Applied MANOVA and Discriminant Analysis, 2nd Ed.pdf

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关键词：discriminant Discriminan Analysis discrim Analysi

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Brief Contents
PART I: INTRODUCTION 1
Chapter 1 Discriminant Analysis in Research 3
Chapter 2 Preliminaries 15
PART II: ONE-FACTOR MANOVA/DDA 33
Chapter 3 Group Separation 35
Chapter 4 Assessing MANOVA Effects 61
Chapter 5 Describing MANOVA Effects 81
Chapter 6 Deleting and Ordering Variables 103
Chapter 7 Reporting DDA Results 117
PART III: COMPLEX MANOVA 129
Chapter 8 Factorial MANOVA 131
Chapter 9 Analysis of Covariance 163
Chapter 10 Repeated-Measures Analysis 193
Chapter 11 Mixed-Model Analysis 227
PART IV: GROUP-MEMBERSHIP PREDICTION 253
Chapter 12 Classification Basics 255
Chapter 13 Multivariate Normal Rules 269
vii
viii BRIEF CONTENTS
Chapter 14 Classification Results 285
Chapter 15 Hit Rate Estimation 295
Chapter 16 Effectiveness of Classification Rules 315
Chapter 17 Deleting and Ordering Predictors 335
Chapter 18 Two-Group Classification 349
Chapter 19 Nonnormal Rules 361
Chapter 20 Reporting PDA Results 375
Chapter 21 PDA-Related Analyses 385
PART V: ISSUES AND PROBLEMS 391
Chapter 22 Issues in PDA and DDA 393
Chapter 23 Problems in PDA and DDA 401
Contents
List of Figures xix
List of Tables xxi
Preface to Second Edition xxv
Acknowledgments xxvii
Preface to First Edition xxix
Notation xxxi
I INTRODUCTION 1
1 Discriminant Analysis in Research 3
1.1 A Little History, 3
1.2 Overview, 5
1.3 Descriptive Discriminant Analysis, 5
1.4 Predictive Discriminant Analysis, 7
1.5 Design in Discriminant Analysis, 9
1.5.1 Grouping Variables, 9
1.5.2 Response Variables, 9
Exercises, 13
2 Preliminaries 15
2.1 Introduction, 15
2.2 Research Context, 15
2.3 Data, Analysis Units, Variables, and Constructs, 16
2.4 Summarizing Data, 18
2.5 Matrix Operations, 21
2.5.1 SSCP Matrix, 22
ix
x CONTENTS
2.5.2 Determinant, 23
2.5.3 Inverse, 24
2.5.4 Eigenanalysis, 25
2.6 Distance, 26
2.7 Linear Composite, 28
2.8 Probability, 28
2.9 Statistical Testing, 29
2.10 Judgment in Data Analysis, 30
2.11 Summary, 31
Further Reading, 31
Exercises, 32
II ONE-FACTOR MANOVA/DDA 33
3 Group Separation 35
3.1 Introduction, 35
3.2 Two-Group Analyses, 35
3.2.1 Univariate Analysis, 35
3.2.2 Multivariate Analysis, 39
3.3 Test for Covariance Matrix Equality, 41
3.4 Yao Test, 43
3.5 Multiple-Group Analyses—Single Factor, 44
3.5.1 Univariate Analysis, 44
3.5.2 Multivariate Analysis, 47
3.6 Computer Application, 52
3.7 Summary, 56
Exercises, 57
4 Assessing MANOVA Effects 61
4.1 Introduction, 61
4.2 Strength of Association, 62
4.2.1 Univariate, 62
4.2.2 Multivariate, 62
4.2.3 Bias, 65
4.3 Computer Application I, 66
4.4 Group Contrasts, 67
4.4.1 Univariate, 67
4.4.2 Multivariate, 68
4.5 Computer Application II, 72
4.6 Covariance Matrix Heterogeneity, 74
4.7 Sample Size, 74
CONTENTS xi
4.8 Summary, 75
Technical Notes, 76
Exercises, 77
5 Describing MANOVA Effects 81
5.1 Introduction, 81
5.2 Omnibus Effects, 82
5.2.1 An Eigenanalysis, 82
5.2.2 Linear Discriminant Functions, 83
5.3 Computer Application I, 85
5.4 Standardized LDFWeights, 87
5.5 LDF Space Dimension, 88
5.5.1 Statistical Tests, 89
5.5.2 Proportion of Variance, 91
5.5.3 LDF Plots, 91
5.6 Computer Application II, 93
5.7 Computer Application III, 94
5.8 Contrast Effects, 96
5.9 Computer Application IV, 96
5.10 Summary, 98
Technical Note, 99
Further Reading, 100
Exercises, 100
6 Deleting and Ordering Variables 103
