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.
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Carroll, J. D., Green, P. E., & Carmone, F. J.CANDELINC: A new method for multidimensional analysis with constrained solutions. Paper presented at the meeting of the International Congress of Psychology, Paris, France, July 1976.
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Douglas Carroll, J., Pruzansky, S. & Kruskal, J.B. Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters. Psychometrika 45, 3–24 (1980). https://doi.org/10.1007/BF02293596
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DOI: https://doi.org/10.1007/BF02293596