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Introduction to Nonparametric Item Response Theory, by Klaas Sijtsma and Ivo W. Molenaar (2002). Thousand Oaks, CA: Sage, 168 pages. ISBN 0-7619-0812-9.
This book is the fifth installment in Sage's series "Measurement Methods for the Social Sciences" and the second in that series to explicitly focus on item response theory (IRT). Whereas its sibling, Fundamentals of Item Response Theory (Hambleton, Swaminathan, & Rogers, 1991) focuses primarily on parametric IRT models, this volume provides a needed introduction to their nonparametric counterparts. My unrestricted searches of the Psychlnfo and ERIC databases for the term nonparametric item response theory returned only two other books, neither of which is expressly dedicated to the topic. So, at least for the moment, this book is practically the only game in town for instructors wishing to adopt a text for extensive coverage of nonparametric IRT in their courses. Fortunately, it fills the bill well.
Most readers probably associate the term parametric with assumptions about normal distributions. In the context of IRT, however, parametric refers to assumptions about the form of the relations between observed item responses and their corresponding latent constructs, called item response functions (IRFs). The more familiar, parametric IRT models, which are increasingly being applied in organizational settings, typically estimate logistic IRFs, with their characteristic "stair step" shape. Examples include the graded response model for Likert-type response scales and the one-, two-, and three-parameter logistic models for dichotomous response scales (IPL, 2PL, and 3PL, respectively). In contrast, nonparametric IRT models allow IRFs to take virtually any form, rather than constraining them to a logistic shape.
Theoretically, nonparametric models have an advantage over their parametric counterparts in that they can be applied to a wider variety of data, owing to their less restrictive assumptions. In practice, however, there are substantial trade-offs associated with choosing nonparametric models over parametric models. These include the ability to generate point estimates of item and person parameters-something users of parametric models probably take for granted. As a result of these trade-offs, researchers who are considering whether to apply parametric or nonparametric IRT models to their data are faced with a fairly complex set of factors to weigh. Sijtsma and Molenaar do a good job of spelling out the issues and walking...