MCMCglmm is a package for fitting Generalised Linear Mixed Models using Markov chain Monte Carlo techniques (Hadfield 2009). Most commonly used distributions like the normal and the Poisson are supported together with some useful but less popular ones like the zero-inflated Poisson and the multinomial. Missing values and left, right and interval censoring are accommodated for all traits. The package also supports multi-trait models where the multiple responses can follow different types of distribution. The package allows various residual and random-effect variance structures to be specified including heterogeneous variances, unstructured covariance matrices and random regression (e.g. random slope models). Three special types of variance structure that can be specified are those associated with pedigrees (animal models), phylogenies (the comparative method) and measurement error (meta-analysis).
The package makes heavy use of results in Sorensen & Gianola (2002) and Davis (2006) which taken together result in what is hopefully a fast and efficient routine. Most small to medium sized problems should take seconds to a few minutes, but large problems (> 20,000 records) are possible. My interest is in evolutionary biology so there are also several functions for applying Rice's (2004) tensor analysis to real data and functions for visualising and comparing matrices.
Please read the tutorial vignette("Tutorial", "MCMCglmm") or the course notes
vignette("CourseNotes", "MCMCglmm")
Hadfield, J.D. (2009) MCMC methods for Multi-response Generalised Linear Mixed Models: The MCMCglmm R Package, submitted
Sorensen, D. & Gianola, D. (2002) Likelihood, Bayesian and MCMC Methods in Quantitative Genetics, Springer
Davis, T.A. (2006) Direct Methods for Sparse Linear Systems, SIAM
Rice (2004) Evolutionary Theory: Mathematical and Conceptual Foundations, Sinauer