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A Latent Trait Model for Dichotomous Choice Data

Published online by Cambridge University Press:  01 January 2025

Herbert Hoijtink
Herbert Hoijtink*
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen, The Netherlands
*
Requests for reprints should be send 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 stimuli, with a one (zero) indicating agreement (disagreement) with the content of the stimulus. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and stimulus: the smaller the distance, the larger the probability that a person will agree with the content of the stimulus. An estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated.

Keywords

marginal maximum likelihoodexpectation maximizationnonmonotone trace linessingle-peaked preference functionslatent trait theoryunfolding
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 641 - 656
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

I gratefully acknowledge Ivo Molenaar and Wijbrandt van Schuur for their advice and encouragement during the course of the investigation, Derk-Jan Kiewiet who constructed the program for the ML estimator for the person parameter and Anne Boomsma, Wendy Post, Tom Snijders, and David Thissen for their comments on smaller aspects of the investigation.

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