Characterizing the manifest probabilities of latent trait models
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 characterization of the Rasch model as a log-linear model for a 2J-contingency table. Partial results are also obtained for other models. The question of the identifiability of "guessing" parameters is also discussed. 1983 The Psychometric Society.