I need to make linear model for which I need to do Gibbs sampling in MCMC simulations. The model needed to be fitted is a linear mixed model.
Please suggest me for a robust R package for this task.
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The CRAN Task View on Bayesian inference lists several. I recommend
MCMCpack. If you can use BUGS then the
glmmBUGS will help you fits linear mixed models.
For this task, an efficient new method has recently introduced by Havard Rue and his colleagues at NTNU (JRSSB, 2009, 71(2), 319-392) as called Integrated Nested Laplace Approximation (INLA). INLA substitutes MCMC simulations with accurate, deterministic approximations to posterior marginal distributions. The quality of such approximations is very high, such that even very long MCMC runs could not detect any error in them. An R package (with the same name, INLA) is already available from the web-site www.r-inla.org.