Efficient Standard Errors in Item Response Theory Models for Short Tests

Lianne Ippel*, David Magis

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Web of Science)

Abstract

In dichotomous item response theory (IRT) framework, the asymptotic standard error (ASE) is the most common statistic to evaluate the precision of various ability estimators. Easy-to-use ASE formulas are readily available; however, the accuracy of some of these formulas was recently questioned and new ASE formulas were derived from a general asymptotic theory framework. Furthermore, exact standard errors were suggested to better evaluate the precision of ability estimators, especially with short tests for which the asymptotic framework is invalid. Unfortunately, the accuracy of exact standard errors was assessed so far only in a very limiting setting. The purpose of this article is to perform a global comparison of exact versus (classical and new formulations of) asymptotic standard errors, for a wide range of usual IRT ability estimators, IRT models, and with short tests. Results indicate that exact standard errors globally outperform the ASE versions in terms of reduced bias and root mean square error, while the new ASE formulas are also globally less biased than their classical counterparts. Further discussion about the usefulness and practical computation of exact standard errors are outlined.

Original languageEnglish
Article number0013164419882072
Pages (from-to)461-475
Number of pages15
JournalEducational and Psychological Measurement
Volume80
Issue number3
Early online date18 Oct 2019
DOIs
Publication statusPublished - Jun 2020

Keywords

  • item response theory
  • exact standard error
  • ability estimation
  • asymptotic standard error
  • MAXIMUM
  • ESTIMATORS
  • ABILITY
  • LIKELIHOOD

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