A0490
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. However, 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 demonstrate that Bayesian estimators remain robust under the mis-specification of the prior. The analysis then extends 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.
