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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.09495 |
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| _version_ | 1866916553840132096 |
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| author | Oka, Motonori Okada, Kensuke |
| author_facet | Oka, Motonori Okada, Kensuke |
| contents | Diagnostic classification models (DCMs) offer statistical tools to inspect the fined-grained attribute of respondents' strengths and weaknesses. However, the diagnosis accuracy deteriorates when misspecification occurs in the predefined item-attribute relationship, which is encoded into a Q-matrix. To prevent such misspecification, methodologists have recently developed several Bayesian Q-matrix estimation methods for greater estimation flexibility. However, these methods become infeasible in the case of large-scale assessments with a large number of attributes and items. In this study, we focused on the deterministic inputs, noisy "and" gate (DINA) model and proposed a new framework for the Q-matrix estimation to find the Q-matrix with the maximum marginal likelihood. Based on this framework, we developed a scalable estimation algorithm for the DINA Q-matrix by constructing an iteration algorithm that utilizes stochastic optimization and variational inference. The simulation and empirical studies reveal that the proposed method achieves high-speed computation, good accuracy, and robustness to potential misspecifications, such as initial value's choices and hyperparameter settings. Thus, the proposed method can be a useful tool for estimating a Q-matrix in large-scale settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_09495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Scalable Bayesian Approach for the DINA Q-matrix Estimation Combining Stochastic Optimization and Variational Inference Oka, Motonori Okada, Kensuke Computation Diagnostic classification models (DCMs) offer statistical tools to inspect the fined-grained attribute of respondents' strengths and weaknesses. However, the diagnosis accuracy deteriorates when misspecification occurs in the predefined item-attribute relationship, which is encoded into a Q-matrix. To prevent such misspecification, methodologists have recently developed several Bayesian Q-matrix estimation methods for greater estimation flexibility. However, these methods become infeasible in the case of large-scale assessments with a large number of attributes and items. In this study, we focused on the deterministic inputs, noisy "and" gate (DINA) model and proposed a new framework for the Q-matrix estimation to find the Q-matrix with the maximum marginal likelihood. Based on this framework, we developed a scalable estimation algorithm for the DINA Q-matrix by constructing an iteration algorithm that utilizes stochastic optimization and variational inference. The simulation and empirical studies reveal that the proposed method achieves high-speed computation, good accuracy, and robustness to potential misspecifications, such as initial value's choices and hyperparameter settings. Thus, the proposed method can be a useful tool for estimating a Q-matrix in large-scale settings. |
| title | Scalable Bayesian Approach for the DINA Q-matrix Estimation Combining Stochastic Optimization and Variational Inference |
| topic | Computation |
| url | https://arxiv.org/abs/2105.09495 |