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Applied Multivariate Statistics with SAS (2nd ed).pdf
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Commonly Used Notation xiii
1 Multivariate Analysis Concepts 1
1.1 Introduction 1
1.2 Random Vectors, Means, Variances, and Covariances 2
1.3 Multivariate Normal Distribution 5
1.4 Sampling from Multivariate Normal Populations 6
1.5 Some Important Sample Statistics and Their Distributions 8
1.6 Tests for Multivariate Normality 9
1.7 Random Vector and Matrix Generation 17
2 Graphical Representation of Multivariate Data 21
2.1 Introduction 21
2.2 Scatter Plots 22
2.3 Profile Plots 31
2.4 Andrews Function Plots 33
2.5 Biplots: Plotting Observations and Variables Together 38
2.6 Q-Q Plots for Assessing Multivariate Normality 45
2.7 Plots for Detection of Multivariate Outliers 50
2.8 Bivariate Normal Distribution 53
2.9 SAS/INSIGHT Software 58
2.10 Concluding Remarks 59
3 Multivariate Regression 61
3.1 Introduction 61
3.2 Statistical Background 62
3.3 Least Squares Estimation 63
3.4 ANOVA Partitioning 64
3.5 Testing Hypotheses: Linear Hypotheses 66
3.6 Simultaneous Confidence Intervals 84
3.7 Multiple Response Surface Modeling 87
3.8 General Linear HStatistics
3.9 Variance and Bias Analyses for Calibration Problems 98
3.10 Regression Diagnostics 102
3.11 Concluding Remarks 116
4 Multivariate Analysis of Experimental Data 117
4.1 Introduction 117
4.2 Balanced and Unbalanced Data 120
4.3 One-Way Classification 123
4.4 Two-Way Classification 129
4.5 Blocking 137
4.6 Fractional Factorial Experiments 139
4.7 Analysis of Covariance 145
4.8 Concluding Remarks 149
5 Analysis of Repeated Measures Data 151
5.1 Introduction 151
5.2 Single Population 152
5.3 k Populations 176
5.4 Factorial Designs 195
5.5 Analysis in the Presence of Covariates 207
5.6 The Growth Curve Models 219
5.7 Crossover Designs 236
5.8 Concluding Remarks 246
6 Analysis of Repeated Measures Using Mixed Models 247
6.1 Introduction 247
6.2 The Mixed Effects Linear Model 248
6.3 An Overview of the MIXED Procedure 252
6.4 Statistical Tests for Covariance Structures 255
6.5 Models with Only Fixed Effects 265
6.6 Analysis in the Presence of Covariates 274
6.7 A Random Coefficient Model 288
6.8 Multivariate Repeated Measures Data 294
6.9 Concluding Remarks 297
References 299
Appendix A A Brief Introduction to the IML Procedure 305
A.1 The First SAS Statement 305
A.2 Scalars 305
A.3 Matrices 305
A.4 Printing of Matrices 306
A.5 Algebra of Matrices 306
A.6 Transpose 306
A.7 Inverse 306
A.8 Finding the Number of Rows and Columns 307ypotheses 91
A.9 Trace and Determinant 307
A.10 Eigenvalues and Eigenvectors 307
A.11 Square Root of a Symmetric Nonnegative Definite Matrix 308
A.12 Generalized Inverse of a Matrix 308
A.13 Singular Value Decomposition 309
A.14 Symmetric Square Root of a Symmetric Nonnegative
Definite Matrix 309
A.15 Kronecker Product 309
A.16 Augmenting Two or More Matrices 310
A.17 Construction of a Design Matrix 310
A.18 Checking the Estimability of a Linear Function pβ 311
A.19 Creating a Matrix from a SAS Data Set 312
A.20 Creating a SAS Data Set from a Matrix 312
A.21 Generation of Normal Random Numbers 312
A.22 Computation of Cumulative Probabilities 313
A.23 Computation of Percentiles and Cut Off Points 313
Appendix B Data Sets 315
Index 327
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