Applied Multivariate Statistics with SAS Software
Preface
Commonly Used Notation
Chapter 1: Multivariate Analysis Concepts
- Introduction
- Random Vectors, Means, Variances, and Covariances
- Multivariate Normal Distribution
- Sampling from Multivariate Normal Populations
- Some Important Sample Statistics and Their Distributions
- Tests for Multivariate Normality
- Random Vector and Matrix Generation
Chapter 2: Graphical Representation of Multivariate Data
- Introduction
- Scatter Plots
- Profile Plots
- Andrews Function Plots
- Biplots: Plotting Observations and Variables Together
- Q-Q Plots for Assessing Multivariate Normality
- Plots for Detection of Multivariate Outliers
- Bivariate Normal Distribution
- SAS/INSIGHT Software
- Concluding Remarks
Chapter 3: Multivariate Regression
- Introduction
- Statistical Background
- Least Squares Estimation
- ANOVA Partitioning
- Testing Hypotheses: Linear Hypotheses
- Simultaneous Confidence Intervals
- Multiple Response Surface Modeling
- General Linear Hypotheses
- Variance and Bias Analyses for Calibration Problems
- Regression Diagnostics
- Concluding Remarks
Chapter 4: Multivariate Analysis of Experimental Data
- Introduction
- Balanced and Unbalanced Data
- One-Way Classification
- Two-Way Classification
- Blocking
- Fractional Factorial Experiments
- Analysis of Covariance
- Concluding Remarks
Chapter 5: Analysis of Repeated Measures Data
- Introduction
- Single Population
- k Populations
- Factorial Designs
- Analysis in the Presence of Covariates
- The Growth Curve Models
- Crossover Designs
- Concluding Remarks
Chapter 6: Analysis of Repeated Measures Using Mixed Models
- Introduction
- The Mixed Effects Linear Model
- An Overview of the MIXED Procedure
- Statistical Tests for Covariance Structures
- Models with Only Fixed Effects
- Analysis in the Presence of Covariates
- A Random Coefficient Model
- Multivariate Repeated Measures Data
- Concluding Remarks
References
Appendix A: A Brief Introduction to the IML Procedure
- The First SAS Statement
- Scalars
- Matrices
- Printing of Matrices
- Algebra of Matrices
- Transpose
- Inverse
- Finding the Number of Rows and Columns
- Trace and Determinant
- Eigenvalues and Eigenvectors
- Square Root of a Symmetric Nonnegative Definite Matrix
- Generalized Inverse of a Matrix
- Singular Value Decomposition
- Symmetric Square Root of a Symmetric Nonnegative Definite Matrix
- Kronecker Product
- Augmenting Two or More Matrices
- Construction of a Design Matrix
- Checking the Estimability of a Linear Function p' B
- Creating a Matrix from a SAS Data Set
- Creating a SAS Data Set from a Matrix
- Generation of Normal Random Numbers
- Computation of Cumulative Probabilities
- Computation of Percentiles and Cut Off Points
Appendix B: Data Sets
Index