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A Note on ALSCAL: The Estimation of the Additive Constant

Published online by Cambridge University Press:  01 January 2025

N. D. Verhelst
N. D. Verhelst*
Affiliation:
State University of Utrecht
*
Reprint requests should be addressed to N, D. Verhelst, Rijksaniversiteit Utrecht, Subfaculteit der psychologic, St. Jacobsstraat 14, 3511 BS Utrecht, The Netherlands.
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Abstract

A method is given for the least squares regression of a squared variable d2 on the squared variable 02, where the relation between 0 and d is linear. The problem arises in MDS-algorithms where the loss function is defined in terms of squared distances (e.g., ALSCAL). It is pointed out that the Lagrangian multiplier is a root of fourth degree polynomial.

Keywords

additive constantsquared distanceloss function in MDS
Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 465 - 468
Copyright
Copyright © 1981 The Psychometric Society

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References

Takane, Y., Young, F. W., & De Leeuw, J. Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika, 1977, 42, 7–67.CrossRefGoogle Scholar