John Fox, Applied Regression Analysis, Linear Models, and Related Methods (Sage, 1997)

` Preface   `
`      Synopsis  `
`      Computing  `
`      To Readers, Students, and Instructors  `
`      Acknowledgments  `
` Part I Preliminaries  `
`  Chapter 1 Statistics and Social Science   `
`       1.1 Statistical Models and Social Reality  `
`       1.2 Observation and Experiment   `
`       1.3 Populations and Samples   `
`       1.4 Summary    `
`       1.5 Recommended Reading  `
`  Chapter 2 What Is Regression Analysis?         `
`       2.1 Preliminaries  `
`       2.2 Naive Nonparametric Regression   `
`       2.3 Local Averaging  `
`            2.3.1 Weighted Local Averages*    `
`       2.4 Summary    `
`  Chapter 3 Examining Data    `
`       3.1  Univariate Displays    `
`            3.1.1 Histograms  `
`            3.1.2 Density Estimation*   `
`            3.1.3 Quantile-Comparison Plots      `
`            3.1.4 Boxplots  `
`       3.2 Plotting Bivariate Data  `
`       3.3 Plotting Multivariate Data  `
`       3.4 Summary       `
`       3.5 Recommended Reading  `
`  Chapter 4 Transforming Data   `
`       4.1 The Family of Powers and Roots  `
`       4.2 Transforming Skewness            `
`       4.3 Transforming Nonlinearity     `
`       4.4 Transforming Non-Constant Spread   `
`       4.5 Transforming Proportions      `
`       4.6 Summary     `
`       4.7 Recommended Reading  `
` Part II: Linear Models and Least Squares   `
`  Chapter 5 Linear Least-Squares Regression  `
`       5.1 Simple Regression  `
`            5.1.1 Least-Squares Fit      `
`            5.1.2 Simple Correlation  `
`       5.2 Multiple Regression    `
`            5.2.1 Two Independent Variables    `
`            5.2.2 Several Independent Variables   `
`            5.2.3 Multiple Correlation   `
`            5.2.4 Standardized Regression Coefficients    `
`       5.3 Summary     `
`  Chapter 6 Statistical Inference for Regression   `
`       6.1 Simple Regression  `
`            6.1.1 The Simple-Regression Model    `
`            6.1.2 Properties of the Least-Squares Estimator  `
`            6.1.3 Confidence Intervals and Hypothesis Tests  `
`       6.2 Multiple Regression   `
`            6.2.1 The Multiple-Regression Model    `
`            6.2.2 Confidence Intervals and Hypothesis Tests  `
`                Individual Slope Coefficients    `
`                All Slopes   `
`                A Subset of Slopes    `
`       6.3 Empirical versus Structural Relations   `
`       6.4 Measurement Error in Independent Variables*    `
`       6.5 Summary    `
`  Chapter 7 Dummy-Variable Regression  `
`       7.1 A Dichotomous Independent Variable   `
`       7.2 Polytomous Independent Variables   `
`       7.3 Modeling Interactions   `
`            7.3.1 Constructing Interaction Regressors    `
`            7.3.2 The Principle of Marginality  `
`            7.3.3 Interactions With Polytomous Independent Variables  `
`            7.3.4 Hypothesis Tests for Main Effects and Interactions     `
`       7.4 A Caution Concerning Standardized Coefficients  `
`       7.5 Summary   `
`  Chapter 8 Analysis of Variance   `
`       8.1 One-Way Analysis of Variance   `
`       8.2 Two-Way Analysis of Variance   `
`            8.2.1 Patterns of Means in the Two-Way Classification  `
`            8.2.2 The Two-Way ANOVA Model  `
`            8.2.3 Fitting the Two-Way ANOVA Model to Data    `
`            8.2.4 Testing Hypotheses in Two-Way ANOVA  `
`            8.2.5 Equal Cell Frequencies   `
`            8.2.6 Some Cautionary Remarks  `
`       8.3 Higher-Way Analysis of Variance*      `
`            8.3.1 The Three-Way Classification   `
`            8.3.2 Higher-Order Classifications    `
`            8.3.3 Empty Cells in ANOVA   `
`       8.4 Analysis of Covariance   `
`       8.5 Linear Contrasts of Means   `
`       8.6 Summary   `
`  Chapter 9 Statistical Theory for Linear Models*   `
`       9.1 Linear Models in Matrix Form   `
`            9.1.1 Dummy Regression and Analysis of Variance  `
`            9.1.2 Linear Contrasts  `
`       9.2 Least-Squares Fit   `
`       9.3 Properties of the Least-Squares Estimator  `
`            9.3.1 The Distribution of the Least-Squares Estimator  `
`            9.3.2 The Gauss-Markov Theorem  `
`            9.3.3 Maximum-Likelihood Estimation    `
`       9.4 Statistical Inference for Linear Models  `
`            9.4.1 Inference for Individual Coefficients  `
`            9.4.2 Inference for Several Coefficients  `
