Fitting Bayesian multiple random effects models

Bayesian random effects models may be fitted using Gibbs sampling, but the Gibbs sampler can be slow mixing due to what might be regarded as lack of model identifiability. This slow mixing substantially increases the number of iterations required during Gibbs sampling. We present an analysis of data on immunity after Rubella vaccinations which results in a slow-mixing Gibbs sampler. We show that this problem of slow mixing can be resolved by transforming the random effects and then, if desired, expressing their joint prior distribution as a sequence of univariate conditional distributions. The resulting analysis shows that the decline in antibodies after Rubella vaccination is relatively shallow compared to the decline in antibodies which has been shown after Hepatitis B vaccination.