The Use of Nonparametric Item Response Theory to Explore Data Quality

The aim of this chapter is to provide insight into a number of commonly used nonparametric item response theory (NIRT) methods and to show how these methods can be used to describe and explore the psychometric quality of questionnaires used in patient-reported outcome measurement and, more in general, typical performance measurement (personality, mood, health-related constructs). NIRT is an extremely valuable tool for preliminary data analysis and for evaluating whether item response data are acceptable for parametric IRT modeling. This is in particular useful in the field of typical performance measurement where the construct being measured is often very different than in maximum performance measurement (education, intelligence; see Chapter 1 of this handbook). Our basic premise is that there are no “best tools” or “best models” and that the usefulness of psychometric modeling depends on the specific aims of the instrument (questionnaire, test) that is being used. Most important is, however, that it should be clear for a researcher how sensitive a specific method (for example, DETECT, or Mokken scaling) is to the assumptions that are being investigated. The NIRT literature is not always clear about this, and in this chapter we try to clarify some of these ambiguities

Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics

We present a class of periodic solutions of the non-chiral intermediate Heisenberg ferromagnet (ncIHF) equation, which was recently introduced by the authors together with Langmann as a classical, continuum limit of an Inozemtsev-type spin chain. These exact analytic solutions are constructed via a spin-pole ansatz written in terms of certain elliptic functions. The dynamical parameters in our solutions solve an elliptic spin Calogero-Moser (CM) system subject to certain constraints. In the course of our construction, we establish a novel B\"acklund transformation for this constrained elliptic spin CM system.Comment: 37 pages, 3 figure