Item Response Theory (IRT) is a family of statistical models that describe the relationship between a latent trait (e.g., ability, attitude) and the probability of a particular response to a test item. Unlike classical test theory, IRT models item-level behavior, enabling more precise measurement and principled test construction.
Why IRT matters
IRT provides the theoretical backbone for modern educational and psychological measurement. It underlies Computerized Adaptive Testing (CAT), item banking, test equating, and differential item functioning analysis. By modeling each item’s characteristics (difficulty, discrimination, guessing), IRT enables tests that adapt to individual examinees and yield comparable scores across different item sets.
My research in IRT
My work in IRT spans both theoretical foundations and practical applications:
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Finite-sample properties of ability estimation. The standard approach uses the Fisher information as a proxy for the variance of the maximum likelihood estimator (MLE). However, this is an asymptotic approximation that can be inaccurate for short tests. I developed a parametric bootstrap method for estimating standard errors that is both asymptotically valid and practically efficient, with a novel algorithm to reduce computational cost (submitted to PsyArXiv).
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Existence and uniqueness of the MLE. With Che Cheng and Yung-Fong Hsu, I investigated conditions under which the MLE of the latent trait exists and is unique when the prior distribution is log-concave. This work clarifies when standard estimation procedures are well-defined (preprint on PsyArXiv).
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Identifiability of polychoric models. Many structural equation models for ordinal data rely on polychoric correlations, which assume latent normality. We generalized this to latent elliptical distributions and derived the identifiability constraints, published in Psychometrika (2025).
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Bayesian adaptive testing. With Chia-Min Wei and Yu-Chang Chen, I studied the consistency of Bayesian adaptive testing under the Rasch model from a Bayesian decision theory perspective (preprint on arXiv).
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Online Convex Optimization framework for CAT. My dissertation bridges IRT and online learning theory, showing that the classical maximum information method constitutes a no-regret algorithm under the OCO framework, and constructing anytime-valid confidence intervals for ability estimates.
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Applied IRT for education. In collaboration with an online learning platform (PaGamO), I applied the two-parameter IRT model to estimate abilities of 100K+ students from a 1M+ item bank using joint maximum likelihood estimation.