, Volume 54, Issue 3, pp 427–450

Weighted likelihood estimation of ability in item response theory

  • Thomas A. Warm

DOI: 10.1007/BF02294627

Cite this article as:
Warm, T.A. Psychometrika (1989) 54: 427. doi:10.1007/BF02294627


Applications of item response theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. A new method, weighted likelihood estimation (WLE), is derived, and proved to be less biased than maximum likelihood estimation (MLE) with the same asymptotic variance and normal distribution. WLE removes the first order bias term from MLE. Two Monte Carlo studies compare WLE with MLE and Bayesian modal estimation (BME) of ability in conventional tests and tailored tests, assuming the item parameters are known constants. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale.

Key words

maximum likelihood estimationunbiased estimationstatistical biasBayesian modal estimationitem response theorytailored testingadaptive testing

Copyright information

© The Psychometric Society 1989

Authors and Affiliations

  • Thomas A. Warm
    • 1
  1. 1.FAA Academy AAC-934, Mike Monroney Aeronautical CenterOklahoma City