IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v147y2016icp247-264.html
   My bibliography  Save this article

An objective general index for multivariate ordered data

Author

Listed:
  • Sei, Tomonari

Abstract

Multivariate quantitative data are often summarized into a general index as a weighted sum when the variates have a prescribed order. Although the sum of standardized scores is a sensible choice of index, it may have negative correlation with some of the variates. In this paper, a general index that has positive correlation with all the variates is constructed. The index is applied to study the fairness of decathlon scoring. Quantification of ordered categorical data is also discussed. The limit of quantification characterizes the Gaussian distribution.

Suggested Citation

  • Sei, Tomonari, 2016. "An objective general index for multivariate ordered data," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 247-264.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:247-264
    DOI: 10.1016/j.jmva.2016.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16000269
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.02.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kumasaka, Natsuhiko & Shibata, Ritei, 2008. "High-dimensional data visualisation: The textile plot," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3616-3644, March.
    2. Takayuki Saito & Tatsuo Otsu, 1988. "A method of optimal scaling for multivariate ordinal data and its extensions," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 5-25, March.
    3. R. Bradley & S. Katti & Irma Coons, 1962. "Optimal scaling for ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 27(4), pages 355-374, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bando, Takuma & Sei, Tomonari & Yata, Kazuyoshi, 2022. "Consistency of the objective general index in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    2. Ferreira, Priscila & Taylor, Mark, 2011. "Measuring match quality using subjective data," Economics Letters, Elsevier, vol. 113(3), pages 304-306.
    3. Antonello D’Ambra & Pietro Amenta & Anna Crisci & Antonio Lucadamo, 2022. "The generalized Taguchi’s statistic: a passenger satisfaction evaluation," METRON, Springer;Sapienza Università di Roma, vol. 80(1), pages 41-60, April.
    4. A. Fielding, 1993. "Scoring functions for ordered classifications in statistical analysis," Quality & Quantity: International Journal of Methodology, Springer, vol. 27(1), pages 1-17, February.
    5. T. Jefferson & J. May & N. Ravi, 1989. "An entropy approach to the scaling of ordinal categorical data," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 203-215, June.
    6. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
    7. Antonello D’Ambra & Pietro Amenta & Eric J. Beh, 2021. "Confidence regions and other tools for an extension of correspondence analysis based on cumulative frequencies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 405-429, September.
    8. Kuriki, Satoshi, 2005. "Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 420-449, June.
    9. Takayuki Saito & Tatsuo Otsu, 1988. "A method of optimal scaling for multivariate ordinal data and its extensions," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 5-25, March.
    10. Shizuhiko Nishisato & Wen-Jenn Sheu, 1984. "A note on dual scaling of successive categories data," Psychometrika, Springer;The Psychometric Society, vol. 49(4), pages 493-500, December.
    11. Math Candel, 2001. "Recovering the Metric Structure in Ordinal Data: Linear Versus Nonlinear Principal Components Analysis," Quality & Quantity: International Journal of Methodology, Springer, vol. 35(1), pages 91-105, February.
    12. Jan Leeuw, 1977. "Correctness of Kruskal's algorithms for monotone regression with ties," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 141-144, March.
    13. Lu, Jiannan & Ding, Peng & Dasgupta, Tirthankar, 2015. "Construction of alternative hypotheses for randomization tests with ordinal outcomes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 348-355.
    14. Michel Tenenhaus, 1988. "Canonical analysis of two convex polyhedral cones and applications," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 503-524, December.
    15. Shizuhiko Nishisato, 1984. "Forced classification: A simple application of a quantification method," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 25-36, March.
    16. Pasquale Sarnacchiaro & Antonello D’Ambra & Luigi D’Ambra, 2016. "CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2490-2502, October.
    17. Shizuhiko Nishisato, 1996. "Gleaning in the field of dual scaling," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 559-599, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:247-264. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.