| Preface Acknowledgments Acronyms Introduction I.1 Newborn Lung Project I.2 Wisconsin Diabetes Registry I.3 Wisconsin Sleep Cohort Study Suggested Reading 1 Review of Ordinary Linear Regression and Its Assumptions 1.1 The Ordinary Linear Regression Equation and Its Assumptions 1.1.1 Straight-Line Relationship 1.1.2 Equal Variance Assumption 1.1.3 Normality Assumption 1.1.4 Independence Assumption 1.2 A Note on How the Least-Squares Estimators are Obtained Output Packet Ⅰ：Examples of Ordinary Regression Analyses 2 The Maximum Likelihood Approach to Ordinary Regression 2.1 Maximum Likelihood Estimation 2.2 Example 2.3 Properties of Maximum Likelihood Estimators 2.4 How to Obtain a Residual Plot with PROC MIXED Output Packet Ⅱ：Using PROC MIXED and Comparisons to PROC RE G 3 Reformulating Ordinary Regression Analysis in Matrix Notation 3.1 Writing the Ordinary Regression Equation in Matrix Notation 3.1.1 Example 3.2 Obtaining the Least-Squares Estimator β in Matrix Notation 3.2.1 Example：Matrices in Regression Analysis 3.3 List of Matrix Operations to Know 4 Variance Matrices and Linear Transformations 4.1 Variance and Correlation Matrices 4.1.1 Example 4.2 How to Obtain the Variance of a Linear Transformation 4.2.1 Two Variables 4.2.2 Many Variables 5 Variance Matrices of Estimators of Regression Coefficients 5.1 Usual Standard Error of Least-Squares Estimator of Regression Slope in Nonmatrix Formulation 5.2 Standard Errors of Least-Squares Regression Estimators in Matrix Notation 5.2.1 Example 5.3 The Large Sample Variance Matrix of Maximum Likelihood Estimators 5.4 Tests and Confidence Intervals 5.4.1 Example-Comparing PROC REG and PROC MIXED 6 Dealing with Unequal Variance Around the Regression Line 6.1 Ordinary Least Squares with Unequal Variance 6.1.1 Examples 6.2 Analysis Taking Unequal Variance into Account 6.2.1 The Functional Transformation Approach 6.2.2 The Linear Transformation Approach 6.2.3 Standard Errors of Weighted Regression Estimators Output Packet Ⅲ：Applying the Empirical Option to Adjust Standard Errors Output Packet Ⅳ：Analyses with Transformation of the Outcome Variable to Equalize Residual Variance Output Packet Ⅴ：Weighted Regression Analyses of GHb Data on Age 7 Application of Weighting with Probability Sampling and Nonresponse 8 Principles in Dealing with Correlated Data 9 A Further Study of How the Transformation Works with Correlated Data 10 Random Effects 11 The Normal Distribution and Likelihood Revisited 12 The Generalization to Non-normal Distributions. 13 Modeling Binomial and Binary Outcomes 14 Modeling Poisson Outcomes—The Analysis of Rates 15 Modeling Correlated Outcomes with Generalized Estimating Equations References Appendix：Matrix Operations Index |
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