V = 1 and V = 10 are comparable. On p. 128 of the course notes the
following formula is given:

c2 <- (16 * sqrt(3)/(15 * pi))^2
> plot(mcmc.list(m7b.1$VCV[, 1]/(1 + c2 * m7b.1$VCV[, "units"]), m7b.3$VCV[,
> 1]/(1 + c2 * m7b.3$VCV[, "units"])))


Could anyone tell me where this comes from? And how it works? It seems I'll
need to rescale both the fixed effects and variance terms.

Many thanks in advance,

Ewan
--
PhD student
Social Statistics, University of Manchester

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