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2 results

  • Principal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms

  • Pieter M. Kroonenberg, Jan de Leeuw
  • Journal:
    Psychometrika / Volume 45 / Issue 1 / March 1980
    Published online by Cambridge University Press:
    01 January 2025, pp. 69-97

  • 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.

  • Decompositions and Biplots in Three-Way Correspondence Analysis

  • André Carlier, Pieter M. Kroonenberg
  • Journal:
    Psychometrika / Volume 61 / Issue 2 / June 1996
    Published online by Cambridge University Press:
    01 January 2025, pp. 355-373

  • In this paper correspondence analysis for three-way contingency tables is presented using three-way generalisations of the singular value decomposition. It is shown that in combination with Lancaster's (1951) additive decomposition of interactions in three-way tables, a detailed analysis is possible of the deviations from independence. Finally, biplots are shown to produce powerful graphical representations of the results from three-way correspondence analyses. An example from child development is used to illustrate the theoretical developments.