Biweight Estimates of Latent Ability

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Abstract
Maximum likelihood estimates of subjects' abilities in item response curve models are overly sensitive to disturbances that are common in educational testing, such as carelessness and random guessing. Recently Waller (1974) and Wainer and Wright (1980) have suggested more robust methods of estimation. This paper presents an alternative estimator, based on the principle of Tukey's biweight—a robust estimator of location. Among the advantages of the biweight estimator of latent ability are the following: (1) the nature and extent of disturbances are not assumed to be the same for all subjects; (2) each response is utilized in proportion to its apparent value; (3) the biweight estimate agrees with the maximum likelihood estimate when no disturbances are present; and (4) computation requires only a minor modification of the Newton-Raphson method commonly used to obtain maximum likelihood estimates of ability. The biweight estimator is demonstrated with artificial data, and shown to produce smaller meansquared errors than the maximum likelihood estimator even in the presence of only slight disturbances.