Abstract
Consider vectors of item responses obtained from a sample of subjects from a population in which abilityθ is distributed with densityg(θ‖α), where theα are unknown parameters. Assuming the responses depend onθ through a fully specified item response model, this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject. Also provided are asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a non-parametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.
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The author would like to thank R. Darrell Bock for his comments, suggestions, and encouragement during the course of this work.
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Mislevy, R.J. Estimating latent distributions. Psychometrika 49, 359–381 (1984). https://doi.org/10.1007/BF02306026
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DOI: https://doi.org/10.1007/BF02306026