CHARACTERIZING THE MANIFEST PROBABILITIES OF LATENT TRAIT MODELS*

Abstract

ABSTRACTThe 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.