The application of the Bayesian approach with MCMC sampling to IRT models is mainly motivated by the fact that IRT models with complex dependency structures require the evaluation of multiple integrals to solve the estimation equations in a likelihood-based framework. This problem is avoided in an MCMC framework. In recent years, the fully Bayesian approach has been adopted to the estimation of IRT models with multiple raters, multiple item types, missing data (Patz and Junker 1999a, b), testlet structures (Bradlow et al. 1999, Wainer et al. 2000), latent classes (Hoijtink and Molenaar 1997), models with a multi-level structure on the ability parameters (Fox and Glas 2001, 2003) and the item parameters (Janssen et al. 2000), and multidimensional IRT models (Béguin and Glas 2001). In behaviour genetics, the approach has been taken up by Eaves and his co-workers (Eaves et al, 2005; Eaves et al. 2004).
