应用多元统计分析方法 影印版PDF|Epub|txt|kindle电子书版本网盘下载

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1．APPLIED MULTIVARIATE METHODS1

1.1 An Overview of Multivariate Methods1

Contents1

Variable-and Individual-Directed Techniques2

Creating New Variables2

Principal Components Analysis3

Factor Analysis3

Discriminant Analysis4

Cluster Analysis5

Canonical Discriminant Analysis5

Logistic Regression5

Multivariate Analysis of Variance6

Canonical Variates Analysis7

Canonical Correlation Analysis7

Where to Find the Preceding Topics7

1.2 Two Examples8

1.3 Types of Variables11

Independence of Experimental Units11

1.4 Data Matrices and Vectors12

Variable Notation13

Data Matrix13

Data Vectors13

Data Subscripts14

1.5 The Multivariate Normal Distribution15

Some Definitions15

Summarizing Multivariate Distributions16

Mean Vectors and Variance-Covariance Matrices16

Correlations and Correlation Matrices17

The Multivariate Normal Probability Density Function19

Bivariate Normal Distributions19

1.6 Statistical Computing22

Cautions About Computer Usage22

Missing Values22

Removing Rows of the Data Matrix23

Replacing Missing Values by Averages23

Replacing Missing Values by Zeros23

Sampling Strategies24

Data Entry Errors and Data Verification24

1.7 Multivariate Outliers25

Locating Outliers25

Dealing with Outliers25

Outliers May Be Influential26

1.8 Multivariate Summary Statistics26

1.9 Standardized Data and/or Z Scores27

Exercises28

2．SAMPLE CORRELATIONS35

2.1 Statistical Tests and Confidence Intervals35

Are the Correlations Large Enough to Be Useful?36

Confidence Intervals by the Chart Method36

Confidence Intervals by Fisher's Approximation38

Confidence Intervals by Ruben's Approximation39

Variable Groupings Based on Correlations40

Relationship to Factor Analysis46

2.2 Summary46

Exercises47

3．MULTIVARIATE DATA PLOTS55

3.1 Three-Dimensional Data Plots55

3.2 Plots of Higher Dimensional Data59

Chernoff Faces61

Star Plots and Sun-Ray Plots63

Andrews'Plots65

Side-by-Side Scatter Plots66

3.3 Plotting to Check for Multivariate Normality67

Summary73

Exercises73

4．EIGENVALUES AND EIGENVECTORS77

4.1 Trace and Determinant77

Examples78

4.2 Eigenvalues78

4.3 Eigenvectors79

Positive Definite and Positive Semidefinite Matrices80

4.4 Geometric Descriptions（p=2）82

Vectors82

Bivariate Normal Distributions83

4.5 Geometric Descriptions（p=3）87

Vectors87

Trivariate Normal Distributions87

4.6 Geometric Descriptions（p>3）90

Exercises91

Summary91

5．PRINCIPAL COMPONENTS ANALYSIS93

5.1 Reasons for Using Principal Components Analysis93

Data Screening93

Clustering95

Discriminant Analysis95

Regression95

5.3 Principal Components Analysis on the Variance-Covariance Matrix ∑96

5.2 Objectives of Principal Components Analysis96

Principal Component Scores98

Component Loading Vectors98

5.4 Estimation of Principal Components99

Estimation of Principal Component Scores99

5.5 Determining the Number of Principal Components99

Method 1100

Method 2100

5.6 Caveats107

5.7 PCA on the Correlation Matrix P109

Principal Component Scores110

Component Correlation Vectors110

Sample Correlation Matrix110

Determining the Number of Principal Components110

5.8 Testing for Independence of the Original Variables111

5.9 Structural Relationships111

SASR PRINCOMP Procedure112

5.10 Statistical Computing Packages112

Principal Components Analysis Using Factor Analysis Programs118

PCA with SPSS's FACTOR Procedure124

Summary142

Exercises142

6．FACTOR ANALYSIS147

6.1 Objectives of Factor Analysis147

6.3 Some History of Factor Analysis148

6.2 Caveats148

6.4 The Factor Analysis Model150

Assumptions150

Matrix Form of the Factor Analysis Model151

Definitions of Factor Analysis Terminology151

6.5 Factor Analysis Equations151

Nonuniqueness of the Factors152

6.6 Solving the Factor Analysis Equations153

6.7 Choosing the Appropriate Number of Factors155

Objective Criteria156

Subjective Criteria156

6.8 Computer Solutions of the Factor Analysis Equations157

Principal Factor Method on R158

Principal Factor Method with Iteration159

6.9 Rotating Factors170

Examples（m=2）171

Rotation Methods172

The Varimax Rotation Method173

6.10 Oblique Rotation Methods174

6.11 Factor Scores180

Bartlett's Method or the Weighted Least-Squares Method181

Thompson's Method or the Regression Method181

Ad Hoc Methods181

Summary212

Exercises213

7．DISCRIMINANT ANALYSIS217

7.1 Discrimination for Two Multivariate Normal Populations217

A Posterior Probability Rule218

A Mahalanobis Distance Rule218

The Linear Discriminant Function Rule218

