Person-fit assessment (PFA) is concerned with uncovering atypical test performance as reflected in the pattern of scores on individual items on a test. Existing person-fit statistics (PFSs) include both parametric and nonparametric statistics. Comparison of PFSs has been a popular research topic in PFA, but almost all comparisons have employed…

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…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

Inspection of differential item functioning (DIF) in translated test items can be informed by graphical comparisons of item response functions (IRFs) across translated forms. Due to the many forms of DIF that can emerge in such analyses, it is important to develop statistical tests that can confirm various characteristics of DIF when present.…

This study introduces an order-constrained Bayes inference framework useful for analyzing data containing dichotomous scored item responses, under the assumptions of either the monotone homogeneity model or the double monotonicity model of nonparametric item response theory (NIRT). The framework involves the implementation of Gibbs sampling to…

A method for ordering persons and items when all responses are ordinal was developed and applied to several sets of questionnaire data (from undergraduates) and one set of archeological data. The method provides a possible nonparametric treatment of data usually treated by more traditional psychometric methods. (SLD)