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Testing for DIF in a Model with Single Peaked Item Characteristic Curves: The Parella Model

Published online by Cambridge University Press:  01 January 2025

Herbert Hoijtink  and
Ivo W. Molenaar
Herbert Hoijtink*
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen, The Netherlands
Ivo W. Molenaar
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen, The Netherlands
*
Requests for reprints should be sent to Herbert Hoijtink, Department of Statistics and Measurement Theory, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

The PARELLA model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. The data analyzed are the dichotomous responses of persons to items, with a one (zero) indicating agreement (disagreement) with the content of the item. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and item: the smaller the distance, the larger the probability that a person will agree with the content of the item. This paper discusses how the approach to differential item functioning presented by Thissen, Steinberg, and Wainer can be implemented for the PARELLA model.

Keywords

marginal maximum likelihoodEM-algorithmnonmonotone trace linessingle-peaked preference functionslatent trait theoryunfoldingDIFdifferential item functioning
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 383 - 397
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

Requests for the PARELLA software should be sent to Iec Progamma PO Box 841, 9700 AV Groningen, The Netherlands.

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