This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Junker, B. W. Articles by Sijtsma, K. Search for Related Content Social Bookmarking                   What's this?

Latent and Manifest Monotonicity in Item Response Models

Carnegie Mellon Universitybrian{at}stat.cmu.edu

Klaas Sijtsma

Tilburg University

The monotonicity of item response functions(IRF) is a central feature of most parametric andnonparametric item response models. Monotonicityallows items to be interpreted as measuring a trait,and it allows for a general theory of nonparametricinference for traits. This theory is based on monotonelikelihood ratio and stochastic ordering properties.Thus, confirming the monotonicity assumption isessential to applications of nonparametric itemresponse models. The results of two methods ofevaluating monotonicity are presented: regressingindividual item scores on the total test score andon the ‘rest’ score, which is obtained by omittingthe selected item from the total test score. It wasfound that the item-total regressions of some familiardichotomous item response models with monotoneIRFs exhibited nonmonotonicities that persist as thetest length increased. However, item-rest regressionsnever exhibited nonmonotonicities under the nonparametricmonotone unidimensional item responsemodel. The implications of these results for exploratoryanalysis of dichotomous item response dataand the application of these results to polytomousitem response data are discussed.

CiteULike    Connotea    Del.icio.us    Digg    Reddit    Technorati    What's this?

This article has been cited by other articles:

				G. Karabatsos and C.-F. Sheu Order-Constrained Bayes Inference for Dichotomous Models of Unidimensional Nonparametric IRT Applied Psychological Measurement, March 1, 2004; 28(2): 110 - 125. [Abstract] [PDF]

				E. De Koning, K. Sijtsma, and J. H. M. Hamers Comparison of Four IRT Models When Analyzing Two Tests for Inductive Reasoning Applied Psychological Measurement, September 1, 2002; 26(3): 302 - 320. [Abstract] [PDF]

				B. W. Junker and K. Sijtsma Nonparametric Item Response Theory in Action: An Overview of the Special Issue Applied Psychological Measurement, September 1, 2001; 25(3): 211 - 220. [PDF]

				B. Habing Nonparametric Regression and the Parametric Bootstrap for Local Dependence Assessment Applied Psychological Measurement, September 1, 2001; 25(3): 221 - 233. [Abstract] [PDF]

				B. W. Junker and K. Sijtsma Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory Applied Psychological Measurement, September 1, 2001; 25(3): 258 - 272. [Abstract] [PDF]