`            9.4.3 General Linear Hypotheses   `
`            9.4.4 Joint Confidence Regions  `
`       9.5 Random Regressors   `
`       9.6 Specification Error    `
`       9.7 Summary  `
`       9.8 Recommended Reading  `
`  Chapter 10 The Vector Geometry of Linear Models*     `
`       10.1 Simple Regression   `
`            10.1.1 Variables in Mean-Deviation Form   `
`            10.1.2 Degrees of Freedom `
`       10.2 Multiple Regression  `
`       10.3 Estimating the Error Variance    `
`       10.4 Analysis-of-Variance Models  `
`       10.5 Summary   `
`       10.6 Recommended Reading    `
` Part III: Linear-Model Diagnostics   `
`  Chapter 11 Unusual and Influential Data  `
`       11.1 Outliers, Leverage, and Influence   `
`       11.2 Assessing Leverage: Hat-Values  `
`       11.3 Detecting Outliers: Studentized Residuals   `
`            11.3.1 Testing for Outliers in Linear Models   `
`            11.3.2 Anscombe's Insurance Analogy   `
`       11.4 Measuring Influence  `
`            11.4.1 Influence on Standard Errors   `
`            11.4.2 Influence on Collinearity  `
`       11.5 Numerical Cutoffs for Diagnostic Statistics  `
`            11.5.1 Hat-Values  `
`            11.5.2 Studentized Residuals         `
`            11.5.3 Measures of Influence  `
`       11.6 Joint Influence and Partial-Regression Plots  `
`       11.7 Should Unusual Data Be Discarded?  `
`       11.8 Some Statistical Details*   `
`            11.8.1 Hat-Values and the Hat Matrix         `
`            11.8.2 The Distribution of the Least-Squares Residuals    `
`            11.8.3 Deletion Diagnostics   `
`            11.8.4 Partial-Regression Plots    `
`       11.9 Summary   `
`       11.10 Recommended Reading         `
`  Chapter 12 Nonlinearity and Other Ills         `
`       12.1 Non-Normally Distributed Errors   `
`            12.1.1 Confidence Envelopes by Simulated Sampling*  `
`       12.2 Non-Constant Error Variance    `
`            12.2.1 Residual Plots   `
`            12.2.2 Weighted-Least-Squares Estimation*  `
`            12.2.3 Correcting OLS Standard Errors for Non-Constant Variance*   `
`            12.2.4 How Non-Constant Error Variance Affects the OLS Estimator*   `
`       12.3 Nonlinearity   `
`            12.3.1 Partial-Residual Plots   `
`            12.3.2 When Do Partial-Residual Plots Work?    `
`                CERES Plots*  `
`       12.4 Discrete Data  `
`            12.4.1 Testing for Nonlinearity  `Lack of Fit')    `
`            12.4.2 Testing for Non-Constant Error Variance  `
`       12.5 Maximum-Likelihood Methods*   `
`            12.5.1 Box-Cox Transformation of Y   `
`            12.5.2 Box-Tidwell Transformation of the X's   `
`            12.5.3 Non-Constant Error Variance Revisited   `
`       12.6 Structural Dimension*  `
`       12.7 Summary   `
`       12.8 Recommended Reading   `
`  Chapter 13 Collinearity  `
`       13.1 Detecting Collinearity  `
`            13.1.1 Principal Components*   `
`                Two Variables   `
`                The Data Ellipsoid  `
`                Summary   `
`                Diagnosing Collinearity    `
`            13.1.2 Generalized Variance Inflation*   `
`       13.2 Coping With Collinearity: No Quick Fix   `
`       13.2.1 Model Re-Specification  `
`       13.2.2 Variable Selection  `
`       13.2.3 Biased Estimation  `
`           Ridge Regression*   `
`       13.2.4 Prior Information About the Regression Coefficients   `
`       13.2.5 Some Comparisons  `
`       13.3 Summary  `
` Part IV: Beyond Linear Least Squares  `
`  Chapter 14 Extending Linear Least Squares*   `
`       14.1 Time-Series Regression   `
`            14.1.1 Generalized Least-Squares Estimation   `
`            14.1.2 Serially Correlated Errors  `
`                GLS Estimation With Autoregressive Errors   `
`                Empirical GLS Estimation  `
`            14.1.3 Diagnosing Serially Correlated Errors         `
`            14.1.4 Concluding Remarks    `
`       14.2 Nonlinear Regression  `
`            14.2.1 Polynomial Regression   `
`            14.2.2 Transformable Nonlinearity   `
`            14.2.3 Nonlinear Least Squares   `
`       14.3 Robust Regression  `
`            14.3.1 M-Estimation  `
`                Estimating Location   `
`                M-Estimation in Regression  `
`            14.3.2 Bounded-Influence Regression  `
`       14.4 Nonparametric Regression  `
`            14.4.1 Smoothing Scatterplots by Lowess    `
`                Selecting the Span    `
`                Statistical Inference  `
