On the Identifiability of Diagnostic Classification Models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866913637951602688 |
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| author | Fang, Guanhua Liu, Jingchen Ying, Zhiliang |
| author_facet | Fang, Guanhua Liu, Jingchen Ying, Zhiliang |
| contents | This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In particular, we establish identifiability results of various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. Consistent estimators are constructed. Simulation results show that these estimators perform well under various modeling settings. We also use a real example to illustrate the new method. The results are stated under the setting of general latent class models. For DCM with a specific parameterization, the conditions may be adapted accordingly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_01240 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On the Identifiability of Diagnostic Classification Models Fang, Guanhua Liu, Jingchen Ying, Zhiliang Statistics Theory Methodology This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In particular, we establish identifiability results of various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. Consistent estimators are constructed. Simulation results show that these estimators perform well under various modeling settings. We also use a real example to illustrate the new method. The results are stated under the setting of general latent class models. For DCM with a specific parameterization, the conditions may be adapted accordingly. |
| title | On the Identifiability of Diagnostic Classification Models |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/1706.01240 |