IDEAS home Printed from https://ideas.repec.org/a/vrs/foeste/v20y2020i1p519-530n30.html
   My bibliography  Save this article

The Use of the Incomplete Tetrad Method for Measuring the Similarities in Nonmetric Multidimensional Scaling

Author

Listed:
  • Zaborski Artur

    (Wroclaw University of Economics, Faculty of Economics and Finance, Chair of Econometrics and Computer Science, Nowowiejska 3, 58-500Jelenia Góra, Poland)

Abstract

Research background: So far, many methods of direct measurement of similarity in multidimensional scaling have been developed (e.g. ranking, sorting, pairwise comparison and others). The method selection affects the subjective feelings of the respondents, i.e. fatigue, weariness resulting from making numerous assessments, or difficulties in expressing similarity assessments.Purpose: In the proposed method, for all four-element sets (tetrads) of objects a respondent is asked to pick out the most similar and the least similar pair. Because the number of tetrads increases very rapidly with the number of objects, the aim of the study is to indicate the possibility of measuring similarities based on the reduced number of tetrads.Research methodology: In order to make scaling results independent from respondents’ subjective effects the analysis was made on the basis of the given distance matrix. To construct perceptual maps based on tetrads, multidimensional scaling with the use of the MINISSA program was performed. The quality of matching the resulting points configuration to the configuration determined based on the distance matrix was tested by a Procrustes statistic.Results: It was demonstrated that the choice of the incomplete set of tetrads has no significant effect on the results of multidimensional scaling, even when all pairs of objects in tetrads cannot be presented equally frequently.Novelty: An original method for calculating similarities in nonmetric multidimensional scaling.

Suggested Citation

  • Zaborski Artur, 2020. "The Use of the Incomplete Tetrad Method for Measuring the Similarities in Nonmetric Multidimensional Scaling," Folia Oeconomica Stetinensia, Sciendo, vol. 20(1), pages 519-530, June.
    • Handle: RePEc:vrs:foeste:v:20:y:2020:i:1:p:519-530:n:30
    DOI: 10.2478/foli-2020-0030
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/foli-2020-0030
    Download Restriction: no
    File URL: https://libkey.io/10.2478/foli-2020-0030?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
    ---><---

    References listed on IDEAS

    as
    1. Randall Bissett & Bruce Schneider, 1991. "Spatial and conjoint models based on pairwise comparisons of dissimilarities and combined effects: Complete and incomplete designs," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 685-698, December.
    2. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    3. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    4. Ian Spence & Dennis Domoney, 1974. "Single subject incomplete designs for nonmetric multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 469-490, December.
    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. Muñoz-Mas, Rafael & Vezza, Paolo & Alcaraz-Hernández, Juan Diego & Martínez-Capel, Francisco, 2016. "Risk of invasion predicted with support vector machines: A case study on northern pike (Esox Lucius, L.) and bleak (Alburnus alburnus, L.)," Ecological Modelling, Elsevier, vol. 342(C), pages 123-134.
    2. Simensen, Trond & Halvorsen, Rune & Erikstad, Lars, 2018. "Methods for landscape characterisation and mapping: A systematic review," Land Use Policy, Elsevier, vol. 75(C), pages 557-569.
    3. Willem Heiser, 1991. "A generalized majorization method for least souares multidimensional scaling of pseudodistances that may be negative," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 7-27, March.
    4. Luís Francisco Aguiar & Pedro C. Magalhães & Maria Joana Soares, 2010. "Synchronism in Electoral Cycles: How United are the United States?," NIPE Working Papers 17/2010, NIPE - Universidade do Minho.
    5. Kennen, Jonathan G. & Kauffman, Leon J. & Ayers, Mark A. & Wolock, David M. & Colarullo, Susan J., 2008. "Use of an integrated flow model to estimate ecologically relevant hydrologic characteristics at stream biomonitoring sites," Ecological Modelling, Elsevier, vol. 211(1), pages 57-76.
    6. Keith Poole, 1990. "Least squares metric, unidimensional scaling of multivariate linear models," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 123-149, March.
    7. Berrie Zielman & Willem Heiser, 1993. "Analysis of asymmetry by a slide-vector," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 101-114, March.
    8. Hansohm, Jürgen, 2007. "Algorithms and error estimations for monotone regression on partially preordered sets," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1043-1050, May.
    9. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    10. Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    11. Monteiro, Carlos M.F. & Dibb, Sally & Almeida, Luis Tadeu, 2010. "Revealing doctors' prescribing choice dimensions with multivariate tools: A perceptual mapping approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 909-920, March.
    12. Peter Verboon & Ivo Lans, 1994. "Robust canonical discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 485-507, December.
    13. Patrick Groenen & Bart-Jan Os & Jacqueline Meulman, 2000. "Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 511-524, December.
    14. Guerdjikova, Ani, 2008. "Case-based learning with different similarity functions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 107-132, May.
    15. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 323-340, December.
    16. Hossein Safizadeh, M. & McKenna, David R., 1996. "Application of multidimensional scaling techniques to facilities layout," European Journal of Operational Research, Elsevier, vol. 92(1), pages 54-62, July.
    17. Guerdjikova, Ani, 2006. "Portfolio Choice and Asset Prices in an Economy Populated by Case-Based Decision Makers," Working Papers 06-13, Cornell University, Center for Analytic Economics.
    18. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    19. Verniest, Fabien & Greulich, Sabine, 2019. "Methods for assessing the effects of environmental parameters on biological communities in long-term ecological studies - A literature review," Ecological Modelling, Elsevier, vol. 414(C).
    20. Raymond, Ben & Hosie, Graham, 2009. "Network-based exploration and visualisation of ecological data," Ecological Modelling, Elsevier, vol. 220(5), pages 673-683.

    More about this item

    Keywords

    measurement of similarities; method of tetrads; nonmetric multidimensional scaling;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

    Statistics

    Access and download statistics

    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:vrs:foeste:v:20:y:2020:i:1:p:519-530:n:30. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.