Applied multivariate techniques:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Wiley
1996
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 493 S. graph. Darst. 1 Diskette (9 cm) |
| ISBN: | 0471310646 |
Internformat
MARC
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| 100 | 1 | |a Sharma, Subhash |d 1944- |e Verfasser |0 (DE-588)124079326 |4 aut | |
| 245 | 1 | 0 | |a Applied multivariate techniques |c Subhash Sharma |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1996 | |
| 300 | |a XVIII, 493 S. |b graph. Darst. |e 1 Diskette (9 cm) | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Analise multivariada |2 larpcal | |
| 650 | 7 | |a Estatistica |2 larpcal | |
| 650 | 7 | |a Multivariate analyse |2 gtt | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
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| adam_text | Contents
CHAPTER 1 INTRODUCTION 1
1.1 Types of Measurement Scales 1
1.1.1 Nominal Scale 2
1.1.2 Ordinal Scale 2
1.1.3 Interval Scale 2
1.1.4 Ratio Scale 3
1.1.5 Number of Variables 3
1.2 Classification of Data Analytic Methods 4
1.3 Dependence Methods 5
1.3.1 One Dependent and One Independent Variable 5
1.3.2 One Dependent Variable and More Than One Independent Variable 5
1.3.3 More Than One Dependent and One or More Independent Variables 9
1.4 Interdependence Methods 10
1.4.1 Metric Variables 11
1.4.2 Nonmetric Data 12
1.5 Structural Models 13
1.6 Overview of the Book 14
Questions 15
CHAPTER 2 GEOMETRIC CONCEPTS OF DATA MANIPULATION 17
2.1 Cartesian Coordinate System 17
2.1.1 Change in Origin and Axes 18
2.1.2 Euclidean Distance 19
2.2 Vectors 19
2.2.1 Geometric View of the Arithmetic Operations on Vectors 20
2.2.2 Projection of One Vector onto Another Vector 23
2.3 Vectors in a Cartesian Coordinate System 23
2.3.1 Length and Direction Cosines 24
2.3.2 Standard Basis Vectors 25
2.4 Algebraic Formulae for Vector Operations 25
2.4.1 Arithmetic Operations 25
2.4.2 Linear Combination 26
2.4.3 Distance and Angle between Any Two Vectors 27
2.4.4 Scalar Product and Vector Projections 27
2.4.5 Projection of a Vector onto Subspace 28
2.4.6 Illustrative Example 29
jri
xii CONTENTS
2.5 Vector Independence and Dimensionality 30
2.5.1 Dimensionality 30
2.6 Change in Basis 31
2.7 Representing Points with Respect to New Axes 32
2.8 Summary 33
Questions 34
CHAPTER 3 FUNDAMENTALS OF DATA MANIPULATION 36
3.1 Data Manipulations 36
3.1.1 Mean and Mean Corrected Data 36
3.1.2 Degrees of Freedom 36
3.1.3 Variance, Sum of Squares, and Cross Products 38
3.1.4 Standardization 39
3.1.5 Generalized Variance 39
3.1.6 Group Analysis 40
3.2 Distances 42
3.2.1 Statistical Distance 42
3.2.2 Mahalanobis Distance 44
3.3 Graphical Representation of Data in Variable Space 45
3.4 Graphical Representation of Data in Observation Space 47
3.5 Generalized Variance 50
3.6 Summary 51
Questions 52
Appendix 54
A3.1 Generalized Variance 54
A3.2 Using PROC IML in SAS for Data Manipulations 55
CHAPTER 4 PRINCIPAL COMPONENTS ANALYSIS 58
4.1 Geometry of Principal Components Analysis 59
4.1.1 Identification of Alternative Axes and Forming New Variables 59
4.1.2 Principal Components Analysis as a Dimensional Reducing
Technique 64
4.1.3 Objectives of Principal Components Analysis 66
4.2 Analytical Approach 66
4.3 How To Perform Principal Components Analysis 67
4.3.1 SAS Commands and Options 67
4.3.2 Interpreting Principal Components Analysis Output 68
4.4 Issues Relating to the Use of Principal Components Analysis 71
4.4.1 Effect of Type of Data on Principal Components Analysis 72
4.4.2 Is Principal Components Analysis the Appropriate Technique? 75
4.4.3 Number of Principal Components to Extract 76
4.4.4 Interpreting Principal Components 79
4.4.5 Use of Principal Components Scores 80
4.5 Summary 81
Questions 81
Appendix 84
A4.1 Eigenstructure of the Covariance Matrix 84
CONTENTS xiii
A4.2 Singular Value Decomposition 85
A4.2.1 Singular Value Decomposition of the Data Matrix 85
A4.3 Spectral Decomposition of a Matrix 86
