1 Generalized Inverse Matrices and Related Topics
1.1 Generalized Inverse Matrices
1.2 Solutions to Linear Equations
1.3 Exercises
2 The General Linear Model
2.1 Model Definition and Examples
2.2 The Least Squares Estimation
2.2.1 The Principle of Least Squares
2.2.2 Properties of the Least Squares Estimation
2.2.3 Some Examples
2.3 Estimable Functions and Gauss-Markov Theorem
2.4 Generalized Least Squares Estimation
2.5 Estimation Subject to Linear Restrictions
2.6 Exercises
3 Multivariate Normal and Related Distributions
3.1 Moments of Random Vectors
3.2 Multivariate Normal Distributions
3.3 Noncentral Distributions
3.4 Quadratic Forms in Normal Variates
3.4.1 Distribution of Quadratic Forms
3.4.2 Independence of Quadratic Forms
3.4.3 More Results about Quadratic Forms .
3.5 Distributions of the Sample Mean and Covariance Matrix
3.6 Distributions Related to Correlation Coefficients
3.7 Exercises
4 Inference for the General Linear Model
4.1 Properties of Least Squares Estimation
4.2 Testing Linear Hypotheses
4.2.1 The F-Test for the General Linear Hypothesis
4.2.2 Testing Orthogonal Contracts
4.3 Confidence Intervals and Regions
4.4 Multiple Comparisons
4.5 Lack-of-Fit Tests
4.6 Exercises
5 Linear Regression Models
5.1 Departures from Model Assumptions
5.1.1 Residual Plots
5.1.2 Normality
5.1.3 Homoscedasticity
5.1.4 Serial Correlation
5.1.5 Stochastic Design Matrix
5.2 Model Misspecification
5.3 Sequential and Partial F-Tests
5.4 Model Selection
5.4.1 Model Selection Criteria
5.4.2 Variable Selection Procedures
5.5 Orthogonality and Collinearity in Regression
5.5.1 Orthogonality in Regression
5.5.2 Multicollinearity in Regression
5.5.3 Ridge Regression
5.5.4 Principal Components Regression
5.6 Confidence and Prediction Intervals
5.7 Regression Diagnostics
5.7.1 Properties of Projection or Hat Matrix
5.7.2 Types of Residuals
5.7.3 Outliers and Influential Points
5.8 Exercises
6 Fixed-Effects, Random-Effects and Mixed Models
6.1 Fixed-Effects Models
6.1.1 Checking Model Assumptions
6.1.2 ANOCOVA Models
6.2 Random-Effects Models
6.2.1 One-Factor Random-Effects Model
6.2.2 ANOVA Method
6.2.3 Maximum Likelihood Estimation
6.3 Mixed-Effects Models
6.4 Exercises
7 Generalized Linear Models
7.1 The Structure of GLMs
7.1.1 Components of the GLM
7.1.2 Mean and Variance Functions
7.2 Link Functions
7.3 Parameter Estimation
7.3.1 The MLE of β
7.3.2 Newton-Raphson and Fisher Scoring Algorithms
7.3.3 MLE of β as the Iterative Weighted LSE
7.3.4 Estimating the Dispersion Parameter
7.4 Inference and Diagnostics for GLMs
7.4.1 Deviance and Goodness of Fit
7.4.2 Residuals and Diagnostics for GLMs
7.5 Exercises
Appendix A: Table of Common Distributions
Appendix B: Statistical Tables
Table 1. The Standard Normal Distribution
Table 2. Distribution of t
Table 3. Distribution of X2
Table 4. Distribution of F
References
Index
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