Multidimensional Scaling

by G. David Garson

MULTIDIMENSIONAL SCALING Overview Multidimensional scaling (MDS) uncovers underlying dimensions based on a series of similarity or distance judgments by subjects. MDS is popular in marketing research for brand comparisons and in psychology, where it has been used to study the dimensionality of personality traits. Other uses include analysis of particular academic disciplines using citation data (Small, 1999) and any application involving ratings, rankings, differences in perceptions, or voting. In spite of being designed for judgment data, MDS can be used to analyze any correlation matrix, treating correlation as a type of similarity measure. That is, the higher the correlation of two variables, the closer they will be located in the map created by MDS. SPSS.The full content is now available from Statistical Associates Publishers. Click here. Below is the unformatted table of contents. Table of ContentsMultidimensional Scaling6Overview6Key Terms and Concepts7Objects and subjects7Objects7Subjects7Data collection methods7Compositional and decompositional approaches8Decompositional MDS8Compositional MDS9Distance9Similarity vs. dissimilarity matrices9Default distance matrices9Creating distance matrices from metric variables10Example12Subject, object, and objective matrices13Subject matrices14Object matrices14Objective matrices15Matrix shape in SPSS16Square symmetric16Square asymmetric16Rectangular16SPSS matrix conditionality17Matrix17Row17Unconditional17Level of measurement17MDS as a test of near-metricity of ordinal data18Dimensions18Optimal number of dimensions18Rotation of axes19Labeling of dimensions19Models in SPSS ALSCAL20Models20Classical MDS (CMDS)20Classical MDS (CMDS) is also known as Principal Coordinate Analysis or metric CMDS. In SPSS press the Model button in the MDS dialog, then in the Model dialog select"Euclidean distance" in the Scaling Model area. If data are a single matrix, CMDS is performed.20Nonmetric CMDS20Replicated MDS (RMDS)20Multiple-matrix principal coordinates analysis21Individual differences Euclidean distance (INDSCAL)21Asymmetric Euclidean distance model (ASCAL)22Asymmetric individual differences Euclidean distance model (AINDS)22Generalized Euclidean metric individual differences model (GEMSCAL)22ALSCAL Output Options in SPSS22SPSS menu22Example23S-Stress and Interation History24Scree plots25Local minima25Interpretability26Goodness of fit measures26Stimulus coordinates and MDS plots27Fit plots29Other output options32PROXSCAL Input and Output Options in SPSS34SPSS34Scaling models37Example42Iteration history43Stress and Fit Measures44MDS coordinates46MDS maps47Assumptions49Proper specification of the model49Proper level of measurement49Objects >= dimensions49Similar scales49Comparability49History50Sample size50Missing values50Few ties50Data distribution50SPSS limits50Frequently Asked Questions51What other procedures are related to MDS?51How does MDS work?52If one has multiple data matrices, why do RMDS or INDSCAL? Why not just do a series of CMDS models, one on each matrix?52What computer programs handle MDS?53<

66 pages, Kindle Edition

First published September 2, 2012