BanditCAT and AutoIRT: Machine Learning Approaches to Computerized Adaptive Testing and Item Calibration

In this paper, we present a complete framework for quickly calibrating and administering a robust large-scale computerized adaptive test (CAT) with a small number of responses. Calibration - learning item parameters in a test - is done using AutoIRT, a new method that uses automated machine learning (AutoML) in combination with item response theory (IRT), originally proposed in [Sharpnack et al., 2024]. AutoIRT trains a non-parametric AutoML grading model using item features, followed by an item-specific parametric model, which results in an explanatory IRT model. In our work, we use tabular AutoML tools (AutoGluon.tabular, [Erickson et al., 2020]) along with BERT embeddings and linguistically motivated NLP features. In this framework, we use Bayesian updating to obtain test taker ability posterior distributions for administration and scoring. For administration of our adaptive test, we propose the BanditCAT framework, a methodology motivated by casting the problem in the contextual bandit framework and utilizing item response theory (IRT). The key insight lies in defining the bandit reward as the Fisher information for the selected item, given the latent test taker ability from IRT assumptions. We use Thompson sampling to balance between exploring items with different psychometric characteristics and selecting highly discriminative items that give more precise information about ability. To control item exposure, we inject noise through an additional randomization step before computing the Fisher information. This framework was used to initially launch two new item types on the DET practice test using limited training data. We outline some reliability and exposure metrics for the 5 practice test experiments that utilized this framework.

AutoIRT: Calibrating Item Response Theory Models with Automated Machine Learning

Item response theory (IRT) is a class of interpretable factor models that are widely used in computerized adaptive tests (CATs), such as language proficiency tests. Traditionally, these are fit using parametric mixed effects models on the probability of a test taker getting the correct answer to a test item (i.e., question). Neural net extensions of these models, such as BertIRT, require specialized architectures and parameter tuning. We propose a multistage fitting procedure that is compatible with out-of-the-box Automated Machine Learning (AutoML) tools. It is based on a Monte Carlo EM (MCEM) outer loop with a two stage inner loop, which trains a non-parametric AutoML grade model using item features followed by an item specific parametric model. This greatly accelerates the modeling workflow for scoring tests. We demonstrate its effectiveness by applying it to the Duolingo English Test, a high stakes, online English proficiency test. We show that the resulting model is typically more well calibrated, gets better predictive performance, and more accurate scores than existing methods (non-explanatory IRT models and explanatory IRT models like BERT-IRT). Along the way, we provide a brief survey of machine learning methods for calibration of item parameters for CATs.