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An efficient algorithm for TUCKALS3 on data with large numbers of observation units

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Abstract

A modification of the TUCKALS3 algorithm is proposed that handles three-way arrays of order I × J × K for any I. When I is much larger than JK, the modified algorithm needs less work space to store the data during the iterative part of the algorithm than does the original algorithm. Because of this and the additional feature that execution speed is higher, the modified algorithm is highly suitable for use on personal computers.

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References

  • Bentler, P. M., & Lee, S.-Y. (1978). Statistical aspects of a three-mode factor analysis model.Psychometrika, 43, 343–352.

    Article  Google Scholar 

  • Bentler, P. M., & Lee, S.-Y. (1979). A statistical development of three-mode factor analysis.British Journal of Mathematical and Statistical Psychology, 32, 87–104.

    Google Scholar 

  • Bentler, P. M., Poon, W.-Y., & Lee, S.-Y. (1988). Generalized multimode latent variable models: Implementation by standard programs.Computational Statistics and Data Analysis, 6, 107–118.

    Google Scholar 

  • Bloxom, B. (1968). A note on invariance in three-mode factor analysis.Psychometrika, 33, 347–350.

    PubMed  Google Scholar 

  • Browne, M. W. (1984). The decomposition of multitrait-multimethod matrices.British Journal of Mathematical and Statistical Psychology, 37, 1–21.

    PubMed  Google Scholar 

  • Cliff, N. (1966). Orthogonal rotation to congruence.Psychometrika, 31, 33–42.

    Article  Google Scholar 

  • Kiers, H. A. L., & Krijnen, W. P. (1991). An efficient algorithm for PARAFAC of three-way data with large numbers of observation units.Psychometrika, 56, 147–152.

    Google Scholar 

  • Kroonenberg, P. M. (1983).Three-mode principal component analysis. Leiden: DSWO Press.

    Google Scholar 

  • Kroonenberg, P. M., & de Leeuw, J. (1980). Principal component analysis of three-mode data by means of alternating least squares algorithms.Psychometrika, 45, 69–97.

    Article  Google Scholar 

  • Kroonenberg, P. M., ten Berge, J. M. F., Brouwer, P., & Kiers, H.A.L. (1989). Gram-Schmidt versus Bauer-Rutishauser in alternating least-squares algorithms for three-mode principal component analysis.Computational Statistics Quarterly, 5, 81–87.

    Google Scholar 

  • Lawson, C. L., & Hanson, R. J. (1974).Solving least squares problems. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Lee, S.-Y., & Fong, W.-K. (1983). A scale invariant model for three-mode factor analysis.British Journal of Mathematical and Statistical Psychology, 36, 217–223.

    Google Scholar 

  • McDonald, R. P. (1984). The invariant factors model for multimode data. In H. G. Law, C. W. Snyder, J. A. Hattie, & R. P. McDonald (Eds.),Research methods for multimode data analysis (pp. 285–307). New York: Praeger.

    Google Scholar 

  • Murakami, T. (1983). Quasi three-mode principal component analysis—A method for assessing the factor change.Behaviormetrika, 14, 27–48.

    Google Scholar 

  • Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis.Psychometrika, 31, 279–311.

    PubMed  Google Scholar 

  • ten Berge, J. M. F., de Leeuw, J., & Kroonenberg, P. M. (1987). Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms.Psychometrika, 52, 183–191.

    Article  Google Scholar 

  • Verhees, J. (1989).Econometric analysis of multidimensional models. Unpublished doctoral dissertation, University of Groningen.

  • Verhees, J., & Wansbeek, T. J. (1990). A multimode direct product model for covariance structure analysis.British Journal of Mathematical and Statistical Psychology, 43, 231–240.

    Google Scholar 

  • Weesie, H. M., & Van Houwelingen, J. C. (1983).GEPCAM users' manual: Generalized principal components analysis with missing values. Unpublished manuscript, University of Utrecht, Institute of Mathematics.

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This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author.

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Kiers, H.A.L., Kroonenberg, P.M. & ten Berge, J.M.F. An efficient algorithm for TUCKALS3 on data with large numbers of observation units. Psychometrika 57, 415–422 (1992). https://doi.org/10.1007/BF02295429

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  • DOI: https://doi.org/10.1007/BF02295429

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