A new class of parametric IRT models for dichotomous item scores.

A new class of parametric IRT models for dichotomously scored items is presented. The new class of models is a subclass of both the class of models defined by the four-parameter logistic item response function and the nonparametric Double Monotonicity (DM) model. Three special cases of this new class of models are discussed. One of these special cases is shown to be the one-parameter logistic Rasch model. Both specific objectivity at the interval level of measurement and the sufficiency of the total score for the latent trait are shown to be measurement properties of the whole new class of models. For maximum likelihood estimation of the model parameters, both a joint and a conditional likelihood function are proposed.