IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v325y2023i1d10.1007_s10479-022-04803-3.html
   My bibliography  Save this article

An extension of correspondence analysis based on the multiple Taguchi’s index to evaluate the relationships between three categorical variables graphically: an application to the Italian football championship

Author

Listed:
  • Antonello D’Ambra

    (University of Campania “L.Vanvitelli”)

  • Pietro Amenta

    (University of Sannio)

Abstract

The aim of this paper is to evaluate the relationships between three categorical variables, of which at least one is ordinal, from a graphical point of view and using also inferential tools. Three way Correspondence Analysis is a useful data science visualisation technique to find and display these relationships. This analysis, like the classical two-way analysis, cannot be applied in an efficient way in the presence of ordinal categorical variables because this characteristic is not taken directly into account by the Pearson’s chi-square contingency coefficient. Taguchi (Statistical analysis, Maruzen, Tokyo, 1966, Igaku 29:806–813, 1974) introduced a statistic that considers the ordinal nature of a categorical variable using the cumulative frequency of the cells of the contingency table across this variable. He introduced it as a simple alternative to Pearson’s statistic for ordered contingency tables. This index is also at the base of several Correspondence Analysis extensions that have been proposed in the literature. We have developed a multiple extension of Taguchi’s index. An enhancement of Correspondence Analysis has also been developed based on decomposition of this index. An orthogonal decomposition of this new index has been introduced to test the statistical significance of each aggregated column category. Moreover, a confidence region for each row and aggregated column category of the table has been developed. An application has been developed to highlight the easy applicability and graphical reading of the results of our approach. In this study, we evaluate the relationships between the ranking of the Italian football “Serie A” championship of the last 10 seasons and a set of two factors defined by average percentage of ball possession and number of tags for each team. This new approach may represent a useful guide for researchers who graphically analyse ranking data.

Suggested Citation

  • Antonello D’Ambra & Pietro Amenta, 2023. "An extension of correspondence analysis based on the multiple Taguchi’s index to evaluate the relationships between three categorical variables graphically: an application to the Italian football cham," Annals of Operations Research, Springer, vol. 325(1), pages 219-244, June.
    • Handle: RePEc:spr:annopr:v:325:y:2023:i:1:d:10.1007_s10479-022-04803-3
    DOI: 10.1007/s10479-022-04803-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-04803-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-022-04803-3?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. 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.
    2. Antonello D'Ambra & Anna Crisci & Pasquale Sarnacchiaro, 2015. "A generalized analysis of the dependence structure by means of ANOVA," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2192-2202, October.
    3. S. K. Vines, 2000. "Simple principal components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 441-451.
    4. Hannes Lepschy & Hagen Wäsche & Alexander Woll, 2018. "How to be Successful in Football: A Systematic Review," The Open Sports Sciences Journal, Bentham Open, vol. 11(1), pages 3-23, June.
    5. Valentin Rousson & Theo Gasser, 2004. "Simple component analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 539-555, November.
    6. Luigi D’Ambra & Pietro Amenta & Antonello D’Ambra, 2018. "Decomposition of cumulative chi-squared statistics, with some new tools for their interpretation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 297-318, June.
    Full references (including those not matched with items on IDEAS)

    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. Trendafilov, Nickolay T. & Vines, Karen, 2009. "Simple and interpretable discrimination," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 979-989, February.
    2. Sabatier, Robert & Reynès, Christelle, 2008. "Extensions of simple component analysis and simple linear discriminant analysis using genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4779-4789, June.
    3. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    4. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    5. Basile, Vincenzo & Sorooshian, Shahryar & Pizzichini, Lucia, 2024. "A scientometrics-based journal Management framework: A strategic move," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    6. 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.
    7. Norman R. Swanson, 2016. "Comment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 348-353, July.
    8. Rosaria Lombardo & Eric J. Beh & Luis Guerrero, 2019. "Analysis of three-way non-symmetrical association of food concepts in cross-cultural marketing," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2323-2337, September.
    9. Łukasz Radzimiński & Alexis Padrón-Cabo & Marek Konefał & Paweł Chmura & Andrzej Szwarc & Zbigniew Jastrzębski, 2021. "The Influence of COVID-19 Pandemic Lockdown on the Physical Performance of Professional Soccer Players: An Example of German and Polish Leagues," IJERPH, MDPI, vol. 18(16), pages 1-11, August.
    10. Daniel Velez & Jorge Sueiras & Alejandro Ortega & Jose F. Velez, 2016. "A method for K-Means seeds generation applied to text mining," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 477-499, August.
    11. E. Raffinetti & I. Romeo, 2015. "Dealing with the biased effects issue when handling huge datasets: the case of INVALSI data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2554-2570, December.
    12. Hugh Chipman & Hong Gu, 2005. "Interpretable dimension reduction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 969-987.
    13. Todisco, Lucio & Tomo, Andrea & Canonico, Paolo & Mangia, Gianluigi & Sarnacchiaro, Pasquale, 2021. "Exploring social media usage in the public sector: Public employees' perceptions of ICT's usefulness in delivering value added," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    14. Choulakian, V. & Allard, J. & Almhana, J., 2006. "Robust centroid method," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 737-746, November.
    15. Herteliu, Claudiu & Jianu, Ionel & Dragan, Irina Maria & Apostu, Simona & Luchian, Iuliana, 2021. "Testing Benford’s Laws (non)conformity within disclosed companies’ financial statements among hospitality industry in Romania," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    16. 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.
    17. T. F. Cox & D. S. Arnold, 2018. "Simple components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 83-99, January.
    18. José Fernando Romero Cañizares & Purificación Vicente Galindo & Yannis Phillis & Evangelos Grigoroudis, 2022. "Graphical sustainability analysis using disjoint biplots," Operational Research, Springer, vol. 22(2), pages 1575-1596, April.
    19. Antonio Cordón-Carmona & Abraham García-Aliaga & Moisés Marquina & Jorge Lorenzo Calvo & Daniel Mon-López & Ignacio Refoyo Roman, 2020. "What Is the Relevance in the Passing Action between the Passer and the Receiver in Soccer? Study of Elite Soccer in La Liga," IJERPH, MDPI, vol. 17(24), pages 1-15, December.
    20. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2023. "Hierarchical disjoint principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 537-574, September.

    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:spr:annopr:v:325:y:2023:i:1:d:10.1007_s10479-022-04803-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.