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.
Similar content being viewed by others
References
Andersen, E. B. Asymptotic properties of conditional maximum likelihood estimators.Journal of the Royal Statistical Society, B, 1970,32, 283–301.
Andersen, E. B. Conditional inference and models for measuring. Copenhagen: Mentalhygiejnisk Forlag, 1973a.
Andersen, E. B. Conditional inference for multiple choice questionnaires.British Journal of Mathematical and Statistical Psychology, 1973b,26, 31–44.
Bradley, R. A. Incomplete block rank analysis: On the appropriateness of the model for a method of paired comparisons.Biometrics, 1954a,10, 375–390.
Bradley, R. A. Rank analysis of incomplete block designs II. Additional tables for the method of paired comparisons.Biometrika, 1954b,11, 502–537.
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, 450–470.
Bradley, R. A. and Terry, M. E. Rank analysis of incomplete block designs I. The method of paired comparisons.Biometrika, 1952,39, 324–345.
Birnbaum, A. Some latent trait models. In F. M. Lord and M. R. Novick,Statistical theories of mental test scores. Reading: Addison-Wesley, 1968.
Cox, D. R.Analysis of binary data. London: Methuen and Co., 1970.
David, H. A.The method of paired comparisons. New York: Haffner, 1963.
Kousgard, N. Models for paired comparisons with ties.Scandinavian Journal of Statistics, 1976,1, (in press).
Lehmann, E. L.Testing statistical hypotheses. New York: J. Wiley and Sons, 1959.
Lord, F. M. and Novick, M. R.Statistical theories of mental test scores. Reading: Addison-Wesley, 1968.
Luce, R. D.Individual choice behavior. New York: J. Wiley and Sons, 1959.
Neymann, J. and Scott, E. L. Consistent estimates based on partially consistent observations.Econometrika, 1948,16, 1–32.
Pfanzagl, J.Theory of measurement. New York: J. Wiley and Sons, 1969.
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, 321–333.
Rasch, G. An item analysis which takes individual differences into account.British Journal of Mathematical and Statistical Psychology, 1966,19, 49–57.
Schönemann, P. H. and Wang, M. M. An individual model for the multidimensional analysis of preference data.Psychometrika, 1972,37, 275–310.
Sixtl, F. Probabilistic unfolding.Psychometrika, 1973,38, 235–248.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andersen, E.B. Paired comparisons with individual differences. Psychometrika 41, 141–157 (1976). https://doi.org/10.1007/BF02291835
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02291835