ABSTRACT
The nominal categories model (Bock, 1972, 1997) was originally proposed soon after Samejima (1969, 1997) described the first general item response theory (IRT) model for polytomous responses. Samejima's graded models (in normal ogive and logistic form) had been designed for item responses that have some a priori order as they relate to the latent variable being measured (θ) (Volume One, Chapter 6). The nominal model was designed for responses with no predetermined order; it uses the multivariate logistic distribution as the model for the probability of the selection of each of A > 2 response alternatives, conditional on the value of a latent individual differences variable. The model was originally developed as a logistic approximation to an individual differences version of the extension of Thurstone's (1927) method of paired comparisons to first choices among three or more objects. It can also be viewed as an individual differences extension of Luce's (1959) choice model, or less theoretically as the use of the multivariate logistic function as a link function in a standard nonlinear latent variable regression model; for a more extensive discussion of the theoretical underpinnings of the model, see Thissen et al. (2010).