A4.3.1 Spectral Decomposition of the Covariance Matrix 86
A4.4 Illustrative Example 87
CHAPTER 5 FACTOR ANALYSIS 90
5.1 Basic Concepts and Terminology of Factor Analysis 90
5.1.1 Two Factor Model 93
5.1.2 Interpretation of the Common Factors 96
5.1.3 More Than Two Factors 96
5.1.4 Factor Indeterminacy 97
5.2 Objectives of Factor Analysis 99
5.3 Geometric View of Factor Analysis 99
5.3.1 Estimation of Communalities Problem 100
5.3.2 Factor Rotation Problem 100
5.3.3 More Than Two Factors 102
5.4 Factor Analysis Techniques 102
5.4.1 Principal Components Factoring (PCF) 103
5.4.2 Principal Axis Factoring 107
5.4.3 Which Technique Is the Best? 108
5.4.4 Other Estimation Techniques 108
5.5 How to Perform Factor Analysis 109
5.6 Interpretation of SAS Output 110
5.6.1 Are the Data Appropriate for Factor Analysis? 116
5.6.2 How Many Factors? 116
5.6.3 The Factor Solution 117
5.6.4 How Good Is the Factor Solution? 118
5.6.5 What Do the Factors Represent? 118
5.6.6 Rotation 119
5.7 An Empirical Illustration 121
5.7.1 Identifying and Evaluating the Factor Solution 123
5.7.2 Interpreting the Factor Structure 125
5.8 Factor Analysis versus Principal Components Analysis 125
5.9 Exploratory versus Confirmatory Factor Analysis 128
5.10 Summary 129
Questions 129
Appendix 132
A5.1 One Factor Model 132
A5.2 Two Factor Model 133
A5.3 More Than Two Factors 135
A5.4 Factor Indeterminacy 136
A5.4.1 Communality Estimation Problem 136
A5.4.2 Factor Rotation Problem 136
A5.5 Factor Rotations 137
A5.5.1 Orthogonal Rotation 137
A5.6 Factor Extraction Methods 141
A5.6.1 Principal Components Factoring (PCF) 141
A5.6.2 Principal Axis Factoring (PAF) 142
A5.7 Factor Scores 142
xiv CONTENTS
CHAPTER 6 CONFIRMATORY FACTOR ANALYSIS 144
6.1 Basic Concepts of Confirmatory Factor Analysis 144
6.1.1 Covariance or Correlation Matrix? 144
6.1.2 One Factor Model 145
6.1.3 Two Factor Model with Correlated Constructs 147
6.2 Objectives of Confirmatory Factor Analysis 148
6.3 LISREL 148
6.3.1 LISREL Terminology 148
6.3.2 LISREL Commands 150
6.4 Interpretation of the LISREL Output 152
6.4.1 Model Information and Parameter Specifications 152
6.4.2 Initial Estimates 152
6.4.3 Evaluating Model Fit 157
6.4.4 Evaluating the Parameter Estimates and the Estimated Factor
Model 162
6.4.5 Model Respecification 164
6.5 Multigroup Analysis 170
6.6 Assumptions 173
6.7 An Illustrative Example 174
6.8 Summary 176
Questions 177
Appendix 180
A6.1 Squared Multiple Correlations 181
A6.2 Maximum Likelihood Estimation 181
CHAPTER 7 CLUSTER ANALYSIS 185
7.1 What Is Cluster Analysis? 185
7.2 Geometrical View of Cluster Analysis 186
7.3 Objective of Cluster Analysis 187
7.4 Similarity Measures 187
7.5 Hierarchical Clustering 188
7.5.1 Centroid Method 188
7.5.2 Single Linkage or the Nearest Neighbor Method 191
7.5.3 Complete Linkage or Farthest Neighbor Method 192
7.5.4 Average Linkage Method 192
7.5.5 Ward s Method 193
7.6 Hierarchical Clustering Using SAS 194
7.6.1 Interpreting the SAS Output 195
7.7 Nonhierarchical Clustering 202
7.7.1 Algorithm I 203
7.7.2 Algorithm II 205
7.7.3 Algorithm III 205
7.8 Nonhierarchical Clustering Using SAS 207
7.8.1 Interpreting the SAS Output 208
7.9 Which Clustering Method Is Best? 211
7.9.1 Hierarchical Methods 211
7.9.2 Nonhierarchical Methods 217
CONTENTS xv
7.10 Similarity Measures 218
7.10.1 Distance Measures 218
7.11 Reliability and External Validity of a Cluster Solution 221
7.11.1 Reliability 221
7.11.2 External Validity 221
7.12 An Illustrative Example 221
7.12.1 Hierarchical Clustering Results 221
7.12.2 Nonhierarchical Clustering Results 228
7.13 Summary 232
Questions 233
Appendix 235
CHAPTER 8 TWO GROUP DISCRIMINANT ANALYSIS 237
8.1 Geometric View of Discriminant Analysis 237
8.1.1 Identifying the Best Set of Variables 238
8.1.2 Identifying a New Axis 239
8.1.3 Classification 242
8.2 Analytical Approach to Discriminant Analysis 244
8.2.1 Selecting the Discriminator Variables 244
8.2.2 Discriminant Function and Classification 245
