# Multidimensional Item Response Theory in the Style of Collaborative Filtering

arXiv: https://arxiv.org/abs/2301.00909 · HTML: https://mlsanity.com/paper/2301.00909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 61 references that are in the map.
- First posted on arXiv 3 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics](https://mlsanity.com/paper/1412.5967/) (2014)
- [Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications](https://mlsanity.com/paper/1712.08966/) (2017)
- [Sparse Bilinear Logistic Regression](https://mlsanity.com/paper/1404.4104/) (2014)

## Abstract (arXiv)

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.