{"product_id":"foundations-of-linear-and-generalized-linear-models-isbn-9781118730034","title":"Foundations of Linear and Generalized Linear Models","description":"\u003cp\u003e\u003cb\u003eA valuable overview of the most important ideas and results in statistical modeling\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWritten by a highly-experienced author, \u003ci\u003eFoundations of Linear and Generalized Linear Models \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003eThe 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, \u003ci\u003eFoundations of\u003c\/i\u003e\u003ci\u003eLinear and Generalized Linear Models \u003c\/i\u003ealso features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAn introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods\u003c\/li\u003e \u003cli\u003eAn 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 problems\u003c\/li\u003e \u003cli\u003eNumerous examples that use R software for all text data analyses\u003c\/li\u003e \u003cli\u003eMore than 400 exercises for readers to practice and extend the theory, methods, and data analysis\u003c\/li\u003e \u003cli\u003eA supplementary website with datasets for the examples and exercises\u003c\/li\u003e \u003c\/ul\u003e An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, \u003ci\u003eFoundations of Linear and Generalized Linear Models \u003c\/i\u003eis also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Linear and Generalized Linear Models 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Components of a Generalized Linear Model 2\u003c\/p\u003e \u003cp\u003e1.2 Quantitative\/Qualitative Explanatory Variables and Interpreting Effects 6\u003c\/p\u003e \u003cp\u003e1.3 Model Matrices and Model Vector Spaces 10\u003c\/p\u003e \u003cp\u003e1.4 Identifiability and Estimability 13\u003c\/p\u003e \u003cp\u003e1.5 Example: Using Software to Fit a GLM 15\u003c\/p\u003e \u003cp\u003eChapter Notes 20\u003c\/p\u003e \u003cp\u003eExercises 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear Models: Least Squares Theory 26\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Least Squares Model Fitting 27\u003c\/p\u003e \u003cp\u003e2.2 Projections of Data Onto Model Spaces 33\u003c\/p\u003e \u003cp\u003e2.3 Linear Model Examples: Projections and SS Decompositions 41\u003c\/p\u003e \u003cp\u003e2.4 Summarizing Variability in a Linear Model 49\u003c\/p\u003e \u003cp\u003e2.5 Residuals Leverage and Influence 56\u003c\/p\u003e \u003cp\u003e2.6 Example: Summarizing the Fit of a Linear Model 62\u003c\/p\u003e \u003cp\u003e2.7 Optimality of Least Squares and Generalized Least Squares 67\u003c\/p\u003e \u003cp\u003eChapter Notes 71\u003c\/p\u003e \u003cp\u003eExercises 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Normal Linear Models: Statistical Inference 80\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Distribution Theory for Normal Variates 81\u003c\/p\u003e \u003cp\u003e3.2 Significance Tests for Normal Linear Models 86\u003c\/p\u003e \u003cp\u003e3.3 Confidence Intervals and Prediction Intervals for Normal Linear Models 95\u003c\/p\u003e \u003cp\u003e3.4 Example: Normal Linear Model Inference 99\u003c\/p\u003e \u003cp\u003e3.5 Multiple Comparisons: Bonferroni Tukey and FDR Methods 107\u003c\/p\u003e \u003cp\u003eChapter Notes 111\u003c\/p\u003e \u003cp\u003eExercises 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Generalized Linear Models: Model Fitting and Inference 120\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Exponential Dispersion Family Distributions for a GLM 120\u003c\/p\u003e \u003cp\u003e4.2 Likelihood and Asymptotic Distributions for GLMs 123\u003c\/p\u003e \u003cp\u003e4.3 Likelihood-Ratio\/Wald\/Score Methods of Inference for GLM Parameters 128\u003c\/p\u003e \u003cp\u003e4.4 Deviance of a GLM Model Comparison and Model Checking 132\u003c\/p\u003e \u003cp\u003e4.5 Fitting Generalized Linear Models 138\u003c\/p\u003e \u003cp\u003e4.6 Selecting Explanatory