A note on converting calibrated parameters of item response theory models

Abstract

Many item response theory models were proposed to estimate ability levels of test takers using their responses to a set of polytomously scored items. Recently, an increased number of calibrated item parameters have become publicly available. Unfortunately, these parameters are often calibrated under some model that is not the researcher’s target model. This note presents a straightforward computational method to convert one set of calibrated item parameters to the corresponding parameters of another target model. The core of the method stands in equating the response category probabilities of both models. The accuracy of the method is assessed through several examples.

Keywords:

• Item response theory
• Polytomous responses
• Difference model
• Divide-by-total model
• Calibration

Acknowledgments

David Magis is Research Associate of the Fonds de la Recherche Scientifique – FNRS at the University of Liège (Belgium). Correspondence should be sent to: David Magis, Department of Psychology (B32), University of Liège, Quartier Agora, Place des Orateurs 2, B-4000 Liège, Belgium (E-mail: [email protected]).