Foundations of Linear and Generalized Linear Models

A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, i...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Agresti, Alan
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2015.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo

MARC

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020 |a 1118730305 
035 |a (OCoLC)1347023194 
050 |a QA299.8 |b A37 2015 
082 0 4 |a 003/.74  |q OCoLC  |2 23/eng/20231120 
049 |a UAMI 
100 1 |a Agresti, Alan. 
245 1 0 |a Foundations of Linear and Generalized Linear Models  |h [electronic resource]. 
260 |a Newark :  |b John Wiley & Sons, Incorporated,  |c 2015. 
300 |a 1 online resource (472 p.). 
490 1 |a New York Academy of Sciences Ser. 
500 |a Description based upon print version of record. 
505 0 |a Intro -- Foundations of Linear and Generalized Linear Models -- Contents -- Preface -- Purpose of this book -- Use as a textbook -- Acknowledgments -- 1 Introduction to Linear and Generalized Linear Models -- 1.1 Components of a Generalized Linear Model -- 1.1.1 Random Component of a GLM -- 1.1.2 Linear Predictor of a GLM -- 1.1.3 Link Function of a GLM -- 1.1.4 A GLM with Identity Link Function is a "Linear Model" -- 1.1.5 GLMs for Normal, Binomial, and Poisson Responses -- 1.1.6 Advantages of GLMs versus Transforming the Data 
505 8 |a 1.2 Quantitative/Qualitative Explanatory Variables and Interpreting Effects -- 1.2.1 Quantitative and Qualitative Variables in Linear Predictors -- 1.2.2 Interval, Nominal, and Ordinal Variables -- 1.2.3 Interpreting Effects in Linear Models -- 1.3 Model Matrices and Model Vector Spaces -- 1.3.1 Model Matrices Induce Model Vector Spaces -- 1.3.2 Dimension of Model Space Equals Rank of Model Matrix -- 1.3.3 Example: The One-Way Layout -- 1.4 Identifiability and Estimability -- 1.4.1 Identifiability of GLM Model Parameters -- 1.4.2 Estimability in Linear Models 
505 8 |a 1.5 Example: Using Software to Fit a GLM -- 1.5.1 Example: Male Satellites for Female Horseshoe Crabs -- 1.5.2 Linear Model Using Weight to Predict Satellite Counts -- 1.5.3 Comparing Mean Numbers of Satellites by Crab Color -- Chapter Notes -- Exercises -- 2 Linear Models: Least Squares Theory -- 2.1 Least Squares Model Fitting -- 2.1.1 The Normal Equations and Least Squares Solution -- 2.1.2 Hat Matrix and Moments of Estimators -- 2.1.3 Bivariate Linear Model and Regression Toward the Mean -- 2.1.4 Least Squares Solutions When X Does Not Have Full Rank 
505 8 |a 2.1.5 Orthogonal Subspaces and Residuals -- 2.1.6 Alternatives to Least Squares -- 2.2 Projections of Data Onto Model Spaces -- 2.2.1 Projection Matrices -- 2.2.2 Projection Matrices for Linear Model Spaces -- 2.2.3 Example: The Geometry of a Linear Model -- 2.2.4 Orthogonal Columns and Parameter Orthogonality -- 2.2.5 Pythagoras's Theorem Applications for Linear Models -- 2.3 Linear Model Examples: Projections and SS Decompositions -- 2.3.1 Example: Null Model -- 2.3.2 Example: Model for the One-way Layout -- 2.3.3 Sums of Squares and ANOVA Table for One-Way Layout 
505 8 |a 2.3.4 Example: Model for Two-Way Layout with Randomized Block Design -- 2.4 Summarizing Variability in a Linear Model -- 2.4.1 Estimating the Error Variance for a Linear Model -- 2.4.2 Sums of Squares: Error (SSE) and Regression (SSR) -- 2.4.3 Effect on SSR and SSE of Adding Explanatory Variables -- 2.4.4 Sequential and Partial Sums of Squares -- 2.4.5 Uncorrelated Predictors: Sequential SS = Partial SS = SSR Component -- 2.4.6 R-Squared and the Multiple Correlation -- 2.5 Residuals, Leverage, and Influence -- 2.5.1 Residuals and Fitted Values Are Uncorrelated -- 2.5.2 Plots of Residuals 
500 |a 2.5.3 Standardized and Studentized Residuals 
520 |a A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is 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 Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An 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 Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
655 0 |a Electronic books. 
758 |i has work:  |a Foundations of linear and generalized linear models (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGgmpHw8Cfc9Qp38bWcKFq  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Agresti, Alan  |t Foundations of Linear and Generalized Linear Models  |d Newark : John Wiley & Sons, Incorporated,c2015  |z 9781118730034 
830 0 |a New York Academy of Sciences Ser. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=7104002  |z Texto completo 
938 |a ProQuest Ebook Central  |b EBLB  |n EBL7104002 
994 |a 92  |b IZTAP 

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