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Paired Comparison, Triple Comparison, and Ranking Experiments as Generalized Linear Models, and Their Implementation on GLIM

Published online by Cambridge University Press:  01 January 2025

Douglas E. Critchlow  and
Michael A. Fligner
Douglas E. Critchlow
Affiliation:
Department of Statistics, The Ohio State University
Michael A. Fligner*
Affiliation:
Department of Statistics, The Ohio State University
*
Requests for reprints should be sent to Michael A. Fligner, Department of Statistics, The Ohio State University, 1958 Neil Avenue, Columbus, Ohio 43210.
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Abstract

A wide variety of paired comparison, triple comparison, and ranking experiments may be viewed as generalized linear models. These include paired comparison models based on both the Bradley-Terry and Thurstone-Mosteller approaches, as well as extensions of these models that allow for ties, order of presentation effects, and the presence of covariates. Moreover, the triple comparison model of Pendergrass and Bradley, as well as models for complete rankings of more than three items, can also be represented as generalized linear models. All such models can be easily fit by maximum likelihood, using the widely available GLIM computer package. Additionally, GLIM enables the computation of likelihood ratio statistics for testing many hypotheses of interest. Examples are presented that cover a variety of cases, along with their implementation on GLIM.

Keywords

paired comparisonsranking modelsgeneralized linear modelsBradley-Terry modelsThurstone-Mosteller models

Information

Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 3 , September 1991 , pp. 517 - 533
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The work of both authors was supported by the National Science Foundation. The first author was also supported by an Ohio State University Seed Grant. The authors thank Edward Richter and Maria Vargo Thomas for supplying the salad dressing data in Example 3, and the Associate Editor and referees for suggestions which led to a much improved version of the manuscript.

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