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Psychometrika

, Volume 45, Issue 1, pp 3–24 | Cite as

Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters

  • J. Douglas Carroll
  • Sandra Pruzansky
  • Joseph B. Kruskal
Article

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 ofN-way data and anN-linear model for generalN. The caseN = 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.

Key words

constrained least-squares multilinear models bilinear models INDSCAL multidimensional scaling 3-mode factor analysis CANDECOMP LINCINDS multivariate analysis 

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Reference notes

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Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • J. Douglas Carroll
    • 1
  • Sandra Pruzansky
    • 1
  • Joseph B. Kruskal
    • 1
  1. 1.Bell Laboratories, 2C-553Murray Hill

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