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| Preface | |
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| Examples and Limits of the GLM | |
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| Motivation | |
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| A Review of Basic Statistical Ideas | |
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| GLM Definition | |
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| GLM Examples | |
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| Student Goals | |
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| Homework Exercises | |
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| Statement of the Model, Estimation, and Testing | |
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| Motivation | |
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| Statement of the Model | |
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| Least Squares Assumptions | |
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| Discussion of Homogeneity | |
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| Gaussian Errors Assumption | |
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| Estimation of the GLM | |
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| Hypothesis Testing for the GLM | |
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| Homework Exercises | |
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| Some Distributions for the GLM | |
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| Motivation | |
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| A Full-Rank Basis for Less-than-Full-Rank Models | |
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| Definitions and Theorems | |
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| GLM Distributions | |
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| Definitions and Properties of Residuals | |
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| Homework Exercises | |
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| Multiple Regression: General Considerations | |
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| Motivation | |
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| Definitions of Basic Sums of Squares | |
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| The Nature of the Intercept | |
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| Models that Span but May Not Include an Intercept | |
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| Corrected SS | |
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| Intercept-Only Model | |
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| Null Model | |
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| Overall ANOVA Table for Multiple Regression | |
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| Usual ("Corrected") Overall Test for Regression | |
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| "Uncorrected" Overall Test for Regression | |
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| Strength of Association | |
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| Homework Exercises | |
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| Testing Hypotheses in Multiple Regression | |
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| Motivation | |
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| Choosing an Error Term | |
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| Review of GLH Concepts | |
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| Model Pools | |
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| Test Class 1: Overall | |
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| Test Class 2: Addition of One Variable | |
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| Test Class 3: Tests of the Intercept | |
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| Test Class 4: Addition of a Group of Variables | |
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| Test Class 5: GLH Tests | |
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| The Multiple Testing Issue | |
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| Interaction | |
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| Homework Exercises | |
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| Correlations | |
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| Motivation | |
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| Interpreting [rho superscript 2] | |
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| Correlation Formulas | |
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| Partial Correlation | |
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| Semipartial Correlation | |
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| Relating Semipartial Correlations to Standardized Regression Coefficients | |
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| Multiple Partial Correlation | |
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| Multiple Semipartial Correlation | |
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| Hypothesis Tests for Correlations | |
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| Relating Multiple Partials and Semipartials to Regression Coefficient Tests | |
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| Using Correlations to Interpret Added-in-Order Tests | |
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| Computing Partial Correlations | |
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| Some Useful Properties of Correlations | |
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| The Importance and Utility of Correlations | |
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| Homework Exercises | |
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| GLM Assumption Diagnostics | |
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| Motivation | |
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| The First Step: Get to Know Your Data | |
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| Residual Analysis | |
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| Outliers | |
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| Homework Exercises | |
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| GLM Computation Diagnostics | |
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| Motivation | |
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| Single Variable Problems and Solutions | |
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| Collinearity Definitions and Concepts | |
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| Matrices of Interest | |
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| Models Corresponding to Cross-Products Matrices | |
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| Eigenanalysis | |
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| R[superscript 2 subscript j], Tolerance and VIF | |
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| Detecting Numerical Inaccuracy | |
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| Treating Regression Problems | |
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| Homework Exercises | |
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| Polynomial Regression | |
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| Motivation | |
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| Polynomial Models of Most Interest | |
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| Examples | |
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| Lack-of-Fit Tests | |
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| Limitations of Natural Polynomials | |
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| Orthogonal Polynomials | |
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| Strategies for Accurate Computations with Polynomials | |
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| Strategy for Choosing a Model | |
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| Polynomial Interactions and Response Surfaces | |
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| Homework Exercises | |
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| Transformations | |
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| Motivation | |
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| General Principles | |
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| Power Transformation of the Response | |
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| Other Comments | |
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| Transformations of Predictors | |
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| Pitfalls | |
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| Homework Exercises | |
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| Selecting the Best Model | |
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| Motivation | |
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| Overview of Solution Strategies | |
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| Step 1: Specify the Maximum Model | |
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| Step 2: Specify a Criterion | |
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| Step 3: Specify a Strategy | |
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| Step 4: Conduct the Analysis | |
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| Step 5: Evaluate the Reliability | |
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| Overall Implementation | |
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| Homework Exercises | |
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| Coding Schemes for Regression | |
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| Motivation | |
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| Reference Cell Coding | |
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| Cell Mean Coding | |
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| Classical ANOVA Coding | |
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| Effect Coding | |
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| Polynomial Coding | |
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| The Essence Matrix | |
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| Comments on Coding Schemes | |
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| Relationships among Coding Schemes | |
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| Homework Exercises | |
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| One-Way ANOVA | |
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| Motivation | |
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| Specification of the Model | |
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| (Usual) Overall Test | |
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| Defining and Estimating Cell Means | |
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| Which Means Are Different? | |
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| Contrasts | |
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| Conducting Multiple Comparisons | |
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| Homework Exercises | |
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| Complete, Two-Way Factorial ANOVA | |
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| Motivation | |
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| Model Concepts | |
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| Coding Schemes | |
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| Generating Cell Means | |
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| Computing Estimates and Tests | |
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| Contrast Matrices for Marginal Means | |
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| Choosing and Interpreting Tests | |
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| Step-Down Tests | |
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| Missing Data | |
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| Homework Exercises | |
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| Special Cases of Two-Way ANOVA and Random Effects Basics | |
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| Motivation | |
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| Blocking Variables and Block Designs | |
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| Fixed Block Design | |
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| Introduction to Random Effects Models | |
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| The Classical Approach to a Random Block Design | |
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| Role of Nonindependence of Observations | |
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| Computations for Mixed Models | |
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| Review Comments | |
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| Homework Exercises | |
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| The Full Model in Every Cell (ANCOVA as a Special Case) | |
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| Motivation | |
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| Cell Mean Style Coding of Full Model | |
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| Properties of the Model | |
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| Testing Strategies | |
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| Implementing Strategy 1, Adjusted ANOVA | |
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| Implementing Strategy 2, GLM Testing | |
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| Models of Interest | |
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| Implementing Strategy 3: Backwards Groupwise | |
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| Difference Scores: A Special Case of ANCOVA | |
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| Other Contrasts of Interest in ANCOVA | |
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| Other Tests of Interest in the Full Model | |
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| Regression (Reference Cell) Style Coding | |
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| Effect Style Coding | |
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| Modeling a Baseline Covariate | |
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| Comparing Coding Schemes | |
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| Generalizations | |
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| Homework Exercises | |
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| Understanding and Computing Power for the GLM | |
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| Motivation | |
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| GLM Theory | |
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| Factors in Choosing a Design | |
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| Using Parameter Estimates in Power Analysis | |
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| Example Power Analysis | |
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| Reporting Power | |
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| Tables and Software | |
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| How Much To Do? | |
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| Benefits | |
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| Homework Exercises | |
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| Matrix Algebra for Linear Models | |
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| Basics | |
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| Matrix Properties and Decompositions | |
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| Principal Components (Basics) | |
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| Homework Exercises in Matrix Arithmetic | |
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| Homework Exercises for a Matrix Language | |
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| Statistical Tables | |
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| Study Guide for Linear Model Theory | |
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| Homework and Example Data | |
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| Introduction to SAS/IML | |
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| A Brief Manual for LINMOD | |
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| SAS/IML Power Program User's Guide | |
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| Regression Model Selection Data | |
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| References | |
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| Index | |