The Additive Constant Problem in Multidimensional Scaling

Author(s):

Abelson, Robert P; Messick, Samuel J.

Publication Year:

1954

Report Number:

RB-54-13

Source:

ETS Research Bulletin

Document Type:

Report

Page Count:

27

Subject/Key Words:

Additive Constant, Mathematical Models, Multidimensional Scaling, Tucker, Ledyard R

Abstract

The problem of choosing the correct additive constant to convert relative inter-stimulus distances to absolute inter-stimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Ledyard Tucker, is presented, and each of the computational steps in this solution are set down for easy reference.

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• http://dx.doi.org/10.1002/j.2333-8504.1954.tb00240.x