6.1 Introduction, 103
6.2 Variable Deletion, 103
6.2.1 Purposes of Deletion, 103
6.2.2 McCabe Analysis, 104
6.2.3 Computer Application, 105
6.3 Variable Ordering, 106
6.3.1 Meaning of Importance, 106
6.3.2 Computer Application I, 108
6.3.3 Variable Ranking, 110
6.4 Contrast Analyses, 110
6.5 Computer Application II, 111
6.6 Comments, 113
Further Reading, 114
Exercises, 115
7 Reporting DDA Results 117
7.1 Introduction, 117
7.2 Example of Reporting DDA Results, 117
xii CONTENTS
7.3 Computer Package Information, 122
7.4 Reporting Terms, 123
7.5 MANOVA/DDA Applications, 124
7.6 Concerns, 124
7.7 Overview, 126
Further Reading, 127
Exercises, 127
III FACTORIAL MANOVA, MANCOVA, AND REPEATED
MEASURES 129
8 Factorial MANOVA 131
8.1 Introduction, 131
8.2 Research Context, 131
8.3 Univariate Analysis, 134
8.4 Multivariate Analysis, 136
8.4.1 Omnibus Tests, 136
8.4.2 Distribution Assumptions, 138
8.5 Computer Application I, 139
8.6 Computer Application II, 146
8.7 Nonorthogonal Design, 150
8.8 Outcome Variable Ordering and Deletion, 151
8.9 Summary, 152
Technical Notes, 152
Exercises, 159
9 Analysis of Covariance 163
9.1 Introduction, 163
9.2 Research Context, 164
9.3 Univariate ANCOVA, 166
9.3.1 Testing for Equality of Regression Slopes, 166
9.3.2 Omnibus Test of Adjusted Means, 168
9.4 Multivariate ANCOVA (MANCOVA), 170
9.4.1 Matrix Calculations, 170
9.4.2 Testing for Equal Slopes, 171
9.5 Computer Application I, 173
9.6 Comparing Adjusted Means—Omnibus Test, 174
9.7 Computer Application II, 175
9.8 Contrast Analysis, 180
9.9 Computer Application III, 180
CONTENTS xiii
9.10 Summary, 184
Technical Note, 184
Exercises, 190
10 Repeated-Measures Analysis 193
10.1 Introduction, 193
10.2 Research Context, 195
10.3 Univariate Analyses, 196
10.3.1 Omnibus Test, 196
10.3.2 Contrast Analysis, 197
10.4 Multivariate Analysis, 199
10.5 Computer Application I, 202
10.6 Univariate and Multivariate Analyses, 204
10.7 Testing for Sphericity, 207
10.8 Computer Application II, 210
10.9 Contrast Analysis, 212
10.10 Computer Application III, 214
10.11 Summary, 216
Technical Notes, 217
Exercises, 223
11 Mixed-Model Analysis 227
11.1 Introduction, 227
11.2 Research Context, 228
11.3 Univariate Analysis, 229
11.4 Multivariate Analysis, 231
11.4.1 Group-by-Time Interaction, 232
11.4.2 Repeated-Measures Variable Main Effect, 235
11.5 Computer Application I, 237
11.6 Contrast Analysis, 240
11.7 Computer Application II, 243
11.8 Summary, 246
Technical Note, 247
Exercises, 249
IV GROUP MEMBERSHIP PREDICTION 253
12 Classification Basics 255
12.1 Introduction, 255
12.2 Notion of Distance, 256
xiv CONTENTS
12.3 Distance and Classification, 259
12.4 Classification Rules in General, 260
12.4.1 Maximum Likelihood, 260
12.4.2 Typicality Probability, 261
12.4.3 Posterior Probability, 262
12.4.4 Prior Probability, 263
12.5 Comments, 264
Technical Note, 265
Further Reading, 265
Exercises, 266
13 Multivariate Normal Rules 269
13.1 Introduction, 269
13.2 Normal Density Functions, 269
13.3 Classification Rules Based on Normality, 271
13.4 Classification Functions, 273
13.4.1 Quadratic Functions, 273
13.4.2 Linear Functions, 274
13.4.3 Distance-Based Classification, 275
13.5 Summary of Classification Statistics, 277
13.6 Choice of Rule Form, 278
13.6.1 Normal-Based Rule, 278
13.6.2 Covariance Matrix Equality, 279
13.6.3 Rule Choice, 280
13.6.4 Priors, 281
13.7 Comments, 281
Technical Notes, 283
Further Reading, 283
Exercises, 284
14 Classification Results 285
14.1 Introduction, 285
14.2 Research Context, 285
