Foundations of Linear and Generalized Linear Models

Alan Agresti 지음

Wiley 2015년 01월 15일 출간 국내도서 : 2015년 08월 01일 출간

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A valuable overview of the most important ideas and results in statistical modelingWritten by a highly-experienced author,Foundations of Linear and Generalized Linear Modelsis a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding.The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models,Foundations ofLinear and Generalized Linear Modelsalso features:An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methodsAn overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problemsNumerous examples that use R software for all text data analysesMore than 400 exercises for readers to practice and extend the theory, methods, and data analysisA supplementary website with datasets for the examples and exercisesAn invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses,Foundations of Linear and Generalized Linear M

목차

Preface xi1 Introduction to Linear and Generalized Linear Models 11.1 Components of a Generalized Linear Model 21.2 Quantitative/Qualitative Explanatory Variables and Interpreting Effects 61.3 Model Matrices and Model Vector Spaces 101.4 Identifiability and Estimability 131.5 Example: Using Software to Fit a GLM 15Chapter Notes 20Exercises 212 Linear Models: Least Squares Theory 262.1 Least Squares Model Fitting 272.2 Projections of Data Onto Model Spaces 332.3 Linear Model Examples: Projections and SS Decompositions 412.4 Summarizing Variability in a Linear Model 492.5 Residuals Leverage and Influence 562.6 Example: Summarizing the Fit of a Linear Model 622.7 Optimality of Least Squares and Generalized Least Squares 67Chapter Notes 71Exercises 713 Normal Linear Models: Statistical Inference 803.1 Distribution Theory for Normal Variates 813.2 Significance Tests for Normal Linear Models 863.3 Confidence Intervals and Prediction Intervals for Normal Linear Models 953.4 Example: Normal Linear Model Inference 993.5 Multiple Comparisons: Bonferroni Tukey and FDR Methods 107Chapter Notes 111Exercises 1124 Generalized Linear Models: Model Fitting and Inference 1204.1 Exponential Dispersion Family Distributions for a GLM 1204.2 Likelihood and Asymptotic Distributions for GLMs 1234.3 Likelihood-Ratio/Wald/Score Methods of Inference for GLM Parameters 1284.4 Deviance of a GLM Model Comparison and Model Checking 1324.5 Fitting Generalized Linear Models 1384.6 Selecting Explanatory Variables for a GLM 1434.7 Example: Building a GLM 149Appendix: GLM Analogs of Orthogonality Results for Linear Models 156Chapter Notes 158Exercises 1595 Models for Binary Data 1655.1 Link Functions for Binary Data 1655.2

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저자(글) Alan Agresti