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Tables of Contents for Multivariate Data Reduction and Discrimination With Sas Software
Chapter/Section Title
Page #
Page Count
Preface
ix
Commonly Used Notation
xiii
Basic Concepts for Multivariate Statistics
1
24
Introduction
1
1
Population Versus Sample
2
1
Elementary Tools for Understanding Multivariate Data
3
3
Data Reduction, Description, and Estimation
6
1
Concepts from Matrix Algebra
7
14
Multivariate Normal Distribution
21
2
Concluding Remarks
23
2
Principal Component Analysis
25
52
Introduction
25
1
Population Principal Components
26
3
Sample Principal Components
29
11
Selection of the Number of Principal Components
40
6
Some Applications of Principal Component Analysis
46
11
Principal Component Analysis of Compositional Data
57
3
Principal Component Regression
60
5
Principal Component Residuals and Detection of Outliers
65
4
Principal Component Biplot
69
7
PCA Using SAS/INSIGHT Software
76
1
Concluding Remarks
76
1
Canonical Correlation Analysis
77
34
Introduction
77
1
Population Canonical Correlations and Canonical Variables
78
1
Sample Canonical Correlations and Canonical Variables
79
12
Canonical Analysis of Residuals
91
1
Partial Canonical Correlations
92
3
Canonical Redundancy Analysis
95
6
Canonical Correlation Analysis of Qualitative Data
101
5
`Partial Tests' in Multivariate Regression
106
2
Concluding Remarks
108
3
Factor Analysis
111
100
Introduction
111
1
Factor Model
112
4
A Difference between PCA and Factor Analysis
116
2
Noniterative Methods of Estimation
118
21
Iterative Methods of Estimation
139
16
Heywood Cases
155
1
Comparison of the Methods
156
2
Factor Rotation
158
19
Estimation of Factor Scores
177
7
Factor Analysis Using Residuals
184
4
Some Applications
188
21
Concluding Remarks
209
2
Discriminant Analysis
211
136
Introduction
211
1
Multivariate Normality
212
19
Statistical Tests for Relevance
231
11
Discriminant Analysis: Fisher's Approach
242
13
Discriminant Analysis for k Normal Populations
255
27
Canonical Discriminant Analysis
282
14
Variable Selection in Discriminant Analysis
296
8
When Dimensionality Exceeds Sample Size
304
10
Logistic Discrimination
314
19
Nonparametric Discrimination
333
11
Concluding Remarks
344
3
Cluster Analysis
347
96
Introduction
347
1
Graphical Methods for Clustering
348
8
Similarity and Dissimilarity Measures
356
3
Hierarchical Clustering Methods
359
21
Clustering of Variables
380
13
Nonhierarchical Clustering: k-Means Approach
393
28
How Many Clusters: Cubic Clustering Criterion
421
6
Clustering Using Density Estimation
427
8
Clustering with Binary Data
435
6
Concluding Remarks
441
2
Correspondence Analysis
443
68
Introduction
443
1
Correspondence Analysis
444
19
Multiple Correspondence Analysis
463
13
CA as a Canonical Correlation Analysis
476
3
Correspondence Analysis Using Andrews Plots
479
11
Correspondence Analysis Using Hellinger Distance
490
8
Canonical Correspondence Analysis
498
11
Concluding Remarks
509
2
Appendix: Data Sets
511
24
References
535
8
Index
543