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

Steven E. Rigdon and Robert K. Tsutakawa

Journal of Educational and Behavioral Statistics, 1987, vol. 12, issue 1, 76-86

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.

Keywords: EM algorithm; item response curve; Rasch model (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:12:y:1987:i:1:p:76-86

DOI: 10.3102/10769986012001076

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