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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.00909 |
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| _version_ | 1866913638272466944 |
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| author | Bergner, Yoav Halpin, Peter F. Vie, Jill-Jênn |
| author_facet | Bergner, Yoav Halpin, Peter F. Vie, Jill-Jênn |
| contents | This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00909 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multidimensional Item Response Theory in the Style of Collaborative Filtering Bergner, Yoav Halpin, Peter F. Vie, Jill-Jênn Machine Learning This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course. |
| title | Multidimensional Item Response Theory in the Style of Collaborative Filtering |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2301.00909 |