Gibbs sampling using the data augmentation scheme for higher-order item response models

Abstract Many latent traits in the human sciences have a hierarchical structure. This article will focus on a higher-order item response theory ( HO-IRT) model, which integrates a single overall ability and several domain-specific abilities in the same model to improve the parameter estimation of assessment data. A DAGS-based (data augmentation scheme) Gibbs sampler procedure to analyze HO-IRT models with three-parameter logistic link will be introduced. This procedure is a generalization of Maris and Maris (2002)’s sampling based Bayesian technique, called the DA-T-Gibbs sampler, are suitable for a wide variety of IRT models. With the introduction of the two latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. The performance of the proposed DAGS-based Bayesian procedure is evaluated via a simulation study and compared with the M–H algorithm. Results indicate that the proposed DAGS-based Bayesian procedure is more efficient and flexible than the M–H algorithm. Finally, applications to a real dataset are conducted to demonstrate the efficiency and utility of the proposed method.