Multidimensional Scaling

by Joseph B. Kruskal, Myron Wish

Overview

Outlines a set of techniques that enables a researcher to explore the hidden structure of large databases. These techniques use proximities to find a configuration of points that reflect the structure in the data.

Product Details

ISBN-13:	9781506320885
Publisher:	SAGE Publications
Publication date:	01/01/1978
Series:	Quantitative Applications in the Social Sciences , #11
Sold by:	Barnes & Noble
Format:	eBook
Pages:	96
File size:	3 MB

About the Author

Interests, Activities, Kudos

    multidimensional scaling
    minimum spanning trees
    clustering
    statistical linguistics
    Past President of the Psychometric Society
    Past President of the Classification Society of North America
    Fellow of ASA
    Fellow of AAAS

Table of Contents

	Editor's Introduction	5
1.	Basic Concepts of Multidimensional Scaling	7
	Introduction	7
	Some Methods for Obtaining Proximities Data	9
	Relationship Between the Proximities and the Spatial Distances	14
	Notation and Terminology	16
	Different Types of MDS	19
	Defining an Objective Function	23
	Computational Procedure	27
	Looking at the Scatter Diagram	28
2.	Interpretation of the Configuration	30
	Application to Perceptions of Nations	30
	Linear Regression for Dimensional Interpretation	35
	Neighborhood Interpretation of MDS Configurations	43
	Embedding Other Information in the MDS Configuration	45
3.	Dimensionality	48
	Introduction	48
	Goodness-of-Fit	49
	Other Considerations Concerning Dimensionality	56
4.	Three-Way Multidimensional Scaling	60
	Introduction	60
	The INDSCAL Model	61
	INDSCAL Analysis of the Nation Similarities Data	63
	Fitting the Friendship Ratings into the Similarities Space	69
	INDSCAL Analysis of Profile Proximities	70
5.	Preparing the Input for Multidimensional Scaling	73
	Preprocessing of Data	73
	Metric Versus Nonmetric MDS, and Transformation of the Proximities	76
	Some Available Computer Programs for MDS	78
	Notes	82
	References	83
Appendix A	Some Comments on Multiple Linear Regression	87
Appendix B	Other Uses for Lines and the "Horseshoe" Phenomenon	88
Appendix C	Statistical Guide to Dimensionality	89
Appendix D	Relationship Between MDS Solutions in Different Dimensionalities	92
Appendix E	Determining Meaningful Directions by INDSCAL and by Other Methods	92