[R-sig-ME] MCMCglmm model and prior specification-incomplete sampling of blocks

[Peter B. Pearman]

Hello MCMCglmm users,

I'm new to mixed models in MCMCglmm and have been trying to get up to
speed by reading in the Course Notes, Overview, Tutorial and items on
this list. I'm hoping that someone would comment on the specification of
the model I'm contemplating. I'm having trouble deciding on the
appropriate specification of the random effects (among other things),
in part because I don't know how to account for potential
non-independence among blocks and sites within block, given that only
one block has been sampled each year.

Some background:
As a preliminary to a study on the power of a monitoring project, I'm
interested in modeling trends in count data (numbers of species) over a
sequence of years, and identifying important sources of variation.
There are 5 blocks of sample sites, with about 60 sites in each block.
The blocks are not geographically distinct, meaning that all the sites
in all blocks are distributed throughout the same area.  Sites are
identified by 'coordID' and are classified by a factor, land.use, with 4
levels.  Each block has been sampled every 5 years in a rotation,
meaning that for each year there are response data for just one block of
sites. Three blocks have been sampled 4 times and two blocks only 3 times.

I have organized the data so that for each year the response,
'richness', has positive integer values for the sites in the block that
was sampled.  For all sites in other blocks that were not sampled in a
year, richness is NA.

Questions and model:
I'd like to know whether the among-site correlations (or covariances)
within blocks are greater than 0. It seems reasonable that values for
sites within a block may be more strongly correlated than values for
sites in different blocks. How I can incorporate and test for
non-independence of sites within block?

Also, how could I incorporate and test for non-zero co-variances among
blocks?  This might be a problem since block and year are confounded.
I should be able to determine whether among-block covariance is
important and should be included, or not, right? Or is this not possible
given this design?

I suggest the following prior:

prior.1 <- list(R = list(V = 1, nu = 0.002), G = list(G1 = list(V = 1,
nu = 0.002)))

(questions: Other priors to consider?  How can I determine whether a
prior is uninformative or not?)

and the following model, to start, realizing that the random
specification could be complete nonsense (large number off-diagonal terms?):

m1 <- MCMCglmm(richness ~ year:land.use -1,
                               random = ~ us(block):coordID,
                               family = "poisson",
                               data = x.3,
                               prior = prior.1,
                               nitt = 100000,
                               thin=  100,
                               burnin = 4000,
                               verbose = FALSE)

Any additional aspects I should consider? Have neglected? Alternatives?

Thank you in advance for any information that might alleviate my confusion.

Peter