14.3 Computer Application, 286
14.4 Individual Unit Results, 287
14.4.1 In-Doubt Units, 288
14.4.2 Outliers, 289
14.5 Group Results, 290
CONTENTS xv
14.6 Comments, 291
Technical Note, 291
Exercises, 292
15 Hit Rate Estimation 295
15.1 Introduction, 295
15.2 True Hit Rates, 296
15.3 Hit Rate Estimators, 297
15.3.1 Formula Estimators, 297
15.3.2 Internal Analysis, 299
15.3.3 External Analysis, 300
15.3.4 Maximum-Posterior-Probability Method, 302
15.4 Computer Application, 304
15.5 Choice of Hit Rate Estimator, 306
15.6 Outliers and In-Doubt Units, 306
15.6.1 Outliers, 307
15.6.2 In-Doubt Units, 307
15.7 Sample Size, 309
15.8 Comments, 310
Further Reading, 311
Exercises, 312
16 Effectiveness of Classification Rules 315
16.1 Introduction, 315
16.2 Proportional Chance Criterion, 316
16.2.1 Definition, 316
16.2.2 Statistical Test, 317
16.3 Maximum-Chance Criterion, 319
16.4 Improvement over Chance, 320
16.5 Comparison of Rules, 320
16.6 Computer Application I, 321
16.7 Effect of Unequal Priors, 323
16.8 PDA Validity/Reliability, 325
16.9 Applying a Classification Rule to New Units, 325
16.9.1 Computer Application II, 326
16.9.2 Computer Application III, 327
16.10 Comments, 330
Technical Notes, 330
Further Reading, 331
Exercises, 332
xvi CONTENTS
17 Deleting and Ordering Predictors 335
17.1 Introduction, 335
17.2 Predictor Deletion, 336
17.2.1 Purposes of Deletion, 336
17.2.2 Deletion Methods, 336
17.2.3 Package Analyses, 337
17.2.4 All Possible Subsets, 337
17.3 Computer Application, 337
17.4 Predictor Ordering, 340
17.4.1 Meaning of Importance, 340
17.4.2 Variable Ranking, 340
17.5 Reanalysis, 343
17.6 Comments, 343
17.7 Side Note, 345
Further Reading, 346
Exercises, 347
18 Two-Group Classification 349
18.1 Introduction, 349
18.2 Two-Group Rule, 349
18.3 Regression Analogy, 351
18.4 MRA–PDA Relationship, 353
18.5 Necessary Sample Size, 355
18.6 Univariate Classification, 356
Further Reading, 357
Exercises, 359
19 Nonnormal Rules 361
19.1 Introduction, 361
19.2 Continuous Variables, 362
19.2.1 Rank Transformation Analysis, 362
19.2.2 Nearest-Neighbor Analyses, 363
19.2.3 Another Density Estimation Analysis, 366
19.2.4 Other Analyses, 366
19.3 Categorical Variables, 366
19.3.1 Direct Probability Estimation Analysis, 367
19.3.2 Dummy Variable Analysis, 367
19.3.3 Overall–Woodward Analysis, 368
19.3.4 Fisher–Lancaster Analysis, 368
19.3.5 Other Analyses, 369
19.4 Predictor Mixtures, 369
CONTENTS xvii
19.5 Comments, 370
Further Reading, 371
Exercises, 373
20 Reporting PDA Results 375
20.1 Introduction, 375
20.2 Example of Reporting PDA Results, 375
20.3 Some Additional Specific PDA Information, 378
20.4 Computer Package Information, 379
20.5 Reporting Terms, 379
20.6 Sources of PDA Applications, 381
20.7 Concerns, 381
20.8 Overview, 382
Further Reading, 383
Exercises, 383
21 PDA-Related Analyses 385
21.1 Introduction, 385
21.2 Nonlinear Methods, 385
21.2.1 Classification and Regression Trees (CART), 385
21.2.2 Logistic Regression, 385
21.2.3 Neural Networks, 386
21.3 Other Methods, 386
21.3.1 Cluster Analysis, 386
21.3.2 Image Analysis, 387
21.3.3 Optimal Allocation, 387
21.3.4 Pattern Recognition, 387
Further Reading, 388
V ISSUES AND PROBLEMS 391
22 Issues in PDA and DDA 393
22.1 Introduction, 393
22.2 Five Choices in PDA, 393
22.2.1 Linear Versus Quadratic Rules, 393
22.2.2 Nonnormal Classification Rules, 394
22.2.3 Prior Probabilities, 394
22.2.4 Misclassification Costs, 394
22.2.5 Hit-Rate Estimation, 395
22.3 Stepwise Analyses, 395
