[R-sig-ME] naive question about output from mcmcsamp v. lmer estimates

[Gibbons,James]

Douglas Bates wrote:

>>
>> I was expecting these numbers to be similar, although not identical, to
>> the lmer output. This is all quite new ground for me so, I readily
>> accept I have probably gone wrong somewhere. But where?
> 
> As a first step I would suggest that you examine the mcmcsamp result
> to see if the chains are stable.  Save the output from mcmcsamp as,
> say, samp.HT02 and plot the chains as parallel time series
> 
> library(coda)
> xyplot(samp.HT02)
> 
> You might also want to examine empirical density estimates derived
> from the chains
> 
> densityplot(samp.HT02, plot.points = FALSE)
> 
> or normal probability plots
> 
> qqmath(samp.HT02, type = c("g", "p"))
> 
> If the distribution of the MCMC sample for a parameter is badly skewed
> or otherwise unstable then  the sample mean will not be near to the
> estimate.

Thanks for the quick reply. I did as you suggested, the xyplots don't 
look unusual (at least to my eyes) and

 > summary(HT02.mcmc)

Iterations = 1:10000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 10000

1. Empirical mean and standard deviation for each variable,
    plus standard error of the mean:

               Mean    SD Naive SE Time-series SE
(Intercept) 122.55  2.42   0.0242        0.02434
sigma^2     570.51 25.13   0.2513        0.45181
Fm:P.(In)    61.39 12.36   0.1236        0.45281
Prvn.(In)    61.97 34.94   0.3494        0.58404
Blck.(In)    17.65 11.28   0.1128        0.27032

2. Quantiles for each variable:

                2.5%    25%    50%    75%  97.5%
(Intercept) 117.953 120.92 122.48 124.10 127.54
sigma^2     523.706 553.22 569.79 586.78 622.33
Fm:P.(In)    40.139  52.95  60.40  68.71  88.91
Prvn.(In)    19.185  38.20  53.86  76.79 150.31
Blck.(In)     3.441  10.09  15.22  22.30  46.02

doesn't suggest much skew. Running 100,000 samples also makes little 
difference.

By way of comparison some output from my winBugs implementation (100,000 
iterations, 10,000 burnin):

node	 mean	 sd	 MC error	2.5%	median	97.5%
intercept	126.6	7.819	0.4338	110.9	128.4	139.8
v.blocks	18.92	12.02	0.08299	4.772	16.16	49.36	
v.fam	3.056	6.032	0.2949	9.606E-4	0.1622	21.77
v.prov	174.9	74.91	1.05	78.63	159.1	361.7

the family posterior does look very skewed. These are with gamma priors 
for the variances and without a centering parameterization (i.e. very 
naive),

James
-- 
Dr James Gibbons
Research Lecturer in Ecological Modelling
School of the Environment & Natural Resources
University of Wales, Bangor
phone: 01248 382461
email: j.gibbons at bangor.ac.uk


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