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Measurement and Multivariate Analysis

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Book cover Measurement and Multivariate Analysis
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Summary

This paper is prepared to serve the purpose of introducing the readers to the main theme of this conference. The emphasis is placed on the introduction of desirable properties of measurements so as to make the outcomes of multivariate analysis meaningful. Starting with such fundamental requirements for measurements to be valid as metric axioms and the Young-Householder theorem, the paper is then extended to the discussion of two topics where we see important interplays between measurement and multivariate analysis. The paper is concluded with a note on the importance of a well-balanced interplay between measurement and multivariate analysis, to which end this international and interdisciplinary conference was planned and successfully organized.

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References

  • Beltrami, E. (1873). Sulle funzioni bilineari [On the bilinear releations[. in G. Battagline and E. Pergola (Eds.) Giornale di hfathematiche, 11, 98–106.

    Google Scholar 

  • Bentler, P.M. (1989). EQS structural equation program manual. Los Angeles: BMDP Statistical Software.

    Google Scholar 

  • Bock, R. D. (1960). Methods and applications of optimal scaling. The University of North Carolina Psychometric Laboratory Research Memorandum, No. 5.

    Google Scholar 

  • Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley Interscience.

    MATH  Google Scholar 

  • Bollen. K. and Long, S. (eds.) (1993) Testing structural equation models. Newbury Park: Sage.

    Google Scholar 

  • Cronbach, L.J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334.

    Article  Google Scholar 

  • de Leeuw, J. (1973). Canonical analysis of relational data. Department of Data Theory, Leiden University, Report RN 007–68.

    Google Scholar 

  • Eckart, C. and Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 211–218.

    Article  MATH  Google Scholar 

  • Escofier-Cordier, E. (1969). L’analyse factorielle des correspondances. Bureau Universitaire de Recherche Operationelle, Cahiers, Série Recherche, 13, 25–29.

    Google Scholar 

  • Gabriel, K.R. (1971). The biplot graphical display of matrices with applications to principal component analysis. Biometrika, 58, 453–457.

    Article  MathSciNet  MATH  Google Scholar 

  • Gorsuch, R.L. (1983). Factor analysis ( second edition ). Hillsdale, N.J.: Lawrence Erlbaum.

    Google Scholar 

  • Hamming, R.`V. (1950). error detecting and error correcting codes. The Bell Sys-tern Technical Journal, 26, 147–160.

    Google Scholar 

  • Hayashi, C. (1950). On the quantification of qualitative data from the mathematicostatistical point of view. Annals of the Institute of Statistical Mathematics, 2, 35–47.

    Article  MathSciNet  MATH  Google Scholar 

  • Hand, D. J. (1996). Statistics and the theory of measurement. Journal of the Royal Statistical Society, A, 150, Part 3, 445–492.

    Google Scholar 

  • Hemsworth, D. (2002). The use of dual scaling for the production of correlation matrices for use in structural equation modeling. Unpublished Ph.D. thesis, University of Toronto.

    Google Scholar 

  • Hill, M.O. (1974). Correspondence analysis: A neglected multivariate method. Applied Statistics, 23, 340–354.

    Article  Google Scholar 

  • Hirschfeld, H.O. (1935). A connection between correlation and contingency. Cambridge Philosophical Society Proceedings, 31, 520–524.

    Article  Google Scholar 

  • Horst, P. (1935). Measuring complex attitudes. Journal of Social Psychology, 6, 369–374.

    Article  Google Scholar 

  • Hotelling, H. (1936). Relation between two sets of variables. Biometrika, 28, 321–377.

    MATH  Google Scholar 

  • Jordan, C. (1874). Mémoire sur les formes bilinieares [Note on bilinear forms]. Journal de Mathématiques Pures et Appliquées, Deuxiéme Série, 19, 35–54.

    MATH  Google Scholar 

  • J6reskog, K. and Sorbom, D. (1981). Analysis of linear structural relationships by maximum likelihood and least squares methods. ( 81–8 ). Uppsala: University of Uppsala.

    Google Scholar 

  • Kendall, M.G. and Stuart, A. (1961). The advanced theory of statistics. Volume II. Longon: Griffin.

    Google Scholar 

  • Minkowski, H. (1896). Geometrie der Zahlen. Leipzig: Teubner.

