ABSTRACT
Chapter 3 introduces nonparametric item response theory (IRT) models. The focus is on the two nonparametric IRT models that Mokken proposed. These models facilitate analysis of real data that is readily accessible to researchers. The models can be considered foundational for parametric IRT models (Chapter 4). Whereas classical test theory, being only an error model without restricting the covariance structure of the items, could not justify the measurement level of the scale, nonparametric IRT, which assumes a latent variable common to the items, implies that the simple test score equaling the sum of the item scores orders persons on the latent variable. We discuss the two nonparametric IRT models, which are the model of monotone homogeneity and the model of double monotonicity. The former model allows a person ordering, and the latter allows an item ordering in addition to a person ordering. We discuss the models’ assumptions and their ordering properties for scale values. Next, we discuss goodness-of-fit methods for each of the assumptions of the models, and for each model, we discuss automated item selection procedures using scalability coefficients. For the model of double monotonicity, we discuss a reliability method.
