Dear list members,

First of all, I would like to say that I think it is great that this list exists. I have learned so much by reading posts regularly and searching for answers when I encounter a problem.

I have searched extensively before making this post, but have not been able to find an answer to some specific issues I encountered:

I need some help regarding results that I get from a model run with the package MCMCglmm. I thought I interpreted things correctly after reading a lot of posts on here and reading through the Course Notes of the package, however a recent paper of mine got rejected and one reviewer had quite a few problems with the model. Before I send the paper anywhere else I would like to make sure that I am interpreting and explaining things correctly.

Some brief explanation about the study:
The data contains counts of birds at 9 different locations before and after a development (several years before, and several years after (up to 15 years post-construction)). We are interested in whether the counts changed after development. Since the initial numbers at each site are variable and differ quite a lot between sites, I used a random effect for site.
I used MCMCglmm due to overdispersion using frequentist methods.

The poisson model looks like this:
MCMCglmm(counts ~ bef_af, random=~Site, data=dataframe, pr=TRUE, pl=TRUE, family="poisson", nitt=65000, thin=50, burnin=15000, start=list(QUASI=FALSE))
where 'counts' is the number of birds per survey, 'bef_af' is a factor with either 0 or 1 (where 0 is before and 1 is after), 'site' is a character vector with the 9 different site names.

The model is run 3 times to give 3 different chains. The chains are then checked for convergence via plotting:
plot(mcmc.list(chain1$Sol, chain2$Sol, chain3$Sol))
In addition, I checked the Gelman and Rubin's convergence diagnostic:
gelman.diag(mcmc.list(chain1$Sol, chain2$Sol, chain3$Sol))

The model gives the following error for the starting values:
Warning message:
In MCMCglmm(counts ~ bef_af, random = ~Site, data = dataframe,  :
  good starting values not obtained: using Norm(0,1)

The plots show adequate mixing of the chains but I am wondering whether the chains started at different appropriate values due to the warning message. Should I be concerned about the warning message? Did it use starting values drawn from a normal distribution?

The Gelman and Rubin's diagnostic gave the following:
Potential scale reduction factors:

              Point est. Upper C.I.
(Intercept)            1       1.00
bef_af1                1       1.00
Site.Site 1b          1       1.01
Site.Site 2           1       1.00
Site.Site 3           1       1.00
Site.Site 4           1       1.00
Site.Site 5           1       1.00
Site.Site 6           1       1.00
Site.Site 7           1       1.00
Site.Site 8           1       1.00
Site.Site 9           1       1.00

Multivariate psrf

1.01

Furthermore, I checked how much variance was explained by the random effect:

HPDinterval(chain1$VCV[, "Site"]/(chain1$VCV[, "Site"] + chain1$VCV[, "units"]))

        lower     upper
var1 0.388643 0.8729441
attr(,"Probability")
[1] 0.95

I interpreted this as follows: the majority of the variation in the data was explained by the difference between the locations. Both the 'Site' random effect and the residuals 'Units' posterior distribution plots show that both are located well away from zero (Plotted via plot(chain1$VCV)). Is my interpretation correct? To me it makes sense as the numbers of birds between the locations varied a lot (from mean of 2 birds at one location to a mean of 20 birds at another location).
When a prior is not given in MCMCglmm() what defaults does it use? From the documentation I can see prior=NULL, but I assume that some prior must be given for bayesian models. Are the defaults: B$mu=0 and B$V=I*1e+10, where where I is an identity matrix of appropriate dimension? I therefore assume that the default priors in MCMCglmm are centered on zero and since the posterior distribution is well away from zero, that therefore the random effects explain some variation in the data (especially 'site' which explains 38.8-87.3%). Is this correct?

Thanks!

Mieke

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