`            14.4.2 Additive Regression Models   `
`                Fitting the Additive Regression Model   `
`                Statistical Inference  `
`                Semi-Parametric Models    `
`       14.5 Summary   `
`           Time-Series Regression   `
`           Nonlinear Regression  `
`           Robust Regression     `
`           Nonparametric Regression   `
`       14.6 Recommended Reading  `
`  Chapter 15 Logit and Probit Models  `
`       15.1 Models for Dichotomous Data   `
`            15.1.1 The Linear-Probability Model   `
`            15.1.2 Transformations of pi: Logit and Probit Models   `
`            15.1.3 An Unobserved-Variable Formulation   `
`            15.1.4 Logit and Probit Models for Multiple Regression  `
`            15.1.5 Estimating the Linear Logit Model*   `
`            15.1.6 Diagnostics for Logit Models*  `
`                Residuals in Logit model         `
`                Residual and Partial-Residual Plots   `
`                Hat-Values and the Hat-Matrix  `
`                Studentized Residuals  `
`                Influence Diagnostics    `
`                Partial-Regression Plot   `
`                Constructed-Variable Plot for Transforming an X   `
`       15.2 Models for Polytomous Data   `
`            15.2.1 The Polytomous Logit Model   `
`                Details of Estimation*  `
`            15.2.2 Nested Dichotomies   `
`                Why Nested Dichotomies are Independent*   `
`            15.2.3 Ordered Logit and Probit Models  `
`            15.2.4 Comparison of the Three Approaches    `
`       15.3 Discrete Independent Variables  `
`            15.3.1 The Binomial Logit Model*   `
`       15.4 Generalized Linear Models*    `
`       15.5 Summary    `
`       15.6 Recommended Reading   `
`  Chapter 16 Assessing Sampling Variation   `
`       16.1 Bootstrapping  `
`            16.1.1 Bootstrapping Basics  `
`            16.1.2 Bootstrap Confidence Intervals   `
`                Normal-Theory Intervals    `
`                Percentile Intervals     `
`                Improved Bootstrap Intervals*    `
`            16.1.3 Bootstrapping Regression Models   `
`            16.1.4 Bootstrap Hypothesis Tests*  `
`            16.1.5 Bootstrapping Complex Sampling Designs  `
`            16.1.6 Concluding Remarks  `
`       16.2 Cross-Validation   `
`            16.2.1 An Illustration     `
`            16.2.2 Concluding Remarks  `
`       16.3 Summary  `
`       16.4 Recommended Reading    `
`  Appendix A: Notation   `
`  Appendix B: Vector Geometry*    `
`       B.1 Basic Operations  `
`       B.2 Vector Spaces and Subspaces   `
`       B.3 Orthogonality and Orthogonal Projections  `
`       B.4 Recommended Reading  `
`  Appendix C Multivariable Differential Calculus  `
`       C.1 Partial Derivatives  `
`       C.2 Lagrange Multipliers   `
`       C.3 Matrix Calculus   `
`  Appendix D Probability and Estimation  `
`       D.1 Elementary Probability Theory  `
`            D.1.1 Basic Definitions  `
`            D.1.2 Random Variables   `
`                Vector Random Variables*         `
`            D.1.3 Transformations of Random Variables   `
`                Transformations of Vector Random Variables*  `
`       D.2 Discrete Distributions*  `
`            D.2.1 The Binomial Distribution  `
`            D.2.2 The Multinomial Distribution    `
`            D.2.3 The Poisson Distribution    `
`       D.3 Continuous Distributions  `
`            D.3.1 The Normal Distribution   `
`            D.3.2 The Chi-Square Distribution   `
`            D.3.3 The t-Distribution   `
`            D.3.4 The F-Distribution  `
`            D.3.5 The Multivariate-Normal Distribution*   `
`       D.4 Asymptotic Distribution Theory*   `
`            D.4.1 Probability Limits   `
`            D.4.2 Asymptotic Expectation and Variance   `
`            D.4.3 Asymptotic Distribution  `
`       D.5 Properties of Estimators      `
`            D.5.1 Bias  `
`                Asymptotic Bias*  `
`            D.5.2 Mean-Squared Error and Efficiency    `
`                Asymptotic Efficiency*   `
`            D.5.3 Consistency*  `
`            D.5.4 Sufficiency*   `
`       D.6 Maximum-Likelihood Estimation         `
`                Generalization of the Example*    `
`            D.6.1 Properties of Maximum-Likelihood Estimators*   `
`            D.6.2 Wald, Likelihood-Ratio, and Score Tests  `
`                An Illustration*         `
`            D.6.3 Several Parameters*     `
`       D.7 Recommended Reading    `