Weighted Likelihood Estimation of ability in item response theory with tests of finite length

Abstract

Applications of Item Response Theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. All current estimation methods produce statistically biased estimates of both item and ability parameters. 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 Model Estimation (BME) of ability in conventional tests and tailored tests. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale.

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