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Nonparametric IRT: Testing the Bi-isotonicity of Isotonic Probabilistic Models (ISOP)

Published online by Cambridge University Press:  01 January 2025

Hartmann Scheiblechner
Hartmann Scheiblechner*
Affiliation:
Philipps-Universität Marburg
*
Requests for reprints should be sent to Hartmann Scheiblechner, FB 04 Universitfit, Marburg, Gutenbergstrae 18, D-35032 Marburg, GERMANY. E-Mail: scheible@mailer.uni-marburg.de
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Abstract

Nonparametric tests for testing the validity of polytomous ISOP-models (unidimensional ordinal probabilistic polytomous IRT-models) are presented. Since the ISOP-model is a very general nonparametric unidimensional rating scale model the test statistics apply to a great multitude of latent trait models. A test for the comonotonicity of item sets of two or more items is suggested. Procedures for testing the comonotonicity of two item sets and for item selection are developed. The tests are based on Goodman-Kruskal's gamma index of ordinal association and are generalizations thereof. It is an essential advantage of polytomous ISOP-models within probabilistic IRT-models that the tests of validity of the model can be performed before and without the model being fitted to the data. The new test statistics have the further advantage that no prior order of items or subjects needs to be known.

Keywords

instrumental pair comparison systemsweak subject independenceweak item independencemultidimensional coordinatewise partial ordersample-free estimatesindex of association and of isotonicity
Type
Articles
Information
Psychometrika , Volume 68 , Issue 1 , March 2003 , pp. 79 - 96
Copyright
Copyright © 2003 The Psychometric Society

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