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An Item Response Model for Nominal Data Based on the Rising Selection Ratios Criterion

Published online by Cambridge University Press:  01 January 2025

Javier Revuelta
Javier Revuelta*
Affiliation:
Autonoma University of Madrid
*
Requests for reprints should be sent to Javier Revuelta, Departamento de Psicologia Social y Metodologia, Universidad Autonoma Madrid, Cantoblanco 28049, Madrid, Spain. Email: javier.revuelta@uam.es
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Abstract

Complete response vectors of all answer options in multiple-choice items can be used to estimate ability. The rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected. This paper introduces the generalized DLT model, which assumes rising selection ratios and uses three parameters to describe each incorrect alternative. It is shown that the nominal categories and the Thissen and Steinberg model do not meet the criterion. A simulation study on goodness of recovery and an example with real data are also included.

Keywords

multiple-choice itemsnominal datarising selection ratioDLTnominal categories modelThissen & Steinberg model.

Information

Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 2 , June 2005, pp. 305 - 324
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

This research was partially supported by the DGICYT grant PB 97-0049 and the Comunidad de Madrid grant 06/HSE/0005/2004. I would like to express my gratitude to three anonymous reviewers, the associate editor and two editors for their helpful and thoughtful comments that contributed for improving an earlier version of the manuscript.

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