A Likelihood Rule218

Sample Discriminant Rules219

Estimating Probabilities of Misclassification220

Resubstitution Estimates220

Estimates from Holdout Data220

Cross-Validation Estimates221

7.2 Cost Functions and Prior Probabilities（Two Populations）229

7.3 A General Discriminant Rule（Two Populations）231

A Cost Function232

Prior Probabilities232

Average Cost of Misclassification232

A Bayes Rule233

Classification Functions233

Unequal Covariance Matrices233

Tricking Computing Packages234

7.4 Discriminant Rules（More than Two Populations）235

Basic Discrimination238

7.5 Variable Selection Procedures245

Forward Selection Procedure245

Backward Elimination Procedure246

Stepwise Selection Procedure246

Recommendations247

Caveats247

7.6 Canonical Discriminant Functions255

The First Canonical Function256

A Second Canonical Function257

Determining the Dimensionality of the Canonical Space260

Discriminant Analysis with Categorical Predictor Variables273

7.7 Nearest Neighbor Discriminant Analysis275

7.8 Classification Trees283

Summary283

Exercises283

8.1 Logistic Regression Model287

8.2 The Logit Transformation287

8．LOGISTIC REGRESSION METHODS287

Model Fitting288

8.3 Variable Selection Methods296

8.4 Logistic Discriminant Analysis（More Than Two Populations）301

Logistic Regression Models301

Model Fitting302

Another SAS LOGISTIC Analysis314

Exercises316

Ruler Distance319

9．CLUSTER ANALYSIS319

9.1 Measures of Similarity and Dissimilarity319

Standardized Ruler Distance320

A Mahalanobis Distance320

Dissimilarity Measures320

9.2 Graphical Aids in Clustering321

Scatter Plots321

9.3 Clustering Methods322

Other Methods322

Andrews'Plots322

Using Principal Components322

Nonhierarchical Clustering Methods323

Hierarchical Clustering323

Nearest Neighbor Method323

A Hierarchical Tree Diagram325

Other Hierarchical Clustering Methods326

Verification of Clustering Methods327

How Many Clusters?327

Comparisons of Clustering Methods327

Beale's F-Type Statistic328

A Pseudo Hotelling's T2 Test329

The Cubic Clustering Criterion329

Clustering Order334

Estimating the Number of Clusters339

Principal Components Plots348

Clustering with SPSS355

SAS's FASTCLUS Procedure369

9.4 Multidimensional Scaling385

Exercises395

10．MEAN VECTORS AND VARIANCE-COVARIANCE MATRICES397

10.1 Inference Procedures for Variance-Covariance Matrices397

A Test for a Specific Variance-Covariance Matrix398

A Test for Sphericity400

A Test for Compound Symmetry403

A Test for the Huynh-Feldt Conditions405

A Test for Independence406

A Test for Independence of Subsets of Variables407

A Test for the Equality of Several Variance-Covariance Matrices408

10.2 Inference Procedures for a Mean Vector408

Hotelling's T2 Statistic409

Hypothesis Test for μ409

Confidence Region for μ409

A More General Result411

Special Case—A Test of Symmetry412

Fitting a Line to Repeated Measures418

A Test for Linear Trend418

Multivariate Quality Control419

10.3 Two Sample Procedures420

Repeated Measures Experiments420

10.4 Profile Analyses431

10.5 Additional Two-Group Analyses432

Paired Samples432

Small Sample Sizes433

Large Sample Sizes433

Unequal Variance-Covariance Matrices433

Summary434

Exercises434

11．MULTIVARIATE ANALYSIS OF VARIANCE439

11.1 MANOVA439

MANOVA Assumptions440

Test Statistics440

Test Comparisons441

Why Do We Use MANOVAs?441

A Conservative Approach to Multiple Comparisons442

11.2 Dimensionality of the Alternative Hypothesis455

11.3 Canonical Variates Analysis456

The First Canonical Variate456

The Second Canonical Variate457

Other Canonical Variates457

11.4 Confidence Regions for Canonical Variates458

Summary485

Exercises485

12.1 Multiple Regression489

12．PREDICTION MODELS AND MULTIVARIATE REGRESSION489

12.2 Canonical Correlation Analysis494

Two Sets of Variables494

The First Canonical Correlation495

The Second Canonical Correlation495

Number of Canonical Correlations496

Estimates496

Hypothesis Tests on the Canonical Correlations497

Interpreting Canonical Functions508

Canonical Correlation Analysis with SPSS511

12.3 Factor Analysis and Regression515

Summary522

Exercises522

APPENDIX A:MATRIX RESULTS525

A.1 Basic Definitions and Rules of Matrix Algebra525

A.2 Quadratic Forms527

A.3 Eigenvalues and Eigenvectors528

A.5 Miscellaneous Results529

A.4 Distances and Angles529

APPENDIX B:WORK ATTITUDES SURVEY531

B.1 Data File Structure536

B.2 SPSS Data Entry Commands538

B.3 SAS Data Entry Commands543

APPENDIX C:FAMILY CONTROL STUDY547

REFERENCES555

Index563