Bayesian estimation and model selection in ordered latent class models for polytomous items

In a latent class IRT model in which the latent classes are ordered on one dimension, the class spe-cific response probabilities are subject to inequality constraints. The number of these inequality constraintsincrease dramatically with the number of response categories per item, if assumptions like monotonicityor double monotonicity of the cumulative category response functions are postulated. A Maxkov chainMonte Carlo method, the Gibbs sampler, can sample from the multivariate posterior distribution of theparameters under the constraints. Bayesian model selection can be done by posterior predictive checksand Bayes factors. A simulation study is done to evaluate results of the application of these methods toordered latent class models in three realistic situations. Also, an example of the presented methods isgiven for existing data with polytomous items. It can be concluded that the Bayesian estimation procedurecan handle the inequality constraints on the parameters very well. However, the application of Bayesianmodel selection methods requires more research