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Linear Models in Statistics

2008-01-07 Mathematics
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Release : 2008-01-07
Genre : Mathematics
Kind : eBook
Book Rating : 607/5 ( reviews)

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Book Synopsis Linear Models in Statistics by : Alvin C. Rencher

Download or read book Linear Models in Statistics written by Alvin C. Rencher. This book was released on 2008-01-07. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

Linear Model Theory

2020-11-02 Mathematics
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Release : 2020-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 633/5 ( reviews)

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Book Synopsis Linear Model Theory by : Dale L. Zimmerman

Download or read book Linear Model Theory written by Dale L. Zimmerman. This book was released on 2020-11-02. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.

Generalized Linear Models With Examples in R

2018-11-10 Mathematics
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Release : 2018-11-10
Genre : Mathematics
Kind : eBook
Book Rating : 183/5 ( reviews)

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Book Synopsis Generalized Linear Models With Examples in R by : Peter K. Dunn

Download or read book Generalized Linear Models With Examples in R written by Peter K. Dunn. This book was released on 2018-11-10. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an introduction to generalized linear models, complete with real-world data sets and practice problems, making it applicable for both beginning and advanced students of applied statistics. Generalized linear models (GLMs) are powerful tools in applied statistics that extend the ideas of multiple linear regression and analysis of variance to include response variables that are not normally distributed. As such, GLMs can model a wide variety of data types including counts, proportions, and binary outcomes or positive quantities. The book is designed with the student in mind, making it suitable for self-study or a structured course. Beginning with an introduction to linear regression, the book also devotes time to advanced topics not typically included in introductory textbooks. It features chapter introductions and summaries, clear examples, and many practice problems, all carefully designed to balance theory and practice. The text also provides a working knowledge of applied statistical practice through the extensive use of R, which is integrated into the text. Other features include: • Advanced topics such as power variance functions, saddlepoint approximations, likelihood score tests, modified profile likelihood, small-dispersion asymptotics, and randomized quantile residuals • Nearly 100 data sets in the companion R package GLMsData • Examples that are cross-referenced to the companion data set, allowing readers to load the data and follow the analysis in their own R session

Linear Models with R

2016-04-19 Mathematics
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Release : 2016-04-19
Genre : Mathematics
Kind : eBook
Book Rating : 349/5 ( reviews)

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Book Synopsis Linear Models with R by : Julian J. Faraway

Download or read book Linear Models with R written by Julian J. Faraway. This book was released on 2016-04-19. Available in PDF, EPUB and Kindle. Book excerpt: A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models

Foundations of Linear and Generalized Linear Models

2015-02-23 Mathematics
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Release : 2015-02-23
Genre : Mathematics
Kind : eBook
Book Rating : 038/5 ( reviews)

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Book Synopsis Foundations of Linear and Generalized Linear Models by : Alan Agresti

Download or read book Foundations of Linear and Generalized Linear Models written by Alan Agresti. This book was released on 2015-02-23. Available in PDF, EPUB and Kindle. Book excerpt: 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 Linear Models 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.

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