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Was Euclid an Unnecessarily Sophisticated Psychologist?

Published online by Cambridge University Press:  01 January 2025

Phipps Arabie
Phipps Arabie*
Affiliation:
Graduate School of Management, Rutgers University
*
Requests for reprints should be sent to Phipps Arabic, Graduate School of Management, Rutgers University, 92 New Street, Newark, NJ 07102-1895.
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Abstract

A survey of the current state of multidimensional scaling using the city-block metric is presented. Topics include substantive and theoretical issues, recent algorithmic developments and their implications for seemingly straightforward analyses, isometries with other metrics, links to graph-theoretic models, and future prospects.

Keywords

multidimensional scalingfacility planingcity-block distancesMinkowski metricsrectangular metricrectilinear metricManhattan metriccombination rules

Information

Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 4 , December 1991, pp. 567 - 587
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

Presented as the 1991 Psychometric Society Presidential Address. I am indebted to Doug Carroll, John Daws, Jan de Leeuw, Geert De Soete, Wayne DeSarbo, Eric Holman, Larry Hubert, Chingis Izmailov, Joe Kruskal, Rob Nosofsky, Akinori Okada, Roger Shepard, Auke Tellegen, and Wijbrandt van Schuur for many helpful comments on this research and to Yuko Minowa for bibliographic assistance. Doug Carroll's comments on an early draft were especially useful. Parts of this research were supported by a grant from AT&T to the University of Illinois. Some of the computational results reported here were obtained during the early 1970's at the Institute for Mathematical Studies in the Social Sciences at Stanford. Grateful acknowledgment is made to the Institute's staff and its Co-Directors, Richard C. Atkinson and Patrick Suppes.

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