, Volume 45, Issue 1, pp 69–97

Principal component analysis of three-mode data by means of alternating least squares algorithms

  • Pieter M. Kroonenberg
  • Jan de Leeuw

DOI: 10.1007/BF02293599

Cite this article as:
Kroonenberg, P.M. & de Leeuw, J. Psychometrika (1980) 45: 69. doi:10.1007/BF02293599


A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.

Key words

three-mode principal component analysisalternating least squaresfactor analysismultidimensional scalingindividual differences scalingsimultaneous iterationconfusion of consonants

Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • Pieter M. Kroonenberg
    • 1
  • Jan de Leeuw
    • 1
  1. 1.University of LeidenThe Netherlands
  2. 2.Vakgroep W.E.P., Subfakulteit der Pedagogische en Andragogische WetenschappenLeidenThe Netherlands