Variables for a GLM 143\u003c\/p\u003e \u003cp\u003e4.7 Example: Building a GLM 149\u003c\/p\u003e \u003cp\u003eAppendix: GLM Analogs of Orthogonality Results for Linear Models 156\u003c\/p\u003e \u003cp\u003eChapter Notes 158\u003c\/p\u003e \u003cp\u003eExercises 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Models for Binary Data 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Link Functions for Binary Data 165\u003c\/p\u003e \u003cp\u003e5.2 Logistic Regression: Properties and Interpretations 168\u003c\/p\u003e \u003cp\u003e5.3 Inference About Parameters of Logistic Regression Models 172\u003c\/p\u003e \u003cp\u003e5.4 Logistic Regression Model Fitting 176\u003c\/p\u003e \u003cp\u003e5.5 Deviance and Goodness of Fit for Binary GLMs 179\u003c\/p\u003e \u003cp\u003e5.6 Probit and Complementary Log–Log Models 183\u003c\/p\u003e \u003cp\u003e5.7 Examples: Binary Data Modeling 186\u003c\/p\u003e \u003cp\u003eChapter Notes 193\u003c\/p\u003e \u003cp\u003eExercises 194\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Multinomial Response Models 202\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Nominal Responses: Baseline-Category Logit Models 203\u003c\/p\u003e \u003cp\u003e6.2 Ordinal Responses: Cumulative Logit and Probit Models 209\u003c\/p\u003e \u003cp\u003e6.3 Examples: Nominal and Ordinal Responses 216\u003c\/p\u003e \u003cp\u003eChapter Notes 223\u003c\/p\u003e \u003cp\u003eExercises 223\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Models for Count Data 228\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Poisson GLMs for Counts and Rates 229\u003c\/p\u003e \u003cp\u003e7.2 Poisson\/Multinomial Models for Contingency Tables 235\u003c\/p\u003e \u003cp\u003e7.3 Negative Binomial GLMS 247\u003c\/p\u003e \u003cp\u003e7.4 Models for Zero-Inflated Data 250\u003c\/p\u003e \u003cp\u003e7.5 Example: Modeling Count Data 254\u003c\/p\u003e \u003cp\u003eChapter Notes 259\u003c\/p\u003e \u003cp\u003eExercises 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Quasi-Likelihood Methods 268\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Variance Inflation for Overdispersed Poisson and Binomial GLMs 269\u003c\/p\u003e \u003cp\u003e8.2 Beta-Binomial Models and Quasi-Likelihood Alternatives 272\u003c\/p\u003e \u003cp\u003e8.3 Quasi-Likelihood and Model Misspecification 278\u003c\/p\u003e \u003cp\u003eChapter Notes 282\u003c\/p\u003e \u003cp\u003eExercises 282\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modeling Correlated Responses 286\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Marginal Models and Models with Random Effects 287\u003c\/p\u003e \u003cp\u003e9.2 Normal Linear Mixed Models 294\u003c\/p\u003e \u003cp\u003e9.3 Fitting and Prediction for Normal Linear Mixed Models 302\u003c\/p\u003e \u003cp\u003e9.4 Binomial and Poisson GLMMs 307\u003c\/p\u003e \u003cp\u003e9.5 GLMM Fitting Inference and Prediction 311\u003c\/p\u003e \u003cp\u003e9.6 Marginal Modeling and Generalized Estimating Equations 314\u003c\/p\u003e \u003cp\u003e9.7 Example: Modeling Correlated Survey Responses 319\u003c\/p\u003e \u003cp\u003eChapter Notes 322\u003c\/p\u003e \u003cp\u003eExercises 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Bayesian Linear and Generalized Linear Modeling 333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Bayesian Approach to Statistical Inference 333\u003c\/p\u003e \u003cp\u003e10.2 Bayesian Linear Models 340\u003c\/p\u003e \u003cp\u003e10.3 Bayesian Generalized Linear Models 347\u003c\/p\u003e \u003cp\u003e10.4 Empirical Bayes and Hierarchical Bayes Modeling 351\u003c\/p\u003e \u003cp\u003eChapter Notes 357\u003c\/p\u003e \u003cp\u003eExercises 359\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Extensions of Generalized Linear Models 364\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Robust Regression and Regularization Methods for Fitting Models 365\u003c\/p\u003e \u003cp\u003e11.2 Modeling With Large p 375\u003c\/p\u003e \u003cp\u003e11.3 Smoothing Generalized Additive Models and Other GLM Extensions 378\u003c\/p\u003e \u003cp\u003eChapter Notes 386\u003c\/p\u003e \u003cp\u003eExercises 388\u003c\/p\u003e \u003cp\u003eAppendix A Supplemental Data Analysis Exercises 391\u003c\/p\u003e \u003cp\u003eAppendix B Solution Outlines for Selected Exercises 396\u003c\/p\u003e \u003cp\u003eReferences 410\u003c\/p\u003e \u003cp\u003eAuthor Index 427\u003c\/p\u003e \u003cp\u003eExample Index 433\u003c\/p\u003e \u003cp\u003eSubject Index 435\u003c\/p\u003e \u003cp\u003e\"The book arose from a one-semester graduate level course taught by Alan Agresti at Harvard University. It has a clear didactic focus, which benefits greatly from Agresti’s well-known clear writing style. Each of the 11 chapters is followed by around 40 exercises, which are diverse and interesting.\"\u003c\/p\u003e \u003cp\u003e\"...I am very happy with the foundational perspective of this book. I think that students who master this material will have a very thorough understanding of the most important aspects of GLMs, which is more valuable than a kaleidoscopic knowledge. This is certainly one of the books I will consider when next I need to teach a course in generalized linear models.\"\u003c\/p\u003e \u003cp\u003e\"...this is a great introduction to GLMs written in a clear and didactic style, and with a thoughtful choice and presentation of the material. Highly recommended.\"\u003cbr\u003e\u003cb\u003e--\u003ci\u003eBiometrics Journal\u003c\/i\u003e, 2016\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\"This book is an essential reference for anyone working with or teaching GLMs.\" (Mathematical Association of America, 2016) \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e  \u003cp\u003e\u003cb\u003eALAN AGRESTI, PhD,\u003c\/b\u003e is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He has presented short courses on generalized linear models and categorical data methods in more than 30 countries. The author of over 200 journal articles, Dr. Agresti is also the author of \u003ci\u003eCategorical Data Analysis\u003c\/i\u003e, Third Edition, \u003ci\u003eAnalysis of Ordinal Categorical Data\u003c\/i\u003e, Second Edition, and \u003ci\u003eAn Introduction to Categorical Data Analysis\u003c\/i\u003e, Second Edition, all published by Wiley.\t   \t\u003c\/p\u003e\u003cp\u003e\u003cb\u003eA valuable overview of the most important ideas and results in statistical modeling\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eWritten by a highly-experienced author, \u003ci\u003eFoundations of Linear and Generalized Linear Models\u003c\/i\u003e is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. \u003c\/p\u003e\u003cp\u003eThe 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, \u003ci\u003eFoundations of Linear and Generalized Linear Models\u003c\/i\u003e also features: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eAn introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods\u003c\/li\u003e \u003cli\u003eAn 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 problems\u003c\/li\u003e \u003cli\u003eNumerous examples that use R software for all text data analyses\u003c\/li\u003e \u003cli\u003eMore than 400 exercises for readers to practice and extend the theory, methods, and data analysis\u003c\/li\u003e \u003cli\u003eA supplementary website with datasets for the examples and exercises\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAn invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, \u003ci\u003eFoundations of Linear and Generalized Linear Models\u003c\/i\u003e is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989238563045,"sku":"NP9781118730034","price":106.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118730034.jpg?v=1761783329","url":"https:\/\/k12savings.com\/products\/foundations-of-linear-and-generalized-linear-models-isbn-9781118730034","provider":"K12savings","version":"1.0","type":"link"}