Applied Multivariate Techniques

Preface......Page 5
Contents......Page 9
1.1 Types of Measurement Scales......Page 17
1.2 Classification of Data Analytic Methods......Page 20
1.3 Dependence Methods......Page 21
1.4 Interdependence Methods......Page 26
1.5 Structural Models......Page 29
1.6 Overview of the Book......Page 30
Questions......Page 31
2.1 Cartesian Coordinate System......Page 33
2.2 Vectors......Page 35
2.3 Vectors in a Cartesian Coordinate System......Page 39
2.4 Algebraic Formulae for Vector Operations......Page 41
2.5 Vector Independence and Dimensionality......Page 46
2.6 Change in Basis......Page 47
2.7 Representing Points with Respect to New Axes......Page 48
2.8 Summary......Page 49
Questions......Page 50
3.1 Data Manipulations......Page 52
3.2 Distances......Page 58
3.3 Graphical Representation of Data in Variable Space......Page 61
3.4 Graphical Representation of Data in Observation Space......Page 63
3.5 Generalized Variance......Page 66
3.6 Summary......Page 67
Questions......Page 68
A3.1 Generalized Variance......Page 70
A3.2 Using PROC IML in SAS for Data Manipulations......Page 71
4 Principal Components Analysis......Page 74
4.1 Geometry of Principal Components Analysis......Page 75
4.2 Analytical Approach......Page 82
4.3 How To Perform Principal Components Analysis......Page 83
4.4 Issues Relating to the Use of Principal Components Analysis......Page 87
Questions......Page 97
A4.1 Eigenstructure of the Covariance Matrix......Page 100
A4.2 Singular Value Decomposition......Page 101
A4.3 Spectral Decomposition of a Matrix......Page 102
A4.4 Illustrative Example......Page 103
5.1 Basic Concepts and Terminology of Factor Analysis......Page 106
5.3 Geometric View of Factor Analysis......Page 115
5.4 Factor Analysis Techniques......Page 118
5.5 How to Perform Factor Analysis......Page 125
5.6 Interpretation of SAS Output......Page 126
5.7 An Empirical Illustration......Page 137
5.8 Factor Analysis versus Principal Components Analysis......Page 141
5.9 Exploratory versus Confirmatory Factor Analysis......Page 144
Questions......Page 145
A5.1 One-Factor Model......Page 148
A5.2 Two-Factor Model......Page 149
A5.3 More Than Two Factors......Page 151
A5.4 Factor Indeterminacy......Page 152
A5.5 Factor Rotations......Page 153
A5.6 Factor Extraction Methods......Page 157
A5.7 Factor Scores......Page 158
6.1 Basic Concepts of Confirmatory Factor Analysis......Page 160
6.3 LISREL......Page 164
6.4 Interpretation of the LISREL Output......Page 168
6.5 Multigroup Analysis......Page 186
6.6 Assumptions......Page 189
6.7 An Illustrative Example......Page 190
6.8 Summary......Page 192
Questions......Page 193
Appendix......Page 196
A6.2 Maximum Likelihood Estimation......Page 197
7.1 What Is Cluster Analysis?......Page 201
7.2 Geometrical View of Cluster Analysis......Page 202
7.4 Similarity Measures......Page 203
7.5 Hierarchical Clustering......Page 204
7.6 Hierarchical Clustering Using SAS......Page 211
7.7 Nonhierarchical Clustering......Page 218
7.8 Nonhierarchical Clustering Using SAS......Page 223
7.9 Which Clustering Method Is Best?......Page 227
7.10 Similarity Measures......Page 234
7.12 An Illustrative Example......Page 237
7.13 Summary......Page 248
Questions......Page 249
Appendix......Page 251
8.1 Geometric View of Discriminant Analysis......Page 253
8.2 Analytical Approach to Discriminant Analysis......Page 260
8.3 Discriminant Analysis Using SPSS......Page 261
8.4 Regression Approach to Discriminant Analysis......Page 278
8.5 Assumptions......Page 279
8.6 Stepwise Discriminant Analysis......Page 280
8.7 External Validation of the Discriminant Function......Page 289
8.8 Summary......Page 290
Questions......Page 291
A8.1 Fisher's Linear Discriminant Function......Page 293
A8.2 Classification......Page 294
A8.3 Illustrative Example......Page 300
9.1 Geometrical View of MDA......Page 303
9.2 Analytical Approach......Page 309
9.3 MDA Using SPSS......Page 310
9.4 An Illustrative Example......Page 320
9.5 Summary......Page 324
Questions......Page 325
Appendix......Page 326
A9.1 Classification for More than Two Groups......Page 327
A9.2 Multivariate Normal Distribution......Page 328
10.1 Basic Concepts of Logistic Regression......Page 333
10.2 Logistic Regression with Only One Categorical Variable......Page 337
10.3 Logistic Regression and Contingency Table Analysis......Page 343
10.4 Logistic Regression for Combination of Categorical and Continuous Independent Variables......Page 344
10.5 Comparison of Logistic Regression and Discriminant Analysis......Page 348
10.6 An Illustrative Example......Page 349
10.7 Summary......Page 351
Questions......Page 352
A10.1 Maximum Likelihood Estimation......Page 355
A10.2 Illustrative Example......Page 356
11.1 Geometry of MANOVA......Page 358
11.2 Analytic Computations for Two-Group MANOVA......Page 362
11.3 Two-Group MANOVA......Page 366
11.4 Multiple-Group MANOVA......Page 371
11.5 MANOVA for Two Independent Variables or Factors......Page 382
11.6 Summary......Page 386
Questions......Page 387
12.1 Significance and Power of Test Statistics......Page 390
12.3 Testing Univariate Normality......Page 391
12.4 Testing for Multivariate Normality......Page 396
12.5 Effect of Violating the Equality of Covariance Matrices Assumption......Page 399
12.6 Independence of Observations......Page 403
Questions......Page 404
Appendix......Page 405
13.1 Geometry of Canonical Correlation......Page 407
13.2 Analytical Approach to Canonical Correlation......Page 413
13.3 Canonical Correlation Using SAS......Page 414
13.4 Illustrative Example......Page 422
13.7 Summary......Page 425
Questions......Page 426
Appendix......Page 428
A13.2 Illustrative Example......Page 431
14.1 Structural Models......Page 435
14.2 Structural Models with Observable Constructs......Page 436
14.3 Structural Models with Unobservable Constructs......Page 442
14.4 An Illustrative Example......Page 451
Questions......Page 456
A14.1 Implied Covariance Matrix......Page 460
A14.2 Model Effects......Page 465
Satistical Tables......Page 471
References......Page 485
Tables, Figures, and Exhibits......Page 489
Index......Page 499