Order-Constrained Bayes Inference for Dichotomous Models of Unidimensional Nonparametric IRT

This study introduces an order-constrained Bayes inference framework useful for analyzing data containing dichotomous-scored item responses, under the assumptions of either the monotone homogeneity model or the double monotonicity model of nonparametric item response theory (NIRT). The framework involves the implementation of Gibbs sampling to estimate order-constrained parameters, followed by inference with the posterior-predictive distribution to test the monotonicity, invariant item ordering, and local independence assumptions of NIRT. The Bayes framework is demonstrated through the analysis of real test data, and possible extensions of it are discussed.