22.4 StandardizedWeights Versus Structure r’s, 396
xviii CONTENTS
22.5 Data-Based Structure, 398
Further Reading, 400
23 Problems in PDA and DDA 401
23.1 Introduction, 401
23.2 Missing Data, 401
23.2.1 Data Inspection, 401
23.2.2 Data Imputation, 402
23.2.3 Missing GValues, 404
23.2.4 Ad Hoc Strategy, 404
23.3 Outliers and Influential Observations, 405
23.3.1 Outlier Identification, 405
23.3.2 Influential Observations, 406
23.4 Initial Group Misclassification, 406
23.5 Misclassification Costs, 407
23.6 Statistical Versus Clinical Prediction, 407
23.7 Other Problems, 409
Further Reading, 409
Appendix A Data Set Descriptions 411
Appendix B Some DA-Related Originators 415
Appendix C List of Computer Syntax 419
Appendix D Contents ofWileyWebsite 421
References 425
Answers to Exercises 449
Index 481
List of Figures
1.1 Classification of multivariate methods. 6
2.1 Distance in a plane. 27
5.1 LDF plot of group centroids for Baumann study. 92
5.2 Plot of group centroids in LDF space. 95
6.1 Plot ofWilks
values versus best subset size for the
3-group Ethington data. 107
7.1 LDF plot of group centroids. 121
7.2 MANOVA and descriptive discriminant analysis. 126
8.1 LDF plot for the three school levels. 145
9.1 Two dimensional plot of adjusted group centroids. 179
12.1 Distance in a plane. 257
12.2 Graphical representations of two density functions. 261
17.1 Total group L-O-O hit rate versus best-subset size for the
3-group Ethington data. 339
20.1 Predictive discriminant analysis. 382
xix

List of Tables
2.1 Scores on the Error Detection Task (Y1) and Degrees of Reading Power
(Y2) for the Think Aloud (TA) and Directed Reading Activity (DRA)
Groups 16
2.2 Mean, Sum-of-Squares, and Variance for Test Scores on the Error
Detection Task (Y1) and Degrees of Reading Power (Y2) for the Think
Aloud (TA) and Directed Reading Activity (DRA) Groups
(n1 = n2 = 22) 19
3.1 Scores on the Error Detection Task (Y1) and Degrees of Reading Power
(Y2) for the Think Aloud (TA), Directed Reading Activity (DRA), and
Directed Reading and Think Aloud (DRTA) Groups 45
3.2 Means and Variances for Test Scores on the Error Detection Task (Y1)
and Degrees of Reading Power (Y2) for the Think Aloud (TA), Directed
Reading Activity (DRA), and Directed Reading and
Think Aloud (DRTA) Groups 45
3.3 Summary of Four MANOVA Test Statistics 56
4.1 Five Multivariate Effect Size Indices 65
5.1 Summary of Dimensionality Tests 90
6.1 Partial McCabe Output for the 3-Group Ethington Data 106
6.2 Results Used to Order Outcome Variables for the
3-Group Ethington Data 110
7.1 Descriptive Information for the 3-Group Ethington Data 119
7.2 Variable Ordering for the 3-Group Ethington Data 120
7.3 Test of Dimensionality for the 3-Group Ethhington Data 120
7.4 LDFs at Group Centroids 120
7.5 Structure r’s for the 3-Group Ethington Data 121
7.6 Structure r’s for Group 1 versus Group 3 122
7.7 DDA Printout Information 123
7.8 DDA versus PDA; Context: J Groups of Units, p Response Variables 125
8.1 Test Scores on Four Measures of Stress for Three School Levels and
Two Levels of Gender 132
8.2 Means and Standard Deviations for Four Measures of Stress
from Three School Levels and Two Levels of Gender 133
xxi
xxii LIST OF TABLES
8.3 Univariate Sum-of-Squares 134
8.4 ANOVA Summary for Variable Y1 135
8.5 Summary of Omnibus Univariate Results for Outcome Variables
Y2, Y3, and Y4 135
8.6 Summary of Pairwise Contrasts Among School Levels with Bonferroni
Adjusted P
Values for Outcome Variables Y2, Y3, and Y4 136
8.7