8.3 Discriminant Analysis Using SPSS 245
8.3.1 Evaluating the Significance of Discriminating Variables 246
8.3.2 The Discriminant Function 250
8.3.3 Classification Methods 254
8.3.4 Histograms for the Discriminant Scores 262
8.4 Regression Approach to Discriminant Analysis 262
8.5 Assumptions 263
8.5.1 Multivariate Normality 263
8.5.2 Equality of Covariance Matrices 264
8.6 Stepwise Discriminant Analysis 264
8.6.1 Stepwise Procedures 265
8.6.2 Selection Criteria 265
8.6.3 Cutoff Values for Selection Criteria 266
8.6.4 Stepwise Discriminant Analysis Using SPSS 267
8.7 External Validation of the Discriminant Function 273
8.7.1 Holdout Method 273
8.7.2 U Method 273
8.7.3 Bootstrap Method 274
8.8 Summary 274
Questions 275
Appendix 277
A8.1 Fisher s Linear Discriminant Function 277
A8.2 Classification 278
A8.2.1 Statistical Decision Theory Method for Developing Classification
Rules 279
A8.2.2 Classification Rules for Multivariate Normal Distributions 281
A8.2.3 Mahalanobis Distance Method 283
A8.3 Illustrative Example 284
A8.3.1 Any Known Distribution 284
A8.3.2 Normal Distribution 285
xvi CONTENTS
CHAPTER 9 MULTIPLE GROUP DISCRIMINANT ANALYSIS 287
9.1 Geometrical View of MDA 287
9.1.1 How Many Discriminant Functions Are Needed? 288
9.1.2 Identifying New Axes 289
9.1.3 Classification 293
9.2 Analytical Approach 293
9.3 MDA Using SPSS 294
9.3.1 Evaluating the Significance of the Variables 294
9.3.2 The Discriminant Function 294
9.3.3 Classification 303
9.4 An Illustrative Example 304
9.4.1 Labeling the Discriminant Functions 307
9.4.2 Examining Differences in Brands 307
9.5 Summary 308
Questions 309
Appendix 310
A9.1 Classification for More than Two Groups 311
A9.1.1 Equal Misclassification Costs 311
A9.1.2 Illustrative Example 312
A9.2 Multivariate Normal Distribution 312
A9.2.1 Classification Regions 313
A9.2.2 Mahalanobis Distance 315
CHAPTER 10 LOGISTIC REGRESSION 317
10.1 Basic Concepts of Logistic Regression 317
10.1.1 Probability and Odds 317
10.1.2 The Logistic Regression Model 319
10.2 Logistic Regression with Only One Categorical Variable 321
10.2.1 Model Information 321
10.2.2 Assessing Model Fit 323
10.2.3 Parameter Estimates and Their Interpretation 324
10.2.4 Association of Predicted Probabilities and Observed Responses 325
10.2.5 Classification 326
10.3 Logistic Regression and Contingency Table Analysis 327
10.4 Logistic Regression for Combination of Categorical and Continuous
Independent Variables 328
10.4.1 Stepwise Selection Procedure 329
10.5 Comparison of Logistic Regression and Discriminant Analysis 332
10.6 An Illustrative Example 333
10.7 Summary 335
Questions 336
Appendix 339
A10.1 Maximum Likelihood Estimation 339
A10.2 Illustrative Example 340
CHAPTER 11 MULTIVARIATE ANALYSIS OF VARIANCE 342
11.1 Geometry of MANOVA 342
11.1.1 One Independent Variable at Two Levels and One Dependent
Variable 343
CONTENTS xvii
11.1.2 One Independent Variable at Two Levels and Two or More
Dependent Variables 343
11.1.3 More Than One Independent Variable and p Dependent
Variables 344
11.2 Analytic Computations for Two Group MANOVA 346
11.2.1 Significance Tests 346
11.2.2 Effect Size 348
11.2.3 Power 349
11.2.4 Similarities between MANOVA and Discriminant Analysis 350
11.3 Two Group MANOVA 350
11.3.1 Cell Means and Homogeneity of Variances 351
11.3.2 Multivariate Significance Tests and Power 351
11.3.3 Univariate Significance Tests and Power 353
11.3.4 Multivariate and Univariate Significance Tests 353
11.4 Multiple Group MANOVA 355
11.4.1 Multivariate and Univariate Effects 356
11.4.2 Orthogonal Contrasts 356
11.5 MANOVA for Two Independent Variables or Factors 366
11.5.1 Significance Tests for the GENDER X AD Interaction 367
11.6 Summary 370
Questions 371
CHAPTER 12 ASSUMPTIONS 374
12.1 Significance and Power of Test Statistics 374
12.2 Normality Assumptions 375
12.3 Testing Univariate Normality 375
12.3.1 Graphical Tests 376
12.3.2 Analytical Procedures for Assessing Univariate Normality 378
