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

Author

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  • Steven E. Rigdon
  • Robert K. Tsutakawa

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.

Suggested Citation

  • Steven E. Rigdon & Robert K. Tsutakawa, 1987. "Estimation for the Rasch Model When Both Ability and Difficulty Parameters Are Random," Journal of Educational and Behavioral Statistics, , vol. 12(1), pages 76-86, March.
    • Handle: RePEc:sae:jedbes:v:12:y:1987:i:1:p:76-86
    DOI: 10.3102/10769986012001076
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