[R] Inconsistent confidence intervals for lmer sigma from mcmcsamp

[Moni Blazej Neradilek]

I have been trying to estimate confidence interval for the residual sigma in
a two-way nested ANOVA, using the lmer and mcmcsamp functions. However, the
MCMC confidence interval for sigma not only does not include the point
estimate for sigma estimated by lmer but is far away.

My model is an intercept only model with random effects for study and animal
(animal nested within study).  Here is the output from lmer and mcmcsamp.
Any idea why this inconsistency between the lmer estimate of sigma and the
corresponding confidence interval from mcmcsamp (is there an alternative way
to calculate the confidence interval)?

Many thanks.

Moni

> summary(test.mod)
Linear mixed model fit by REML 
Formula: log.count ~ 1 + (1 | study_id/animal_id) 
   Data: flow 
 Subset: (cell_type == "B cell") & (cd_group_new == "CD20+") 
 AIC   BIC logLik deviance REMLdev
 686 705.7   -339    675.2     678
Random effects:
 Groups             Name        Variance Std.Dev.
 animal_id:study_id (Intercept) 0.232873 0.48257 
 study_id           (Intercept) 0.097440 0.31215 
 Residual                       0.052352 0.22880 
Number of obs: 1009, groups: animal_id:study_id, 295; study_id, 12

Fixed effects:
            Estimate Std. Error t value
(Intercept)   0.1400     0.0969   1.445

> HPDinterval(mcmcsamp(test.mod,20000))
$fixef
                  lower     upper
(Intercept) -0.02019847 0.2775921
attr(,"Probability")
[1] 0.95

$ST
         lower     upper
[1,] 0.5803595 0.7124204
[2,] 0.4734074 0.9662538
attr(,"Probability")
[1] 0.95

$sigma
         lower     upper
[1,] 0.3348477 0.3748551
attr(,"Probability")
[1] 0.95


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