Weighted likelihood estimation of ability in item response theory |
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Authors: | Thomas A. Warm |
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Affiliation: | (1) FAA Academy AAC-934, Mike Monroney Aeronautical Center, PO Box 25082, 73125 Oklahoma City, OK |
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Abstract: | 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. |
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Keywords: | maximum likelihood estimation unbiased estimation statistical bias Bayesian modal estimation item response theory tailored testing adaptive testing |
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