ABSTRACT
Chapter 4 discusses parametric item response theory (IRT) models that may be considered specializations of the nonparametric IRT models discussed in Chapter 3. Parametric models define a parametric item response function, such as the normal-ogive or the logistic function, for the relation between the probability of producing a particular item score and the latent variable representing the target attribute. Nonparametric models define this relation by ordering restrictions but do not adopt a particular parametric function. Parametric IRT models have the merit that the parameters of the item response functions describing person and item characteristics can be estimated using standard statistical estimation methods, such as maximum likelihood and Bayesian methods. We first discuss some older and newer IRT models. In particular, attention is given to the Rasch model or the one-parameter logistic model, and the two- and three-parameter logistic models for dichotomous items. Next, we discuss three classes of IRT models for polytomous items. Almost all models for dichotomous and polytomous items are organized in hierarchical taxonomies, in particular, two Venn diagrams, clarifying the mutual relations between many models. We devote much attention to goodness-of-fit research. Finally, we discuss a few models for special purposes, such as multidimensional IRT models.
