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Estimation for the Rasch Model When Both Ability and Difficulty Parameters Are Random

Steven E. Rigdon and Robert K. Tsutakawa
Journal of Educational Statistics
Vol. 12, No. 1 (Spring, 1987), pp. 76-86
DOI: 10.2307/1164629
Stable URL: http://www.jstor.org/stable/1164629
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Estimation for the Rasch Model When Both Ability and Difficulty Parameters Are Random
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Abstract

Estimation of the parameters of the Rasch model, a one-parameter item response model, is considered when both the item parameters and the ability parameters are considered random quantities. It is assumed that the item parameters are drawn from a N (γ, τ 2) distribution, and the abilities are drawn from a N(0, σ 2) distribution. A variation of the EM algorithm is used to find approximate maximum likelihood estimates of γ, τ, and σ. A second approach assumes that the difficulty parameters are drawn from a uniform distribution over part of the real line. Real and simulated data sets are discussed for illustration.

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