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Full Description
The linear model and its extensions play fundamental roles in both theoretical and applied statistics, due to their transparency and interpretability in modeling empirical data. This textbook, based on the author's course on linear modeling at UC Berkeley taught over the past ten years, only requires basic knowledge of linear algebra, probability theory, and statistical inference. It assumes minimal knowledge of linear modeling, and reviews basic linear algebra, probability, and statistics in the appendix. It covers linear regression, logistic regression, Poisson regression, generalized estimating equation, quantile regression, and Cox regression, which are widely used statistical models across many areas. It balances rigorous theory, simulation, and data analysis.
Key Features:
- All R code and data sets available at Harvard Dataverse.
- Includes over 200 exercises.
- Solutions manual available for instructors, upon request from the author.
This book is suitable for advanced undergraduate or graduate-level courses on linear modeling, or graduate-level courses on generalized linear modeling. It can also be used as a reference for researchers who are searching for basic properties of the linear model and its extensions.
Contents
Acronyms Symbols Useful R packages Preface I Introduction 1 Motivations for Statistical Models 2 Ordinary Least Squares with a Univariate Covariate II Ordinary Least Squares and Statistical Inference 3 Ordinary Least Squares with Multiple Covariates 4 Gauss-Markov Model and Gauss-Markov Theorem 5 Normal Linear Model: Inference and Prediction 6 Asymptotic Inference in OLS: Eicker-Huber-White (EHW) robust standard error III Interpretation of Ordinary Least Squares Based on Partial Regressions 7 Frisch-Waugh-Lovell Theorem 8 Applications of the Frisch-Waugh-Lovell Theorem 9 Cochran's Formula and Omitted-Variable Bias IV Model Fitting, Checking, and Misspecification 10 Multiple Correlation Coefficient 11 Leverage Scores and Leave-One-Out Formulas 12 Population Ordinary Least Squares and Misspecified Linear Model V Overfitting, Regularization, and Model Selection 13 Perils of Overfitting 14 Ridge Regression 15 Lasso VI Transformation and Weighting 16 Transformations in OLS 17 Interactions in OLS 18 Restricted OLS 19 Weighted Least Squares VII Generalized Linear Models 20 Logistic Regression for Binary Outcomes 21 Logistic Regressions for Categorical Outcomes 22 Regression Models for Count Outcomes 23 Generalized Linear Models: A Unification 24 Misspecified Generalized Linear Models: Restricted Mean Models and Sandwich Covariance Matrix 25 Generalized Estimating Equation for Correlated Multivariate Data VIII Beyond Modeling the Conditional Mean 26 Quantile Regression 27 Modeling Time-to-Event Outcomes IX Appendices A Linear Algebra B Random Variables C Limiting Theorems and Basic Asymptotics D M-Estimation and MLE Bibliography
