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Candelinc: A General Approach to Multidimensional Analysis of Many-Way Arrays with Linear Constraints on Parameters

Published online by Cambridge University Press:  01 January 2025

J. Douglas Carroll ,
Sandra Pruzansky  and
Joseph B. Kruskal
J. Douglas Carroll*
Affiliation:
Bell Telephone Laboratories
Sandra Pruzansky
Affiliation:
Bell Telephone Laboratories
Joseph B. Kruskal
Affiliation:
Bell Telephone Laboratories
*
Requests for reprints should be sent to J. Douglas Carroll, Belt Laboratories, 2C-553, Murray Hill, New Jersey 07974.
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Abstract

Very general multilinear models, called CANDELINC, and a practical least-squares fitting procedure, also called CANDELINC, are described for data consisting of a many-way array. The models incorporate the possibility of general linear constraints, which turn out to have substantial practical value in some applications, by permitting better prediction and understanding. Description of the model, and proof of a theorem which greatly simplifies the least-squares fitting process, is given first for the case involving two-way data and a bilinear model. Model and proof are then extended to the case of N-way data and an N-linear model for general N. The case N = 3 covers many significant applications. Two applications are described: one of two-way CANDELINC, and the other of CANDELINC used as a constrained version of INDSCAL. Possible additional applications are discussed.

Keywords

constrained least-squaresmultilinear modelsbilinear modelsINDSCALmultidimensional scaling3-mode factor analysisCANDECOMPLINCINDSmultivariate analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 3 - 24
Copyright
Copyright © 1980 The Psychometric Society

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References

Reference Notes

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