Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-07T18:37:47.231Z Has data issue: false hasContentIssue false

Paired Comparisons with Individual Differences

Published online by Cambridge University Press:  01 January 2025

Erling B. Andersen*
Affiliation:
University of Copenhagen
*
Requests for reprints should be addressed to Dr. Erling B. Andersen, Department of Statistics, University of Copenhagen, Studiestrade 6, 1455 Copenhagen, Denmark.

Abstract

A model of Bradley-Terry type for paired comparisons is considered. In addition to the usual parameters, the model allows for individual parameters and corresponding parameters for the choice-alternatives. The model is applied to a set of data from a Danish investigation of the attitude of blue collar workers towards alternative social gains. The proposed model is finally compared to a model recently suggested by Schönemann and Wang.

Type
Original Paper
Copyright
Copyright © 1976 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andersen, E. B. Asymptotic properties of conditional maximum likelihood estimators. Journal of the Royal Statistical Society, 1970, 32, 283301.CrossRefGoogle Scholar
Andersen, E. B. Conditional inference and models for measuring, 1973, Copenhagen: Mentalhygiejnisk Forlag.Google Scholar
Andersen, E. B. Conditional inference for multiple choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 3144.CrossRefGoogle Scholar
Bradley, R. A. Incomplete block rank analysis: On the appropriateness of the model for a method of paired comparisons. Biometrics, 1954, 10, 375390.CrossRefGoogle Scholar
Bradley, R. A. Rank analysis of incomplete block designs II. Additional tables for the method of paired comparisons. Biometrika, 1954, 11, 502537.Google Scholar
Bradley, R. A. Rank analysis of incomplete block designs III. Some large sample results on estimation and power for a method of paired comparisons. Biometrika, 1955, 42, 450470.Google Scholar
Bradley, R. A. and Terry, M. E. Rank analysis of incomplete block designs I. The method of paired comparisons. Biometrika, 1952, 39, 324345.Google Scholar
Birnbaum, A. Some latent trait models. In Lord, F. M. and Novick, M. R. (Eds.), Statistical theories of mental test scores, 1968, Reading: Addison-Wesley.Google Scholar
Cox, D. R. Analysis of binary data, 1970, London: Methuen and Co..Google Scholar
David, H. A. The method of paired comparisons, 1963, New York: Haffner.Google Scholar
Kousgard, N. Models for paired comparisons with ties. Scandinavian Journal of Statistics, 1976, 1, (in press).Google Scholar
Lehmann, E. L. Testing statistical hypotheses, 1959, New York: J. Wiley and Sons.Google Scholar
Lord, F. M. and Novick, M. R. Statistical theories of mental test scores, 1968, Reading: Addison-Wesley.Google Scholar
Luce, R. D. Individual choice behavior, 1959, New York: J. Wiley and Sons.Google Scholar
Neymann, J. and Scott, E. L. Consistent estimates based on partially consistent observations. Econometrika, 1948, 16, 132.CrossRefGoogle Scholar
Pfanzagl, J. Theory of measurement, 1969, New York: J. Wiley and Sons.Google Scholar
Rasch, G. On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability Theory, 1961, 5, 321333.Google Scholar
Rasch, G. An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 1966, 19, 4957.CrossRefGoogle ScholarPubMed
Schönemann, P. H., Wang, M. M. An individual model for the multidimensional analysis of preference data. Psychometrika, 1972, 37, 275310.CrossRefGoogle Scholar
Sixtl, F. Probabilistic unfolding. Psychometrika, 1973, 38, 235248.CrossRefGoogle Scholar