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A latent trait model for dichotomous choice data

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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.

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Authors and Affiliations

  1. Department of Statistics and Measurement Theory, University of Groningen, Grote Kruisstraat 2/1, 9712 TS, Groningen, The Netherlands

    Herbert Hoijtink

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  1. Herbert Hoijtink
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Additional information

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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Hoijtink, H. A latent trait model for dichotomous choice data. Psychometrika 55, 641–656 (1990). https://doi.org/10.1007/BF02294613

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  • DOI: https://doi.org/10.1007/BF02294613

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