Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

The (univariate) isotonic psychometric (ISOP) model (Scheiblechner, 1995) is a nonparametric IRT model for dichotomous and polytomous (rating scale) psychological test data. A weak subject independence axiom W1 postulates that the subjects are ordered in the same way except for ties (i.e., similarly or isotonically) by all items of a psychological…

Presented nonparametric tests for testing the validity of polytomous unidimensional ordinal probabilistic polytomous item response theory models along with procedures for testing the comonotonicity of two item sets and for item selection. Describes advantages of the new approach. (SLD)

Presents an overview of nonparametric regression as it allies to differential item functioning analysis and then provides three examples to illustrate how nonparametric regression can be applied to multilingual, multicultural data to study group differences. (SLD)

New items are being calibrated for the next generation of the computerized adaptive (CAT) version of the Armed Services Vocational Aptitude Battery (ASVAB) (Forms 5 and 6). The requirements that the items be "good" three-parameter logistic (3-PL) model items and typically "like" items in the previous CAT-ASVAB tests have…

In the present paper, a new family of item response theory (IRT) models for dichotomous item scores is proposed. Two basic assumptions define the most general model of this family. The first assumption is local independence of the item scores given a unidimensional latent trait. The second assumption is that the odds-ratios for all item-pairs are…