Skip to main content
SpringerLink
Log in

General Introduction

  • Chapter
  • First Online:
Measurement, Mathematics and New Quantification Theory

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

  • 177 Accesses

Abstract

Quantification theory is popular in those areas where data are mostly non-quantitative, qualitative or categorical.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adachi, K. (2006). Tahenryo data Kaiseki Ho (Multivariate data analysis). Nakanishiya Publisher.

    Google Scholar 

  • Adachi, K., & Murakami, T. (2011). Hikeiryou Tahenryou Kaisekihou: Shuseibun Bunseki kara Tajyuu Taiou Bunseki e (Nonmetric multivariate analysis: From principal component analysis to multiple correspondence analysis). Asakura Shoten.

    Google Scholar 

  • Akiyama, S. (1993). Suryouka no graphics: Taido no Tahenryoukaiseki (Graphics for quantification: Multivariate analysis of attitudes). Asakura Shoten.

    Google Scholar 

  • Beh, E. J., & Lombardo, R. (2014). Correspondence analysis: Theory, practice and new strategies. Wiley.

    Google Scholar 

  • Beltrami, E. (1873). Sulle funzioni bilineari (On the bilinear functions). In G. Battagline & E. Fergola (Eds.), Giornale di Mathematiche (Vol. 11, pp. 98–106).

    Google Scholar 

  • Benzécri, J. P. (1992). Correspondence analysis handbook. Marcel Dekker.

    Google Scholar 

  • Benzécri, J. P., et al. (1973). L’analyse des données: II. L’analyse des correspondances. Dunod.

    Google Scholar 

  • Blasius, J., & Greenacre, M. J. (1998). Visualization of categorical data. Academic Press.

    Google Scholar 

  • Bouroche, J. M. (1977). Analyse des Données en Marketing. Masson.

    Google Scholar 

  • Bouroche, J. M., & Saporta, G. (1980). L’Analyse des Données. Presses Univesitaires de France.

    Google Scholar 

  • Caillez, F., & Pagés, J. P. (1976). Introduction a L’Analyse des Données. SMASH.

    Google Scholar 

  • Cibois, P. (1983). L’Analyse Factorielle. Presses Universitaires de France.

    Google Scholar 

  • Clausen, S. E. (1998). Applied correspondence analysis: An introduction. Sage Publications.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • de Lagarde, J. (1983). Initiation á l’Analyse des Données. Dunod.

    Google Scholar 

  • de Leeuw, J. (1984). Canonical analysis of categorical data. DSWO Press, Leiden University.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Escofier, B., & Pagés, J. (1988). Analyses Factorielles Simples et Multiples. Dunod.

    Google Scholar 

  • Gauch, H. G. (1982). Multivariate analysis in community ecology. Cambridge University Press.

    Google Scholar 

  • Gifi, A. (1990). Nonlinear multivariate analysis. Wiley.

    Google Scholar 

  • Gower, J. C., & Hand, D. J. (1996). Biplots. Chapman & Hall.

    Google Scholar 

  • Greenacre, M. J. (1984). Theory and applications of correspondence analysis. Academic Press.

    Google Scholar 

  • Greenacre, M. J. (1993). Correspondence analysis in practice. Academic Press.

    Google Scholar 

  • Greenacre, M. J., & Blasius, J. (Eds.). (1994). Correspondence analysis in the social sciences. Academic Press.

    Google Scholar 

  • Greenacre, M. J., & Blasius, J. (Eds.). (2006). Multiple correspondence analysis and related methods. Chapman and Hall/CRC.

    Google Scholar 

  • Hayashi, C. (1974). Suryouka no Houhou (Methods of quantification). Tokyo Keizai Sha.

    Google Scholar 

  • Hayashi, C. (1993). Suryouka: Riron to Hoho (Quantification: Theory and methods). Asakura Shoten.

    Google Scholar 

  • Hayashi, C. (2001). Data no Kagaku (Data science). Asakura Shoten.

    Google Scholar 

  • Hayashi, C., Higuchi, I., & Komazawa, T. (1970). Johoshori to Tokeisuiri (Information processing and statistical mathematics). Sangyou Tosho.

    Google Scholar 

  • Hayashi, C., & Suzuki, T. (1986). Shakai Chosa to Suryouka (Social surveys and quantification). Iwanami Shoten.

    Google Scholar 

  • Hill, M. O. (1973). Reciprocal averaging: An eigenvector method of ordination. Journal of Ecology, 61, 237–249.

    Article  Google Scholar 

  • Hill, M. O. (1974). Correspondence analysis: a neglected multivariate method. Journal of the Royal Statistical Society C (Applied Statistics), 23, 340–354.

    MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Horst, P. (1936). Obtaining a composite measure from a number of different measures of the same attribute. Psychometrika, 1, 53–60.

    Article  MATH  Google Scholar 

  • Hotelling, H. (1933). Analysis of complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417-441, and 498-520.

