Methodology Review: Nonparametric IRT Approaches to the Analysis of Dichotomous Item Scores

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Abstract
This paper reviews developments in nonparametric item response theory (NIRT). Historically, Mokken's (1971) item response theory (IRT) model and procedure of scale analysis have been the starting point for NIRT models; the developments that Mokken's work have inspired and those that originated independently are discussed here. Attention is focused on results pertaining to dichotomously scored items. The usefulness of new theoretical results for practical test construction is explained. NIRT is especially useful when the purpose of test application is to order persons, items, or both. The assumptions inherent in several NIRT models, model-data fit methods, item selection procedures, and reliability methods are discussed. NIRT models often allow more items into a test than stronger models, yielding higher reliability and better coverage of the latent trait. Moreover, the theoretical results from NIRT are often relevant to parametric IRT. Examples include conditional association and manifest monotonicity, as well as recent results for polytomous NIRT models that concem the ordering of persons, which also hold for several parametric IRT models.