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Characterizing the Manifest Probabilities of Latent Trait Models IRT

Cressie, Noel; Holland, Paul W.
Publication Year:
Report Number:
RR-81-54, PSRTR-81-22
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Item Response Theory (IRT), Probability, Rasch Model, Statistical Analysis


The problem of characterizing the manifest probabilities of a latent trait model is considered. The item characteristic curve is transformed to the item passing-odds curve and a corresponding transformation is made on the distribution of ability. This results in a useful expression for the manifest probabilities of any latent trait model. The result is then applied to give a complete characterization of the Rasch Model. Partial results are also obtained for other models. The question of the identifiability of "guessing" parameters is also discussed. (27pp.)

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