Hi All,

I am working on a hierarchical model for an ordinal outcome using
MCMCglmm.  I am running into substantial mixing issues, to the point it is
essentially becoming an intractable model.  Here is the general structure:

MCMCglmm(outcome~ trait + fixed effects,
  data = dat, family = "categorical",
  random = ~ ID1 + ID2,
  rcov = ~ idh(trait):units,
  start = list(
    R = diag(2),
    G = startsG[[i]]),
  prior = list(
    B = list(mu = rep(0, 28), V = diag(28) * c(1e4, rep(20, 27))),
    R = list(V = diag(2), fix = 1),
    G = list(
      G1 = list(V = diag(1) * .02, nu = 1, alpha.mu = 0, alpha.V = 3000),
      G2 = list(V = diag(1) * .02, nu = .02)
    )),
  pr=TRUE, pl=TRUE, saveX = TRUE, saveZ = TRUE, saveXL = TRUE,
  nitt = 1e6, thin = 1000, burnin = 1e5, slice=TRUE, verbose=TRUE)


The estimated variance for ID1 is usually around 25, and for ID2 around 2.
Observations are cross classified so that is why the IDs have separate,
uncorrelated effects.  There are three levels to the outcome.

There are about 7,000 total observations, 1100 ID1s, and 35 ID2s, so the
sample is not small, nor are the number of level 2 units low.

The outcome is not nearly balanced:

round(table(dat$dv)/nrow(dat), 3)
    0     1     2
0.839 0.094 0.067
still, there is variability.  I have tried variety of different priors on
the random effects with and without parameter expansion to very little
effect.  I can also say that for some ID1s, there is near complete
separation (i.e., the probability of being a 0 is almost 1), but this is
not true for most ID1s.

>From 1 million iterations, with a 100,000 burnin, I am getting an effective
sample size for the ID1 random effect < 100.  I am pretty much out of ideas
on what I can do to help the chains mix better or decrease autocorrelation
in MCMCglmm.  In BUGS I might try a different prior distribution or
something, but there is only one option here.  Does anyone have ideas?
Suggested reading?  I'm pretty much open to anything and more than willing
to work a lot for it at this point.

Cheers,

Josh


-- 
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://joshuawiley.com/
Senior Analyst - Elkhart Group Ltd.
http://elkhartgroup.com

	[[alternative HTML version deleted]]

