The multi-dimensional scaling (MDS) is a statistic computing procedure. Objects on basis of their (Un) similarity are represented by it to each other in two or a three-dimensional area. The distances between points in this area give the dissimilarity of two objects again (borrow & Staufenbiel, 1997). The procedure goes back on the psychologist Warren S. Torgerson.

The MDS is called also similarity structural analysis. The formal goal of the MDS is it to arrange the objects spatially in such a way that the distances (distances) between the objects in the area correspond as accurately as possible to the raised Un-/similarities. The solution area of the MDS, which have so-called configuration, in most cases two dimensions, which facilitates the representation on the paper and the interpretableness. To be accomplished the MDS von Statistikprogrammen can.

Beside the spatial configuration of objects, the MDS supplies a set of indices (e.g. stress, RSQ, see below), on the basis those the quality of the measurement of the perception area to be judged can. Deviations settle in the increase of the stress measure and the decrease of the RSQ.

Information about pairs is raised from objects, in order to determine from it metric information about the objects. The distances between objects in the configuration are to reflect the similarity judgements to the pairs of objects. Different Distanzmetriken is differentiated.

Iterative process of the not-metric MDS

The use of the Euclidean Metrik has the advantage that the interpretation of the configuration is facilitated, since the distances between the objects correspond to air lines. With the determination of the configuration the MDS uses an iterative process.

All objects are arranged first arbitrarily in the area. In the next step the distances between the objects are compared with their similarities. If now two objects in relation to their similarity lie apart too far, they are one on the other too pushed. Two rather dissimilar objects, which lie too near each other, are from each other away moved. This procedure is so long continued, until the configuration of the objects reflects the raised similarities satisfyingly. For this monotonous involution.

Control criterion of the measurement

• STRESS and RSQ (R

A goal of the procedure is an optimal adjustment of the MDS solution to the raw data as possible and thus as small a STRESS. This value is to be understood as difference between mismatch and distance. If the STRESS of the configuration is small enough or no longer substantially changed, after the last optimization step the iteration is broken off and the result of the MDS is spent.

The STRESS computed as root from the sum of the squared deviations of the mismatches from the distances, divided by the sum of the squared distances.

In principle there are no accurate defaults for it, which stress value is still acceptable and which value one "„well "“call can. "„Around at all a standard to have, one has "‚nullste all null hypotheses' examined and by MDS scaled and thereby registered thousands of coincidence data, which stress values result "“(see BORROW STAUFENBIEL 1989).

Kruskal provided reference values for the stress value in its work, at which one can orient oneself:

Apart from the STRESS a further measure than control criterion for the adjustment of the configuration is regarded to the raw data. It concerns here RSQ (also R mentioned). R is the squared correlation of the distances with the mismatches. She is to be seen as levels of the linear adjustment of the mismatches to the distances. In practice apply values, which are larger as 0.9 for R than acceptable.

Literature

• Torgerson, W.S. (1958). Theory & Methods OF Scaling. New York: Wiley.
• Borrow, I. & Staufenbiel, Th. (1997). Theories and methods of the scaling. Berne: Huber.
• Baking house, Erichson, Plinke, women (2000). Multivariate analysis methods Berlin: Springer publishing house
• Mathar, R. (1997). Multi-dimensional scaling Stuttgart: Teubner

Articles in category "Multi-dimensional scaling"

We found here 3 articles.

Related Websites

We found here 4 related websites.

• Multidimensional Scaling
  Multidimensional scaling (MDS) can be considered to be an alternative to factor analysis (see Factor Analysis). In general, the goal of the analysis is to ...


• MULTIDIMENSIONAL SCALING
  In this entry we summarize the major types of multidimensional scaling (MDS), ... Multidimensional scaling (MDS) is a set of data analysis techniques that ...


• Multidimensional Scaling
  Following a review of the available MDS algorithms and programs, a Lisp program implementing a multidimensional scaling algorithm will be written as the ...


• Multidimensional Scaling
  Searchable bibliography and selection of recent papers, from the University of Newcastle.