Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T18:26:45.458Z Has data issue: false hasContentIssue false
  • English
  • Français

Ordmet: A General Algorithm for Constructing All Numerical Solutions to Ordered Metric Structures

Published online by Cambridge University Press:  01 January 2025

Gary H. McClelland  and
Clyde H. Coombs
Gary H. McClelland
Affiliation:
University of Colorado
Clyde H. Coombs
Affiliation:
The University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

The algorithm is applicable to structures such as are obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, some special types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, the size and shape of which is informative. The Abelson-Tukey maximin r2 solution is provided.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 3 , September 1975 , pp. 269 - 290
Copyright
Copyright © 1975 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.)

Footnotes

1

This research was supported in part by NIGMS Grant GM-01231 to the University of Michigan.

References

Abelson, R. P. and Tukey, J. W.. Efficient utilization of non-numerical information in quantitative analysis: General theory and the case of simple order. Annals of Mathematical Statistics, 1963, 34, 1347–1369.CrossRefGoogle Scholar
Birnbaum, M. H.. Morality judgments: Test of an averaging model. Journal of Experimental Psychology, 1972, 93, 35–42.CrossRefGoogle Scholar
Coombs, C. H.. A Theory of Data, 1964, New York: Wiley.Google Scholar
Davidson, D., Suppes, P., and Siegel, S.. Decision making: An experimental approach, 1957, Stanford: Stanford University Press.Google Scholar
Dawkins, R.. A threshold model of choice behavior. Animal Behavior, 1969, 17, 120–133.CrossRefGoogle Scholar
Farkas, J.. Veber die Theorie der einfachen Ungleichungen. Journal fur die Reine and Angewandte Mathematik, 1902, 124, 1–27.Google Scholar
Goode, F. M.. An algorithm for the additive conjoint measurement of finite data matrices. American Psychologist, 1964, 19, 579–579.Google Scholar
Krantz, D. H., Luce, R. D., Suppes, P., and Tversky, A.. Foundations of Measurement, Volume I, 1971, New York: Academic Press.Google Scholar
Luce, R. D., and Suppes, P.. Preference, utility, and subjective probability. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of Mathematical Psychology, Vol. III. New York: Wiley. 1965, 249–410.Google Scholar
Phillips, J. P. N.. A note on representation of ordered metric scaling. British Journal of Mathematical and Statistical Psychology, 1971, 24, 239–250.CrossRefGoogle Scholar
Tversky, A., and Zivian, A.. A computer program for additivity analysis. Behavioral Science, 1966, 11, 78–79.Google Scholar
Wets, R. J. B., and Witzgall, C.. Algorithms for frames and linearity spaces of cones. Journal of Research of the National Bureau of Standards, 1967, 71B, 1–7.CrossRefGoogle Scholar
Yellott, J. I. Jr. Generalized Thurstone representations for three choice theories: Uniqueness results. Paper presented at Mathematical Psychology Meetings, Princeton, New Jersey, September 1–2, 1971.Google Scholar