Hi Charlie,  

If you really want to do variance components analysis with Bayesian inference your best bet is going to be OpenBUGS or JAGS, both of which can be run through R.

Having said that, you could probably get away with MLE methods (lme4 etc) and just use the standard deviations of the random effects (finite-population components) instead of the estimated super-population components (which as you point out don't have any uncertainty in lme(4)). The finite-population VCA approach should be relatively simple using approximate Bayesian simulation of the point estimates and standards errors of the random effects.

Here are some refs, both use full Bayes models, but I think they would apply to approximate Bayes analyses as well.


Hector, A., Bell, T., Hautier, Y., Isbell, F., Kéry, M., Reich, P. B., van Ruijven, J., et al. (2011). BUGS in the Analysis of Biodiversity Experiments: Species Richness and


Composition Are of Similar Importance for Grassland Productivity. (T. Romanuk, Ed.)Plos One, 6(3), e17434. doi:10.1371/journal.pone.0017434.t004






Gelman, A. (2005). Analysis of variance—why it is more important than ever. The Annals of Statistics, 33(1), 1–53.




Will Morris
Masters of Philosophy candidate
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On Thursday, 14 June 2012 at 7:40 AM, Yi (Charlie) Chen wrote:

> Hi All,
>  
> I'm trying to do the Bayesian Inference on variance components of mixed effect models, is there any suggestion about the package I can start with? Especially for the confidence interval, as far as I have tried, I can't get confidence intervals for variance components in NLME and LME4 package, am I right?
>  
> Any recommendation or references are very appreciated.
>  
> Best,
> Charlie
>  
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