Skip to main content

Two-Stage Quantification: A New Look

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

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

  • 176 Accesses

Abstract

In Chap. 8, we discussed a theory of doubled multidimensional space, where we introduced such concepts as major dual space (contingency space), residual space, minor dual space, and then we discussed “dual subspac” as the defining concept of joint graphical display (see Nishisato, 1980, 2016, 2019a, 2019b, Nishisato et al., 2021).

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

Access this chapter

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

  • 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 

  • 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 

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

    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. (2019). Kaisko: Suryouka riron to graph (Reminiscence: Quantification theory and graphs). Theory and Applications of Data Analysis, 8, 47–57. (in Japanese).

    Google Scholar 

  • Nishisato, S. (2019b). Bunkatsu-hyou no tenkai: nibai tajigen kuukann no riron to graph (Expansion of contingency space: Theory of doubled multidimensional space and graphs). An invited talk at the Annual Meeting of the Japanese Classification Society, Tokyo. (in Japanese).

    Google Scholar 

  • Nishisato, S. (2023, in press). Propositions for quantification theory. In A. Okada, K. Shigemasu, R. Yoshino, & S. Yokoyama (Eds.), Facets of behaviormetrics: The 50th anniversary of the behaviormetric society. Springer Nature.

    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 

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

    Google Scholar 

  • Stebbins, G. L. (1950). Variation and evolution in plants. Columbia University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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). Two-Stage Quantification: 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_9

Download citation

Publish with us

Policies and ethics