On the Consistency of Bayesian Adaptive Testing under the Rasch Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913604294410240 |
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| author | Yang, Hau-Hung Wei, Chia-Min Chen, Yu-Chang |
| author_facet | Yang, Hau-Hung Wei, Chia-Min Chen, Yu-Chang |
| contents | This study establishes the consistency of Bayesian adaptive testing methods 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. We derive conditions 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. Our analysis then extends to adaptive item selection methods in which items are chosen endogenously during the test. Additionally, we develop a Bayesian decision-theoretical framework for the item selection problem and propose a novel selection 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Consistency of Bayesian Adaptive Testing under the Rasch Model Yang, Hau-Hung Wei, Chia-Min Chen, Yu-Chang Methodology Applications This study establishes the consistency of Bayesian adaptive testing methods 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. We derive conditions 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. Our analysis then extends to adaptive item selection methods in which items are chosen endogenously during the test. Additionally, we develop a Bayesian decision-theoretical framework for the item selection problem and propose a novel selection 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. |
| title | On the Consistency of Bayesian Adaptive Testing under the Rasch Model |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2412.07170 |