A method for investigating the intersection of item response functions in Mokken’s nonparametric IRT model

For a set of k items having nonintersecting item response functions (IRFS), the H coefficient (Loevinger, 1948; Mokken, 1971) applied to a transposed persons by items binary matrix HThas a non-negative value. Based on this result, a method is proposed for using HT to investigate whether a set of IRFS intersect. Results from a monte carlo study support the proposed use of HT. These results support the use of HT as an exten-sion to Mokken’s nonparametric item response theory approach. Index terms: double monotoni-city, HT coefficient, intersection of item response func-tions, item response theory, Mokken models, non-parametric models. In item response models, the item response function (IRF) specifies the relationship between th