(i) Values for the Two-Factor (3 × 3) Ethington Data 151
9.1 Vocabulary Scores for Three Treatment Interventions and a
Control Group 165
9.2 Means and Variances for Morphemic Only (MO), Context Only (CO),
Morphemic and Context (MC), and Control (C) Groups on Five
Vocabulary Tests 166
9.3 SSCP and E Matrices 167
9.4 Analysis of Covariance Summary Table 169
9.5 Adjusted Means for the Four Participating Groups 169
9.6 Sum-of-Squares and Cross-Products for Grand-Mean Centered (Total),
Each of the Group-Mean Centered (MO, CO, MC, and C), and the Error
Matrices 172
10.1 Scores from the Rosenberg Self-Esteem Inventory 196
10.2 ANOVA Summary Table for Changes in Self-Esteem Over the Second
and Third Trimesters 197
10.3 Coefficients for Linear to Quintic Polynomial Trend Analysis
for Six Measurements 198
10.4 Orthonormal Polynomial Coefficients 205
11.1 Self-Esteem Scores for Pregnant and NonpregnantWomen 229
11.2 Self-Esteem Means and (Standard Deviations) by Group
and Month 229
11.3 Formulas for the Univariate Sum-of-Squares for the Mixed-Model
Analysis of Variance 230
11.4 Univariate Analysis of Variance Summary Table
for the Mixed Model 230
11.5 Separate Group and Summed Error SSCP Matrices 233
13.1 LCFs for the 3-Group Ethington Data 275
13.2 Classification Statistics 277
13.3 Alternative Forms of Classification Statistics 278
14.1 Some Unit Classification Results for the 3-Group Ethington Data 288
14.2 Classification Table for J = 3 290
14.3 Classification Table for the 3-Group Ethington Data 291
15.1 PDA and MCA/MRA Indices 297
15.2 Leave-One-Out Results for the 3-Group Ethington Data 305
15.3 Hit Rate Estimates for the 3-Group Ethington Data 305
15.4 SAS Linear L-O-O Results for the 3-Group Ethington Data with
THRESHOLD = .45 308
15.5 Threshold Classification Rates for Group 2 of the 3-Group
Ethington Data 309
LIST OF TABLES xxiii
15.6 Smallest Group Sizes for a PDA 310
16.1 Classification Table Notation 316
16.2 Linear L-O-O Results for the 3-Group Ethington Data 318
16.3 Hypothetical Classification Table 319
16.4 Comparison of Rules 321
16.5 Summary of Linear and Quadratic L-O-O Classification Results for
the 3-Group Ethington Data 323
16.6 Linear L-O-O Results for the 3-Group Ethington Data Using Equal
Priors 324
16.7 Summary of Total-Group Linear L-O-O Results for the 3-Group
Ethington Data 324
16.8 Scores on Nine Predictor Variables for Five Hypothetical
New Students 326
16.9 Classification Results for New Students 328
16.10 Classification Results for New Students Using a Quadratic Rule 329
17.1 Total-Group L-O-O Hit Rates for Variable Subsets from the
3-Group Ethington Data 339
17.2 Linear L-O-O Group 2 Hit Rates, Transformed Hit Rates, and Predictor
Ranks for the 3-Group Ethington Data 341
18.1 Regression Classification Results for Groups 1 and 2 of the
3-Group Ethington Data 353
18.2 Minimum Sample Size, n(= n1 = n2), in Each Group Required
for P to beWithin γ of P(o) 356
19.1 Linear L-O-O Rank-Based PDA Results for the 3-Group
Ethington Data 363
19.2 L-O-O Linear 3-NN Results for the 3-Group
Ethington Data 365
19.3 CategoryWeights for X3 and X4 in the HSB Data 370
19.4 SuggestedWays of Handling Nonnormal Predictors 371
20.1 Linear L-O-O Group Classification Results 377
20.2 Classification RuleWeights (and Constants) 377
20.3 DA Printout Information 379
A.1 Variables Selected from the CCSEQ 412
A.2 Cell Sizes for the Race-by-Grade Design 412
A.3 Categorical Response Variables 412

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