[R-sig-ME] MCMCglmm for binomial models?

[Bob Farmer]

Thanks for the further detail.  I wasn't familiar with these two
methods of overdispersion; I think I only understood them in the
WinBUGS sense, which, I believe, is additive (e.g. overdisp[i] as a
parameter).  I'll have to explore the family() helpfiles a bit more.

Below is a summary of the model outputs from the three methods
described earlier.  Note that here, I bumped the WinBUGS iterations to
750E3 to reduce the Rhats a bit further.
I also use an adaptation of the bugsParallel function to make my
WinBUGS runs 3x faster (time for this run:  5.8 minutes); I can
provide details if anybody else would like to use this function (and
some other bugs summary functions I've written).
Hope this is useful or interesting -- I appreciate this discussion!

--Bob

**glmer**
> summary(gm3)@coefs
              Estimate Std. Error   t value
(Intercept) -1.3985351 0.01698321 -82.34810
period2     -0.9923347 0.02275838 -43.60304
period3     -1.1286754 0.02429833 -46.45075
period4     -1.5803739 0.03195596 -49.45474

**MCMCglmm**
> summary(mc3)
 Iterations = 749351
 Thinning interval  = 100001
 Sample size  = 1000
 DIC: 539.7889
 G-structure:  ~herd
     post.mean  l-95% CI u-95% CI eff.samp
herd    0.2894 1.309e-06    1.035     1000
 R-structure:  ~units
      post.mean l-95% CI u-95% CI eff.samp
units      0.93 0.003825     1.98     1000
 Location effects: cbind(incidence, size - incidence) ~ period
            post.mean l-95% CI u-95% CI eff.samp  pMCMC
(Intercept)   -1.5263  -2.2221  -0.9602   1000.0 <0.001 ***
period2       -1.2407  -2.2072  -0.2449    947.2  0.012 *
period3       -1.3574  -2.4534  -0.3472   1000.0  0.012 *
period4       -1.9126  -3.2662  -0.8298   1136.0  0.002 **

**WinBUGS**
> bug3$summary[which(rownames(bug3$summary) %in% params), c("mean", "sd", "2.5%", "97.5%", "Rhat", "n.eff")]
                     mean        sd        2.5%      97.5%     Rhat n.eff
B.0            -1.6070301 0.3556674 -2.33980000 -0.9947425 1.039548    69
B.period2      -1.2761798 0.4895902 -2.14292500 -0.2391200 1.018612   210
B.period3      -1.5100405 0.6337780 -2.63680000 -0.2266425 1.123427    22
B.period4      -2.0678331 0.6539004 -3.31892500 -0.8586700 1.018622   270
sigma.overdisp  1.1975969 0.3147531  0.69358404  1.8740000 1.045062    55
sigma.b.herd    0.5120043 0.3825848  0.01658429  1.3659249 1.542432     7
(note that I can provide a link to parameter histograms, if you want
more detail)

--Bob