Hierarchical centering for RJMCMC

My co-authors and I are pleased that our paper on hierarchical centering for RJMCMC algorithms was recently published in Computational Statistics and Data Analysis. It can be downloaded here.

In short, the methods describe a reparameterisation applicable to random effects models that improves mixing of models in the context of reversible jump Markov chain Monte Carlo (RJMCMC) methods.

Although these methods may be applicable to models with other error distributions, we described the case for a log-linear Poisson model where the expected value includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation:

Please refer to the paper for parameter definitions and more details. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modelling the mean of the random effect coefficients as a function of the intercept of the model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups.

When including only one covaraite in hierarchical centering equation (1) becomes:

When including all available covaraites in hierarchical centering equation (1) becomes:

We show that this has an effect on the dynamics of the RJMCMC algorithm and improves model mixing.

Case study and conclusions:

We applied the methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the startingmodel. With hierarchical centering on the other hand, the chain moved freely over model and parameterspace. These results are confirmed with a simulation study. Hence, the proposed methodsshould be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference onmodel parameters.