Joint Maximum Likelihood Estimation for High-dimensional Exploratory Item Response Analysis

Multidimensional item response theory is widely used in education and psychology for measuring multiple latent traits. However, exploratory analysis of large-scale item response data with many items, respondents, and latent traits is still a challenge. In this paper, we consider a high-dimensional setting that both the number of items and the number of respondents grow to infinity. A constrained joint maximum likelihood estimator is proposed for estimating both item and person parameters, which yields good theoretical properties and computational advantage. Specifically, we derive error bounds for parameter estimation and develop an efficient algorithm that can scale to very large datasets. The proposed method is applied to a large scale personality assessment data set from the Synthetic Aperture Personality Assessment (SAPA) project. Simulation studies are conducted to evaluate the proposed method.