$\beta^3$-IRT: A New Item Response Model and its Applications

Item Response Theory (IRT) aims to assess latent abilities of respondents based on the correctness of their answers in aptitude test items with different difficulty levels. In this paper, we propose the $\beta^3$-IRT model, which models continuous responses and can generate a much enriched family of Item Characteristic Curve (ICC). In experiments we applied the proposed model to data from an online exam platform, and show our model outperforms a more standard 2PL-ND model on all datasets. Furthermore, we show how to apply $\beta^3$-IRT to assess the ability of machine learning classifiers. This novel application results in a new metric for evaluating the quality of the classifier's probability estimates, based on the inferred difficulty and discrimination of data instances.