12.3.3 Assessing Univariate Normality Using SPSS 378
12.4 Testing for Multivariate Normality 380
12.4.1 Transformations 382
12.5 Effect of Violating the Equality of Covariance Matrices
Assumption 383
12.5.1 Tests for Checking Equality of Covariance Matrices 385
12.6 Independence of Observations 387
12.7 Summary 388
Questions 388
Appendix 389
CHAPTER 13 CANONICAL CORRELATION 391
13.1 Geometry of Canonical Correlation 391
13.1.1 Geometrical Illustration in the Observation Space 397
13.2 Analytical Approach to Canonical Correlation 397
13.3 Canonical Correlation Using SAS 398
13.3.1 Initial Statistics 401
13.3.2 Canonical Variates and the Canonical Correlation 401
13.3.3 Statistical Significance Tests for the Canonical Correlations 402
13.3.4 Interpretation of the Canonical Variates 404
13.3.5 Practical Significance of the Canonical Correlation 404
xviii CONTENTS
13.4 Illustrative Example 406
13.5 External Validity 409
13.6 Canonical Correlation Analysis as a General Technique 409
13.7 Summary 409
Questions 410
Appendix 412
A13.1 Effect of Change in Scale 415
A13.2 Illustrative Example 415
CHAPTER 14 CO VARIANCE STRUCTURE MODELS 419
14.1 Structural Models 419
14.2 Structural Models with Observable Constructs 420
14.2.1 Implied Matrix 420
14.2.2 Representing Structural Equations as LISREL Models 421
14.2.3 An Empirical Illustration 422
14.3 Structural Models with Unobservable Constructs 426
14.3.1 Empirical Illustration 428
14.4 An Illustrative Example 435
14.4.1 Assessing the Overall Model Fit 435
14.4.2 Assessing the Measurement Model 437
14.5 Summary 440
Questions 440
Appendix 444
A14.1 Implied Covariance Matrix 444
A14.1.1 Models with Observable Constructs 444
A14.1.2 Models with Unobservable Constructs 446
A14.2 Model Effects 449
A 14.2.1 Effects among the Endogenous Constructs 450
A14.2.2 Effects of Exogenous Constructs on Endogenous Constructs 452
A14.2.3 Effects of the Constructs on Their Indicators 452
STATISTICAL TABLES 455
REFERENCES 469
TABLES, FIGURES, AND EXHIBITS 473
INDEX 483
|
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| id | DE-604.BV010890939 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:38Z |
| institution | BVB |
| isbn | 0471310646 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007282691 |
| oclc_num | 32349165 |
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| physical | XVIII, 493 S. graph. Darst. 1 Diskette (9 cm) |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Wiley |
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| spelling | Sharma, Subhash 1944- Verfasser (DE-588)124079326 aut Applied multivariate techniques Subhash Sharma New York [u.a.] Wiley 1996 XVIII, 493 S. graph. Darst. 1 Diskette (9 cm) txt rdacontent n rdamedia nc rdacarrier Analise multivariada larpcal Estatistica larpcal Multivariate analyse gtt Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007282691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sharma, Subhash 1944- Applied multivariate techniques Analise multivariada larpcal Estatistica larpcal Multivariate analyse gtt Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 |
| title | Applied multivariate techniques |
| title_auth | Applied multivariate techniques |
| title_exact_search | Applied multivariate techniques |
| title_full | Applied multivariate techniques Subhash Sharma |
| title_fullStr | Applied multivariate techniques Subhash Sharma |
| title_full_unstemmed | Applied multivariate techniques Subhash Sharma |
| title_short | Applied multivariate techniques |
| title_sort | applied multivariate techniques |
| topic | Analise multivariada larpcal Estatistica larpcal Multivariate analyse gtt Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Analise multivariada Estatistica Multivariate analyse Multivariate analysis Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007282691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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