Download full text
(2.128Mb)
Citation Suggestion
Please use the following Persistent Identifier (PID) to cite this document:
https://nbn-resolving.org/urn:nbn:de:0168-ssoar-49167-7
Exports for your reference manager
Some analytical foundations of multidimensional scaling for ordinal data
Einige analytische Grundlagen der multidimensionalen Skalierung von Ordinaldaten
[collection article]
This document is a part of the following document:
Beyond the horizon of measurement: Festschrift in honor of Ingwer Borg
Corporate Editor
GESIS-ZUMA
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 co... view more
"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)... view less
Keywords
survey research; data collection method; data; data preparation; data acquisition; data capture; data organization; data quality; scaling; multidimensional scaling
Classification
Methods and Techniques of Data Collection and Data Analysis, Statistical Methods, Computer Methods
Method
basic research; development of methods
Collection Title
Beyond the horizon of measurement: Festschrift in honor of Ingwer Borg
Editor
Braun, Michael; Mohler, Peter Ph.
Document language
English
Publication Year
2006
City
Mannheim
Page/Pages
p. 15-39
Series
ZUMA-Nachrichten Spezial, 10
ISBN
978-3-924220-28-0
Status
Published Version; reviewed
Licence
Deposit Licence - No Redistribution, No Modifications