[R] MCMCglmm and iteration

[Ben Bolker]

Rémi Lesmerises <remilesmerises <at> yahoo.ca> writes:

>  Hi everyone, I'm running a bayesian regression using the package
> MCMCglmm (Hadfield 2010) and to reach a normal posterior
> distribution of estimates, I increased the number of iteration as
> well as the burnin threshold. However, it had unexpected
> outcomes. Although it improved posterior distribution, it also
> increased dramatically the value of estimates and decrease DIC. 
> Here's an example:

head(spring)

pres large_road  small_road  cab 
0      2011         32         78 
1       102        179        204 
0      1256        654        984 
1       187        986        756 
0        21        438         57 
1        13          5        439 

# pres is presence/absence data and other variable are distance to these
features
# with 200,000 iteration and 30,000 burnin

prior <- list(R = list(V = 1, nu=0.002))
sp.simple <- MCMCglmm(pres ~ large_road + cab + small_road,
   family = "categorical", nitt = 200000, thin = 200,
    burnin = 30000, data = spring, prior = prior, verbose = FALSE, pr = TRUE)
------------

(1) you will do much better with this kind of question on r-sig-mixed-models.
(2) it looks like your chain is mixing very, very badly.  If I'm reading
the output correctly, it looks like your effective sample sizes for the
first run (200K iterations) are 1-3 (!) -- you should be aiming for 
effective sample sizes of 100s to 1000s.  Even with a million iterations
you're only getting up to effective sample sizes of ~150 for some
parameters.  I would recommend (a) centring and scaling your parameters
to improve mixing and (b) cross-checking with a different method
(e.g. lme4 or glmmADMB) to make sure you're in the right ballpark.

  You shouldn't necessarily expect a Normal posterior as you increase
the number of iterations; the posterior distributions are only 
asymptotically Normal as the number of *observations* increases.