    Google Scholar 

  • Iwatsubo, S. (1987). Suryouka no Kiso (Foundations of quantification). Asakura Shoten.

    Google Scholar 

  • Jambu, M. (1989). Exploration Informatique et Statistique de Données. Dunod.

    Google Scholar 

  • Jambu, M., & Lebeaux, M. O. (1978). Classification Automatique pour l’Analyse des Données. Métodes et Algorithmes: Dunod.

    Google Scholar 

  • Johnson, P. O. (1950). The quantification of qualitative data in discriminant analysis. Journal of the American Statistical Association, 45, 65–76.

    Article  MATH  Google Scholar 

  • Johnson, R. M. (1963). On a theorem stated by Eckart and Young. Psychometrika, 28, 259–263.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Kalantari, B., Lari, I., Rizzi, A., & Simeone, B. (1993). Sharp bounds for the maximum of the chi-square index in a class of contingency tables with given marginals. Computational Statistics and Data Analysis, 16, 19–34.

    Article  MathSciNet  MATH  Google Scholar 

  • Kendall, M. G. (1957). A course in multivariate analysis. Charles Griffin and Company.

    Google Scholar 

  • Kiers, H. (1989). Three-way methods for the analysis of qualitative and quantitative two-way data. DSWO Press, Leiden University.

    Google Scholar 

  • Komazawa, T. (1978). Tagenteki Data Bunseki no Kiso (Foundations of multidimensional data analysis). Asakura Shoten (in Japanese).

    Google Scholar 

  • Komazawa, T. (1982). Suryouka Riron to Data Shori (Quantification theory and data analysis). Asakura Shoten (in Japanese).

    Google Scholar 

  • Komazawa, T., Higuchi, I., & Ishizaki, R. (1998). Pasokon Suryoukabunseki (Quantification analysis with personal computers). Asakura Shoten.

    Google Scholar 

  • Koster, J. T. A. (1989). Mathematical aspects of multiple correspondence analysis for ordinal variables. DSWO Press, Leiden University.

    Google Scholar 

  • Lancaster, H. O. (1953). A reconciliation of ${\chi ^2}$, considered from metrical and enumerative aspects. Sakhya, 13, 1–10.

    MathSciNet  MATH  Google Scholar 

  • Lebart, L., Morineau, A., & Fénelon, J. P. (1979). Traitement des Données Statistiques. Dunod.

    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 

  • Lebart, L., Morineau, A., & Warwick, K. M. (1984). Multivariate descriptive statistical analysis. Wiley.

    Google Scholar 

  • Lefevre, J. (1976). Introduction aux analyses statistiques multidimensionnelles. Masson.

    Google Scholar 

  • Le Roux, B., & Rouanet, H. (2004). Geometric data analysis: From correspondence analysis to structured data. Kluwer.

    Google Scholar 

  • Likert, A. A. (1932). A technique for the measurement of attitudes. Archives of Psychology, 140, 1–55.

    Google Scholar 

  • Lingoes, J. C. (1964). Simultaneous linear regression: An IBM 7090 program for analyzing metric/nonmetric or linear/nonlinear data. Behavioral Science, 9, 87–88.

    Google Scholar 

  • Lingoes, J. C. (1978). Geometric representation of relational data. Mathesis Press.

    Google Scholar 

  • Lingoes, J. C., Roskam, E. E., & Borg, I. (1978). Geometric representation of relational data. Mathesis Press.

    Google Scholar 

  • Lord, F. M. (1958). Some relations between Guttman’s principal components of scale analysis and other psychometric theory. Psychometrika, 23, 291–296.

    Article  MATH  Google Scholar 

  • Maung, K. (1941). Measurement of association in contingency tables with special reference to the pigmentation of hair and eye colours of Scottish children. Annals of Eugenics, 11, 189–223.

    Article  Google Scholar 

  • McDonald, R. P. (1968). A unified treatment of the weighting problem. Psychometrika, 33, 351–381.

    Article  MathSciNet  MATH  Google Scholar 

  • McKeon, J. J. (1966). Canonical analysis: Some relations between canonical correlation, factor analysis, discriminant function analysis and scaling theory. Psychometric Monograph No. 13.

    Google Scholar 

  • Meulman, J. (1982). Homogeneity analysis of incomplete data. DSWO Press, Leiden University.

    Google Scholar 

  • Michailidis, G., & de Leeuw, J. (1998). The gifi system of descriptive multivariate analysis. Statistical Science, 13, 307–336.

    Article  MathSciNet  MATH  Google Scholar 

  • Moreau, J., Doudin, P. A., & Cazes, P. (1999). L’Analyse des Correspondances et les Techniques Connexes: Approches Nouvelles pour l’Analyse Statistique des Données. Springer.

    Google Scholar 

  • Mosier, C. I. (1946). Machine methods in scaling by reciprocal averages. In Proceedings, Research Forum (pp. 35–39). International Business Corporation.

