Bayesian hypothesis testing for hierarchical models using transdimensional Markov chain Monte Carlo methods

Bayesian hypothesis testing for hierarchical models is greatly facilitated by the use of sophisticated sampling methods such as transdimensional Markov chain Monte Carlo methods. These methods use a model indicator to switch from one model to another, sample values from the posterior distribution of the active model, and perform an operation to jump between models with different dimension. Here we explore the possibilities of a method proposed by Carlin and Chib (1995). This method is in fact a Gibbs sampler for the model parameters and the model indicator. The Bayes factor can be approximated from a posterior sample of the model indicator. We apply this method for hypothesis testing in the context of subliminal priming (Rouder, Morey, Speckman and Pratte, 2007; Zeelenberg, Wagenmakers and Raaijmakers, 2002), using graphical binomial models with probit-transformed rate parameters. Both non-hierarchical, subject-level comparisons and hierarchical, group-level comparisons are carried out and all hypotheses contain order restrictions. The results from the Carlin and Chib algorithm were found to closely match the results of an importance sampling algorithm. Because of its satisfactory performance and ease of implementation, this method is likely to be a prime candidate for the implementation of Bayesian hypothesis tests in experimental psychology.status: publishe