    Google Scholar 

  • Muthén, B. 0. (1987). LISCOMP: Analysis of linear structure equations with a comprehensive measurement model. Moorresville, Indiana: Scientific Software.

    Google Scholar 

  • Nishisato, S. (1980). Analysis of categorical data. Toronto: University of Toronto Press.

    MATH  Google Scholar 

  • Nishisato, S. (1993). On quantifying different types of categorical data. Psychometrika. 58, 617–629.

    Article  MATH  Google Scholar 

  • Nishisato, S. (1994). Elements of dual scaling. Hillsdale, N.J.: Lawrence Erlbaum.

    Google Scholar 

  • Nishisato, S. (1996). Gleaning in the field of dual scaling. Psychometrika, 61, 559–599.

    Article  MATH  Google Scholar 

  • Nishisato, S. (1998). Unifying a spectrum of data types under a comprehensive framework for data analysis. A talk presented at a symposium at the Institute of Statistical Mathematics, Tokyo, Japan.

    Google Scholar 

  • Nishisato, S. (2000). Data types and information: Beyond the current practice of data analysis. In Decker, R., and Gaul, W. (eds.), Classification and Information Processing at the Turn of the Millennium. Heidelberg: Springer-Verlag, 40–51.

    Chapter  Google Scholar 

  • Nishisato, S., and Arri, P. S. (1976). Nonlinear programming approach to optimal scaling of partially ordered categories. Psychometrika, 40, 525–548.

    Article  Google Scholar 

  • Nishisato, S. and Hemsworth, D. (2001, in press). Quantification of ordinal variables: A critical inquiry into polychoric and canonical correlation. To appear in Baba. Y. et al. (eds.), Recent Advances in Statistical Research and Data Analysis. Tokyo: Springer-Verlag.

    Google Scholar 

  • Nishisato, S. and Sheu, W. J. (1980). Piecewise method of reciprocal averages for dual scaling of multiple-choice data. Psychometrika, 45, 467–478.

    Article  MATH  Google Scholar 

  • Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine and Journal of Science, Series 6, 2, 559–572.

    Google Scholar 

  • Pierce, J.R. (1961). Symbols, signals and noise: The nature and process of communication. New York Harper and Row.

    Google Scholar 

  • Richardson, M. and Kuder, G.F. (1933). Making a rating scale that measures. Personnel Journal, 12, 36–40.

    Google Scholar 

  • Schmidt, E. (1907). Zür Teheorie der linearen and nichtlinearen Integralgleichungen. Erster Teil. Entwicklung willk-“urlicher Funktionen nach Systemen vorgeschriebener [On theory of linear and nonlinear integral equations. Part one. Development of arbitrary functions according to prescribed systems]. Mathematische Annalen, 63, 433–476.

    Article  MathSciNet  MATH  Google Scholar 

  • Stevens, S. S. (1951). Mathematics, measurement, and psychophysics. In Stevens, S.S. (ed.), Handbook of experimental psychology. Wiley, Chapter 1, 1–19.

    Google Scholar 

  • Tallis, G. (1962). The maximum likelihood estimation of correlation from contingency tables. Biometrics, 18, 342–353.

    Article  MathSciNet  MATH  Google Scholar 

  • Torgerson, W.S. (1952). Multidimensional scaling. I. Theory and method. Psychometrika, 17, 401–419.

    Article  MathSciNet  MATH  Google Scholar 

  • Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley.

    Google Scholar 

  • Yanai, H., Shigemasu, K., Maekawa, S. and Ichikawa, M. (1990). Inshi bunseki (Factor analysis. Tokyo: Asakura Shoten (in Japanese).

    Google Scholar 

  • Young, G. and Householder, A.S. (1938). A note on multi-dimensional psychophysical analysis. Psychometrika, 6, 331–333.

    Article  Google Scholar 

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© 2002 Springer Japan

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Nishisato, S. (2002). Measurement and Multivariate Analysis. In: Nishisato, S., Baba, Y., Bozdogan, H., Kanefuji, K. (eds) Measurement and Multivariate Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65955-6_3

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  • DOI: https://doi.org/10.1007/978-4-431-65955-6_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65957-0

  • Online ISBN: 978-4-431-65955-6

  • eBook Packages: Springer Book Archive

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