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Multidimensional Item Response Theory in the Style of Collaborative Filtering.

Authors
  • Bergner, Yoav1
  • Halpin, Peter2
  • Vie, Jill-Jênn3
  • 1 Steinhardt School of Culture, Education, and Human Development, New York University, 82 Washington Square East, New York, NY, 10003, USA.
  • 2 School of Education, Peabody Hall, University of North Carolina-Chapel Hill, Office 111, Chapel Hill, NC, 27599-3500, USA.
  • 3 Inria, UMR 9189 CRIStAL, 40 avenue Halley, 59650, Villeneuve-d'Ascq, France. jill-j[email protected] , (France)
Type
Published Article
Journal
Psychometrika
Publication Date
Mar 01, 2022
Volume
87
Issue
1
Pages
266–288
Identifiers
DOI: 10.1007/s11336-021-09788-9
PMID: 34698979
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

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 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. 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 examination in the course. © 2021. The Psychometric Society.

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