Multidimensional Item Response Theory in the Style of Collaborative Filtering

Yoav Bergner (), Peter Halpin () and Jill-Jênn Vie ()
Additional contact information
Yoav Bergner: New York University
Peter Halpin: University of North Carolina-Chapel Hill
Jill-Jênn Vie: Inria

Psychometrika, 2022, vol. 87, issue 1, No 11, 266-288

Abstract: 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.

Keywords: item response theory; multidimensionality; machine learning; collaborative filtering; joint maximum likelihood (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11336-021-09788-9

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