Title: Joint Maximum Likelihood Estimation for High-dimensional Exploratory Item Response Analysis,
Abstract: 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.