Some analytical foundations of multidimensional scaling for ordinal data

Abstract: "Ingwer Borg has contributed intensively and successfully to MDS, in theory and applications (e.g., Borg 1981a,b; Borg & Lingoes 1987; Roskam, Lingoes & Borg 1977). This paper offers some notes on the foundations of MDS, based on ranks of proximities. Two approaches are sketched, one working with contingencies of distance ranks, represented by boundaries in a dimensional space. The other approach uses the generalized betweenness relation, leading to configurations of object points. Details of the procedures and examples for both approaches are given for the one- and two-dimensional case. A procedure to find an optimal solution in a given dimensionality for data with random error is illustrated. The role of facet theory for theory testing by MDS is emphasized. Using the concepts of this paper will allow a fine-grained evaluation of a MDS solution for ordinal data." (author's abstract)

Object Details

• Alternative title: Einige analytische Grundlagen der multidimensionalen Skalierung von Ordinaldaten
• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource, 15-39 S.
• Language: Englisch
• Notes: Veröffentlichungsversion ; begutachtet ; In: Braun, Michael (Hg.), Mohler, Peter Ph. (Hg.): Beyond the horizon of measurement: Festschrift in honor of Ingwer Borg. 2006. S. 15-39. ISBN 978-3-924220-28-0

References and Relationships

• Bibliographic citation: Beyond the horizon of measurement: Festschrift in honor of Ingwer Borg ; Bd. 10 ; ZUMA-Nachrichten Spezial ; Bd. 10

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Mannheim
• (when): 2006
• Creator: Feger, Hubert
• Contributor: Braun, Michael ; Mohler, Peter Ph ; GESIS-ZUMA

Further information

• URN: urn:nbn:de:0168-ssoar-49167-7
• Rights: Open Access unbekannt; Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:46 PM CET