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Geometry of Space: A New Look

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Measurement, Mathematics and New Quantification Theory

Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior ((BQAHB,volume 16))

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Abstract

We have outlined quantification approaches to analysis of nominal data, and we also noted problems associated with joint graphical display of rows and columns of the contingency table.

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References

  • Carroll, J. D., Green, P. E., & Schaffer, C. M. (1986). Interpoint distance comparisons in correspondence analysis. Journal of Marketing Research, 23, 271–280.

    Article  Google Scholar 

  • Carroll, J. D., Green, P. E., & Schaffer, C. M. (1987). Comparing interpoint distances in correspondence analysis: A clarification. Journal of Marketing Research, 24, 445–450.

    Article  Google Scholar 

  • Carroll, J. D., Green, P. E., & Schaffer, C. M. (1989). Reply to Greenacre’s commentary on the Carroll-Green-Schaffer scaling of two-way correspondence analysis solutions. Journal of Marketing Research, 26, 366–368.

    Article  Google Scholar 

  • Garmize, L. M., & Rychlak, J. F. (1964). Role-play validation of a socio-cultural theory of symbolism. Journal of Consulting Psychology, 28, 107–115.

    Article  Google Scholar 

  • Greenacre, M. J. (1989). The Carroll-Green-Schaffer scaling in correspondence analysis: A theoretical and empirical appraisal. Journal of Marketing Research, 26, 358–365.

    Article  Google Scholar 

  • Greenacre, M. J. (1989). An invited talk on the CGS scaling at the meeting of the International Federation of Classification Societies. Charlottesville.

    Google Scholar 

  • Lebart, L., & Mirkin, B. D. (1993). Correspondence analysis and classification. Multivariate Analysis: Future Directions, 2, 341–357.

    MATH  Google Scholar 

  • Lebart, L., Morineau, A., & Tabard, N. (1977). Techniques de la Description Statistique: Méthodes et Logiciels pour l’Analyse des Grands Tableaux. Dunod.

    Google Scholar 

  • Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications. The University of Toronto Press.

    Google Scholar 

  • Nishisato, S. (1984a). Dual scaling by reciprocal medians. Proceedings of the 32nd Scientific Conference of the Italian Statistical Society (pp. 141–147), Sorrento, Italy.

    Google Scholar 

  • Nishisato, S. (1984). Forced classification: A simple application of a quantification technique. Psychometrika, 49, 25–36.

    Article  Google Scholar 

  • Nishisato, S. (1985). Methods of handling outlier responses in dual scaling. Proceedings of the 49th Annual Meeting of the Japanese Psychological Association (p. 501). Tokyo, Japan.

    Google Scholar 

  • Nishisato, S. (1987). Robust techniques for quantifying categorical data. In I. B. MacNeil & G. J. Umphrey (Eds.), Foundations of statistical inference (pp. 209–217). D. Reidel Publishing Company.

    Google Scholar 

  • Nishisato, S. (1991). Standardizing multidimensional space for dual scaling. Proceedings of the 20th Annual Meeting of the German Operations Research Society (pp. 584–591), Hohenheim University.

    Google Scholar 

  • Nishisato, S. (1994). Elements of dual scaling: An introduction to practical data analysis. Lawrence Erlbaum Associates.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Nishisato, S. (2007). Multidimensional nonlinear descriptive analysis. Chapman-Hall/CRC.

    Google Scholar 

  • Nishisato, S. (2016). Quantification theory: Dual space and total space. Paper presented at the Annual Meeting of the Behaviormetric Society, Sapporo, Japan, p. 27 (In Japanese).

    Google Scholar 

  • Nishisato, S. (2019a). Reminiscence: Quantification theory and graphs. Theory and Applications of Data Analysis, 8, 47–57 (in Japanese).

    Google Scholar 

  • Nishisato, S. (2019b). Expansion of contingency space: Theory of doubled multidimensional space and graphs. In An invited talk at the Annual Meeting of the Japanese Classification Society, Tokyo (in Japanese).

    Google Scholar 

  • Nishisato, S., & Baba, Y. (1999). On contingency, projection and forced classification of dual scaling. Behaviormetrika, 26, 207–219.

    Article  Google Scholar 

  • Nishisato, S., Beh, E. J., Lombardo, R., & Clavel, J. G. (2021). Modern quantification theory: Joint graphical display, biplots, and alternatives. Springer Nature.

    Google Scholar 

  • Verboon, P. (1994). A Robust approach to nonlinear multivariate analysis. DSWO Press: Leiden University.

    MATH  Google Scholar 

  • Young, G., & Householder, A. A. (1938). Discussion of a set of points in terms of their mutual distances. Psychometrika, 3, 19–22.

    Article  MATH  Google Scholar 

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Correspondence to Shizuhiko Nishisato .

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Nishisato, S. (2023). Geometry of Space: A New Look. In: Measurement, Mathematics and New Quantification Theory. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 16. Springer, Singapore. https://doi.org/10.1007/978-981-99-2295-6_8

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