Three-way scaling and clustering / Phipps Arabie, J. Douglas Carroll, Wayne S. DeSarbo.

Format:

Book

Author/Creator:

Arabie, Phipps.

Contributor:

Carroll, J. Douglas.

DeSarbo, Wayne S.

Series:

Quantitative applications in the social sciences ; 07-065.

Quantitative applications in the social sciences ; 65

Sage university paper

Language:

English

Subjects (All):

Scaling (Social sciences).

Multidimensional scaling.

Cluster analysis.

Physical Description:

92 pages : illustrations ; 22 cm.

Place of Publication:

Newbury Park, Calif. : Sage Publications, [1987]

Summary:

Three Way Scaling assumes a working knowledge of multidimensional scaling and Matrix Algebra, which are both introduced in earlier volumes of this series. Arabie, Carroll and DeSarbo begin their discussion with an example of the use of the INDSCAL model, they explain the model and give a second extended example. The authors then present a detailed analysis of SINDSCAL and provide an introduction to three-way scaling models as well as individual differences "clustering "models.

Contents:

Terminology 8

2. Illustrative Application of INDSCAL 12

Design of Rosenberg and Kim's (1975) Experiment 12

The Data 13

Interpretation of the Results 14

3. The INDSCAL Model 17

Inherently Unique Orientation of an INDSCAL Object Space 21

Noteworthy Patterns of Source Weights 24

A Second Example: The Miller and Nicely (1955) Data 25

Interpretation of Miller-Nicely Object Space 27

Interpretation of Miller-Nicely Source Space 29

The Role of Source Weights in Presenting an INDSCAL Analysis 32

4. Decisions to Be Made in Running SINDSCAL Analyses 33

Matrix (Un)conditionality 33

Dimensionality and Required Amounts of Data 35

Number of Iterations 37

Initial (or "Starting") Configuration 39

Constrained Solutions 40

Variance Accounted For (VAF) 40

Additional Points Concerning SINDSCAL's Output 42

Diagnostics 43

5. Other Three-Way MDS Spatial Representations 44

The IDIOSCAL Model and Some Special Cases 44

PARAFAC-1 45

MULTISCALE 46

ALSCAL 48

TUCKALS3 50

6. Three-Way ("Individual Differences") Clustering 53

Choosing a Method of Clustering 54

The (Two-Way) ADCLUS Model for Overlapping, Nonhierarchical Clustering 55

INDCLUS: A Clustering Counterpart to INDSCAL 57

Fitting the INDCLUS Model 59

Example: Rosenberg and Kim's (1975) Data 61

Future Prospects 64

7 Software for Three-Way MDS 64

Appendix A Control Parameters for a SINDSCAL Analysis of Miller-Nicely Data 66

Setting Up Control Cards for SINDSCAL 68

Optional Configuration for Objects' Coordinates 70

Appendix B The Carroll-Chang-Pruzansky Approach to Fitting the INDSCAL Model 71

Converting the Proximities to Estimated Distances 71

Conversion of Estimated Distances to Estimated Scalar Products 72

The INDSCAL Model in Scalar Product Form 75

An Algorithm for Fitting the CANDECOMP Model in the Three-Way Case 76

Direct Scalar Products Data (Called "Correlations or Covariances") in SINDSCAL 77

Appendix C The Multiscale II Procedure for Fitting the INDSCAL Model 78

Appendix D The ALSCAL Procedure for Fitting the INDSCAL Model 80

Initialization Phase 81

Optimal Scaling Phase 81

Termination Phase 83

Model Estimation Phase 83

Estimate W 83

Estimation Procedure for X 83.

Notes:

Bibliography: pages 84-89.

ISBN:

0803930682

OCLC:

22276593