Recommendation with item response theory

In this study, we propose to use Multidimensional Item Response Theory (MIRT) to model the rating matrix in a recommendation context. In contrast to most existing recommender systems, this enables an explainable low-dimensional latent profile and offers to efficiently explore user preferences through computerized adaptive testing (CAT). We use elastic-net regularisation to accommodate large amounts of missing data. Through simulations, we demonstrate the accuracy of our model in recovering data generation parameters. Furthermore, we apply MIRT to the Movielens 1M dataset, showcasing that a three-dimensional MIRT model outperforms matrix factorization methods with up to 20 dimensions. Additionally, we demonstrate how MIRT combined with CAT can optimize for exploration in a second simulation study. Our findings highlight that MIRT increases interpretability and control over the exploration-exploitation trade-off. We conclude by discussing limitations and avenues for future research on MIRT-based recommender systems. We openly share all data and code.