A Method for Investigating the Intersection of Item Response Functions in Mokken's Nonparametric IRT Model

Klaas Sijtsma · Rob R. Meijer

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Psychometric Methodologies and Testing Psychological Testing and Assessment Educational Assessment and Pedagogy

Abstract

For a set of k items having nonintersecting item response functions (IRFS), the H coefficient (Loevinger, 1948; Mokken, 1971) applied to a transposed persons by items binary matrix H T has a non-negative value. Based on this result, a method is proposed for using H T to investigate whether a set of IRFS intersect. Results from a monte carlo study support the proposed use of H T . These results support the use of H T as an exten sion to Mokken's nonparametric item response theory approach.

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References

1969Statistical Theories of Mental Test Scores 2012Applications of Item Response Theory To Practical Testing Problems 1971A Theory and Procedure of Scale Analysis 1973A Theory and Procedure of Scale Analysis.1987A Nonparametric Approach for Assessing Latent Trait Unidimensionality 1982A Nonparametric Approach to the Analysis of Dichotomous Item Responses 1948The technic of homogeneous tests compared with some aspects of "scale analysis" and factor analysis.1986Conditional Association and Unidimensionality in Monotone Latent Variable Models

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