The Rating Scale Model (RSM) and the Partial Credit Model (PCM) are fairly well-known examples of Rasch models for polytomously scored items. In addition to a number of threshold parameters, both the models contain two scalar parameters characterizing item and person location on a common interval-level scale. The rank order of items and persons defined by the Likert summative scores (i.e. the raw total scores) is compared with that obtained from the Rasch-based measures (i.e. the maximum likelihood estimates of person and item parameters). It is proved that: 1) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for both the person and item parameters of the RSM; 2) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for the PCM only with reference to the person parameters; 3) violations of comonotonicity are possible, for particular datasets, for the item parameters of the PCM.

On the lack of comonotonicity between likert scores and rasch-based measures

BERTOLI BARSOTTI, Lucio
2005

Abstract

The Rating Scale Model (RSM) and the Partial Credit Model (PCM) are fairly well-known examples of Rasch models for polytomously scored items. In addition to a number of threshold parameters, both the models contain two scalar parameters characterizing item and person location on a common interval-level scale. The rank order of items and persons defined by the Likert summative scores (i.e. the raw total scores) is compared with that obtained from the Rasch-based measures (i.e. the maximum likelihood estimates of person and item parameters). It is proved that: 1) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for both the person and item parameters of the RSM; 2) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for the PCM only with reference to the person parameters; 3) violations of comonotonicity are possible, for particular datasets, for the item parameters of the PCM.
journal article - articolo
BERTOLI BARSOTTI, Lucio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/20877
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