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