A0296
Title: On the consistency of Bayesian adaptive testing under the Rasch model
Authors: Yu-Chang Chen - National Taiwan University (Taiwan) [presenting]
Hau-Hung Yang - National Taiwan University (Taiwan)
Chia-Min Wei - University of Wisonsin Madison (United States)
Abstract: The consistency of Bayesian adaptive testing methods is established under the Rasch model, addressing a gap in the literature on their large-sample guarantees. Although Bayesian approaches are recognized for their finite-sample performance and capability to circumvent issues such as the cold-start problem, rigorous proofs of their asymptotic properties, particularly in non-i.i.d. structures, remain lacking. Conditions are derived under which the posterior distributions of latent traits converge to the true values for a sequence of given items, and it is demonstrated that Bayesian estimators remain robust under the misspecification of the prior. The analysis is then extended to adaptive item selection methods in which items are chosen endogenously during the test. Additionally, a Bayesian decision-theoretical framework is developed for the item selection problem, and a novel selection is proposed that aligns the test process with optimal estimator performance. These theoretical results provide a foundation for Bayesian methods in adaptive testing, complementing prior evidence of their finite-sample advantages.
