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. Coverage: SPSS.
The full content is now available from Statistical Associates Publishers. Click here.
Below is the unformatted table of contents.
Table of Contents
Multidimensional Scaling6
Overview6
Key Terms and Concepts7
Objects and subjects7
Objects7
Subjects7
Data collection methods7
Compositional and decompositional approaches8
Decompositional MDS8
Compositional MDS9
Distance9
Similarity vs. dissimilarity matrices9
Default distance matrices9
Creating distance matrices from metric variables10
Example12
Subject, object, and objective matrices13
Subject matrices14
Object matrices14
Objective matrices15
Matrix shape in SPSS16
Square symmetric16
Square asymmetric16
Rectangular16
SPSS matrix conditionality17
Matrix17
Row17
Unconditional17
Level of measurement17
MDS as a test of near-metricity of ordinal data18
Dimensions18
Optimal number of dimensions18
Rotation of axes19
Labeling of dimensions19
Models in SPSS ALSCAL20
Models20
Classical MDS (CMDS)20
Classical 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.20
Nonmetric CMDS20
Replicated MDS (RMDS)20
Multiple-matrix principal coordinates analysis21
Individual differences Euclidean distance (INDSCAL)21
Asymmetric Euclidean distance model (ASCAL)22
Asymmetric individual differences Euclidean distance model (AINDS)22
Generalized Euclidean metric individual differences model (GEMSCAL)22
ALSCAL Output Options in SPSS22
SPSS menu22
Example23
S-Stress and Interation History24
Scree plots25
Local minima25
Interpretability26
Goodness of fit measures26
Stimulus coordinates and MDS plots27
Fit plots29
Other output options32
PROXSCAL Input and Output Options in SPSS34
SPSS34
Scaling models37
Example42
Iteration history43
Stress and Fit Measures44
MDS coordinates46
MDS maps47
Assumptions49
Proper specification of the model49
Proper level of measurement49
Objects >= dimensions49
Similar scales49
Comparability49
History50
Sample size50
Missing values50
Few ties50
Data distribution50
SPSS limits50
Frequently Asked Questions51
What other procedures are related to MDS?51
How does MDS work?52
If one has multiple data matrices, why do RMDS or INDSCAL? Why not just do a series of CMDS models, one on each matrix?52
What computer programs handle MDS?53
What is Torgerson Scaling?53
How does MDS relate to "smallest space analysis"?53
Bibliography54
Pagecount: 55
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. Coverage: SPSS.
The full content is now available from Statistical Associates Publishers. Click here.
Below is the unformatted table of contents.
Table of Contents
Multidimensional Scaling6
Overview6
Key Terms and Concepts7
Objects and subjects7
Objects7
Subjects7
Data collection methods7
Compositional and decompositional approaches8
Decompositional MDS8
Compositional MDS9
Distance9
Similarity vs. dissimilarity matrices9
Default distance matrices9
Creating distance matrices from metric variables10
Example12
Subject, object, and objective matrices13
Subject matrices14
Object matrices14
Objective matrices15
Matrix shape in SPSS16
Square symmetric16
Square asymmetric16
Rectangular16
SPSS matrix conditionality17
Matrix17
Row17
Unconditional17
Level of measurement17
MDS as a test of near-metricity of ordinal data18
Dimensions18
Optimal number of dimensions18
Rotation of axes19
Labeling of dimensions19
Models in SPSS ALSCAL20
Models20
Classical MDS (CMDS)20
Classical 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.20
Nonmetric CMDS20
Replicated MDS (RMDS)20
Multiple-matrix principal coordinates analysis21
Individual differences Euclidean distance (INDSCAL)21
Asymmetric Euclidean distance model (ASCAL)22
Asymmetric individual differences Euclidean distance model (AINDS)22
Generalized Euclidean metric individual differences model (GEMSCAL)22
ALSCAL Output Options in SPSS22
SPSS menu22
Example23
S-Stress and Interation History24
Scree plots25
Local minima25
Interpretability26
Goodness of fit measures26
Stimulus coordinates and MDS plots27
Fit plots29
Other output options32
PROXSCAL Input and Output Options in SPSS34
SPSS34
Scaling models37
Example42
Iteration history43
Stress and Fit Measures44
MDS coordinates46
MDS maps47
Assumptions49
Proper specification of the model49
Proper level of measurement49
Objects >= dimensions49
Similar scales49
Comparability49
History50
Sample size50
Missing values50
Few ties50
Data distribution50
SPSS limits50
Frequently Asked Questions51
What other procedures are related to MDS?51
How does MDS work?52
If one has multiple data matrices, why do RMDS or INDSCAL? Why not just do a series of CMDS models, one on each matrix?52
What computer programs handle MDS?53
What is Torgerson Scaling?53
How does MDS relate to "smallest space analysis"?53
Bibliography54
Pagecount: 55
