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Book Description

Real-world problems and data sets are the backbone of Ravindra Khattree and Dayanand Naik's Applied Multivariate Statistics with SAS Software, Second Edition, which provides a unique approach to the topic, integrating statistical methods, data analysis, and applications. Now extensively revised, the book includes new information about mixed effects models, applications of the MIXED procedure, regression diagnostics with the corresponding IML procedure code, and covariance structures. The authors' approach to the information will aid professors, researchers, and students in a variety of disciplines and industries. Extensive SAS code and the corresponding high-resolution output accompany sample problems, and clear explanations of SAS procedures are included. Emphasis is on correct interpretation of the output to draw meaningful conclusions. Featuring both the theoretical and the practical, topics covered include multivariate analysis of experimental data and repeated measures data, graphical representation of data including biplots, and multivariate regression. In addition, a quick introduction to the IML procedure with special reference to multivariate data is available in an appendix. SAS programs and output integrated with the text make it easy to read and follow the examples.

Table of Contents

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