Multidimensional Scaling

S. P. Mukherjee (), Bikas K. Sinha and Asis Kumar Chattopadhyay ()
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S. P. Mukherjee: University of Calcutta, Department of Statistics
Bikas K. Sinha: Indian Statistical Institute
Asis Kumar Chattopadhyay: University of Calcutta, Department of Statistics

Chapter Chapter 11 in Statistical Methods in Social Science Research, 2018, pp 113-122 from Springer

Abstract: Abstract Multidimensional scaling (MDS) is a set of related statistical techniques to explore and visualize relative positions among members in a group in respect of some feature(s). It starts with a distance matrix giving pair-wise differences (in scores or ranks or some other indicators), uses some least-squares principle, and eventually yields a point for each individual on a low-dimensional plane. We have metric vs non-metric MDS as also one-matrix, replicated (unweighted), and weighted MDS with different types of data and of distance models. The optimization exercise involved is quite complicated in some types of MDS. MDS bears some analogy with factor analysis, though the two serve different purposes and proceed on different lines. MDS finds applications in many fields, especially in market research. Steps involved in developing the distance matrix, applying the “stress”-minimizing algorithm, locating the objects to be compared as points in a two-dimensional plane, and interpreting the output have been demonstrated in terms of an example.

Keywords: Dissimilarity matrix; Stress; Data visualization; Extensions of single matrix; Classical MDS (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-2146-7_11

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DOI: 10.1007/978-981-13-2146-7_11

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