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A Note on the Determination of Configuration and Weights for a Class of Individual Scaling Models

Published online by Cambridge University Press:  01 January 2025

Vina Vani  and
M. Raghavachari
Vina Vani
Affiliation:
M. G. Science Institute, Ahmedabad, India
M. Raghavachari*
Affiliation:
I. I. M. Ahmedabad and University of Pennsylvania
*
Requests for reprints should be sent to M. Raghavachari, Department of Statistics, Wharton School, University of Pennsylvania, Philadelphia, PA, 19104.
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Abstract

Consider the typical problem in individual scaling, namely finding a common configuration and weights for each individual from the given interpoint distances or scalar products. Within the STRAIN framework it is shown that the problem of determining weights for a given configuration can be posed as a standard quadratic programming problem. A set of necessary conditions for an optimal configuration to satisfy are given. A closed form expression for the configuration is obtained for the one dimensional case and an approach is given for the two dimensional case.

Keywords

individual scalingconfigurationweightsquadratic programmingSTRAINeigenvectoreigenvalue
Type
Notes And Comments
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 539 - 542
Copyright
Copyright © 1985 The Psychometric Society

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