    Google Scholar 

  • Murtagh, F. (2005). Correspondence analysis and data coding with R and Java. Chapman and Hall.

    Google Scholar 

  • Nakache, J. P. (1982). Exercices Comment’es de Mathématiques pour l’Analyse des Données. Dunod.

    Google Scholar 

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

    Google Scholar 

  • Nishisato, S. (1982). Shitsuteki Data no Suryouka: Soutsuishakudo-ho to Sono Ohyou (Quantification of qualitative data: Dual scaling and its applications). Asakura Shoten.

    Google Scholar 

  • Nishisato, S. (1987). Robust techniques for quantifying categorical data. In MacNeil, I. B. & Umphrey, G. J. (eds.), Foundations of Statistical Inference, 209-217. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Nishisato, S. (2007). Insight into data analysis: Fundamentals of quantification. Kwansei Gakuin University Press (in Japanese).

    Google Scholar 

  • Nishisato, S. (2010). Data analysis for behavioral sciences: Use of methods appropriate for information retrieval. Baifukan. (in Japanese).

    Google Scholar 

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

    Google Scholar 

  • Nishisato, S. (2019). 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. (2022). Optimal quantification and symmetry. Springer.

    Google Scholar 

  • Nishisato, S., Beh, E. J., Lombardo, R., & Clavel, J. G. (2022). Modern quantification theory: Joint graphical display, biplots and alternatives. Springer.

    Google Scholar 

  • Nishisato, S., & Clavel, J. G. (2003). A note on between-set distances in dual scaling and correspondence analysis. Behaviormetrika, 30, 87–98.

    Article  MathSciNet  MATH  Google Scholar 

  • Nishisato, S., & Nishisato, I. (1984). An introduction to dual scaling. MicroStats.

    Google Scholar 

  • Nishisato, S., & Nishisato, I. (1994). Dual scaling in a Nutshell. MicroStats.

    Google Scholar 

  • Ohsumi, N., Lebart, L., Morineau, A., Warwick, K. M., & Baba, Y. (1994). Kijyutsuteki Tahenryou Kaiseki (Descriptive multivariate analysis). Nikkagiren (in Japanese).

    Google Scholar 

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

    Google Scholar 

  • Saito, T. (1980). Tajigen Shakudo Kouseihou (Multidimensional scale construction). Asakura Shoten.

    Google Scholar 

  • Saporta, G. (1979). Theories et Méthodes de la Statistique. Technip.

    Google Scholar 

  • Schmidt, E. (1907). Zür Theorie der linearen und nichtlinearen Integralgleichungen. Esster Teil. Entwickelung willkürlicher Functionen nach Systemaen 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  Google Scholar 

  • Takane, Y. (1980). Tajigen Shakudo Ho (Multidimensional scaling). University of Tokyo Press (in Japanese).

    Google Scholar 

  • Takane, Y. (1995). Seiyakutsuki Shuseibun Bunsekiho: Atarashii Tahenryou Kaisekiho (Constrained principal component analysis: A new approach to multivariate data analysis). Asakura Shoten.

    Google Scholar 

  • Takeuchi, K., & Yanai, H. (1972). Tahenryou Kaiseki no Kiso (Foundations of multivariate analysis). Toyo Keizai-sha (in Japanese).

    Google Scholar 

  • Tenenhaus, M. (1994). Méthodes Statistiques en Gestion. Dunod.

    Google Scholar 

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

    Google Scholar 

  • van Buuren, S. (1990). Optimal scaling of time series. DSWO Press, Leiden University.

    Google Scholar 

  • van de Geer, J. P. (1993). Multivariate analysis of categorical data: Applications. Sage Publications.

    Google Scholar 

  • van der Burg, E.(1988). Nonlinear canonical correlation and some related techniques. Leiden University, DSWO Press.

    Google Scholar 

  • van der Heijden, P. G. M. (1987). Correspondence analysis of longitudinal data. DSWO Press, Leiden University.

    Google Scholar 

  • van Rijckevorsel, J. (1987). The applications of fuzzy coding and horseshoes in multiple correspondence analysis. DSWO Press, Leiden University.

    Google Scholar 

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

    Google Scholar 

  • Weller, J. C., & Romney, A. K. (1990). Metric scaling: Correspondence analysis. Sage Publications.

    Google Scholar 

  • Whittaker, R. H. (1978). Ordination of plant communities. Junk.

    Google Scholar 

  • Yanai, H., & Takane, Y. (1977). Tahenryou Kaiseki Ho (Multivariate analysis). Asakura Shoten (in Japanese).

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Professor Emeritus, University of Toronto, Toronto, ON, Canada

    Shizuhiko Nishisato

Authors
  1. Shizuhiko Nishisato
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shizuhiko Nishisato .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nishisato, S. (2023). General Introduction. 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_7

Download citation

Publish with us

Policies and ethics

Search

Navigation