Foundations of Linear and Generalized Linear Models

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 1118730038

Category: Mathematics

Page: 444

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"This book presents an overview of the foundations and the key ideas and results of linear and generalized linear models under one cover. Written by a prolific academic, researcher, and textbook writer, Foundations of Linear and Generalized Linear Modelsis soon to become the gold standard by which all existing textbooks on the topic will be compared. While the emphasis is clearly and succinctly on theoretical underpinnings, applications in "R" are presented when they help to elucidate the content or promote practical model building. Each chapter contains approximately 15-20 exercises, primarily for readers to practice and extend the theory, but, also to assimilate the ideas by doing some data analysis. The carefully crafted models and examples convey basic concepts and do not get mired down in non-trivial considerations. An author-maintained web site includes, among other numerous pedagogical supplements, analyses that parallel the "R" routines from the book in SAS, SPSS and Stata"--

Linear models in statistics

Author: Alvin C. Rencher

Publisher: Wiley-Interscience

ISBN: 9780471315643

Category: Mathematics

Page: 578

View: 8416

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* Graphs, charts, and tables as well as extensive references

Generalized Linear Mixed Models

Author: Charles E. McCulloch

Publisher: IMS

ISBN: 9780940600546

Category: Mathematics

Page: 84

View: 6226

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Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models

Introduction to linear regression analysis

Author: Douglas C. Montgomery,Elizabeth A. Peck,G. Geoffrey Vining

Publisher: Wiley-Interscience

ISBN: 9780471315650

Category: Mathematics

Page: 641

View: 7408

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A comprehensive and thoroughly up-to-date look at regression analysis-still the most widely used technique in statistics today As basic to statistics as the Pythagorean theorem is to geometry, regression analysis is a statistical technique for investigating and modeling the relationship between variables. With far-reaching applications in almost every field, regression analysis is used in engineering, the physical and chemical sciences, economics, management, life and biological sciences, and the social sciences. Clearly balancing theory with applications, Introduction to Linear Regression Analysis describes conventional uses of the technique, as well as less common ones, placing linear regression in the practical context of today's mathematical and scientific research. Beginning with a general introduction to regression modeling, including typical applications, the book then outlines a host of technical tools that form the linear regression analytical arsenal, including: basic inference procedures and introductory aspects of model adequacy checking; how transformations and weighted least squares can be used to resolve problems of model inadequacy; how to deal with influential observations; and polynomial regression models and their variations. Succeeding chapters include detailed coverage of: * Indicator variables, making the connection between regression and analysis-of-variance modelss * Variable selection and model-building techniques * The multicollinearity problem, including its sources, harmful effects, diagnostics, and remedial measures * Robust regression techniques, including M-estimators, Least Median of Squares, and S-estimation * Generalized linear models The book also includes material on regression models with autocorrelated errors, bootstrapping regression estimates, classification and regression trees, and regression model validation. Topics not usually found in a linear regression textbook, such as nonlinear regression and generalized linear models, yet critical to engineering students and professionals, have also been included. The new critical role of the computer in regression analysis is reflected in the book's expanded discussion of regression diagnostics, where major analytical procedures now available in contemporary software packages, such as SAS, Minitab, and S-Plus, are detailed. The Appendix now includes ample background material on the theory of linear models underlying regression analysis. Data sets from the book, extensive problem solutions, and software hints are available on the ftp site. For other Wiley books by Doug Montgomery, visit our website at www.wiley.com/college/montgomery.

Linear Statistical Models

Author: James H. Stapleton

Publisher: John Wiley & Sons

ISBN: 0470231467

Category: Mathematics

Page: 474

View: 1515

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Praise for the First Edition "This impressive and eminently readable text . . . [is] a welcome addition to the statistical literature." The Indian Journal of Statistics Revised to reflect the current developments on the topic, Linear Statistical Models, Second Edition provides an up–to–date approach to various statistical model concepts. The book includes clear discussions that illustrate key concepts in an accessible and interesting format while incorporating the most modern software applications. This Second Edition follows an introduction–theorem–proof–examples format that allows for easier comprehension of how to use the methods and recognize the associated assumptions and limits. In addition to discussions on the methods of random vectors, multiple regression techniques, simultaneous confidence intervals, and analysis of frequency data, new topics such as mixed models and curve fitting of models have been added to thoroughly update and modernize the book. Additional topical coverage includes: An introduction to R and S–Plus® with many examples Multiple comparison procedures Estimation of quantiles for regression models An emphasis on vector spaces and the corresponding geometry Extensive graphical displays accompany the book′s updated descriptions and examples, which can be simulated using R, S–Plus®, and SAS® code. Problems at the end of each chapter allow readers to test their understanding of the presented concepts, and additional data sets are available via the book′s FTP site. Linear Statistical Models, Second Edition is an excellent book for courses on linear models at the upper–undergraduate and graduate levels. It also serves as a comprehensive reference for statisticians, engineers, and scientists who apply multiple regression or analysis of variance in their everyday work.

Sensitivity Analysis in Linear Regression

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470317426

Category: Mathematics

Page: 315

View: 9550

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Treats linear regression diagnostics as a tool for application of linear regression models to real-life data. Presentation makes extensive use of examples to illustrate theory. Assesses the effect of measurement errors on the estimated coefficients, which is not accounted for in a standard least squares estimate but is important where regression coefficients are used to apportion effects due to different variables. Also assesses qualitatively and numerically the robustness of the regression fit.

Linear Models

Author: Shayle R. Searle,Marvin H. J. Gruber

Publisher: John Wiley & Sons

ISBN: 1118952855

Category: Mathematics

Page: 696

View: 703

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Provides an easy-to-understand guide to statistical linear models and its uses in data analysis This book defines a broad spectrum of statistical linear models that is useful in the analysis of data. Considerable rewriting was done to make the book more reader friendly than the first edition. Linear Models, Second Edition is written in such a way as to be self-contained for a person with a background in basic statistics, calculus and linear algebra. The text includes numerous applied illustrations, numerical examples, and exercises, now augmented with computer outputs in SAS and R. Also new to this edition is: • A greatly improved internal design and format • A short introductory chapter to ease understanding of the order in which topics are taken up • Discussion of additional topics including multiple comparisons and shrinkage estimators • Enhanced discussions of generalized inverses, the MINQUE, Bayes and Maximum Likelihood estimators for estimating variance components Furthermore, in this edition, the second author adds many pedagogical elements throughout the book. These include numbered examples, end-of-example and end-of-proof symbols, selected hints and solutions to exercises available on the book’s website, and references to “big data” in everyday life. Featuring a thorough update, Linear Models, Second Edition includes: • A new internal format, additional instructional pedagogy, selected hints and solutions to exercises, and several more real-life applications • Many examples using SAS and R with timely data sets • Over 400 examples and exercises throughout the book to reinforce understanding Linear Models, Second Edition is a textbook and a reference for upper-level undergraduate and beginning graduate-level courses on linear models, statisticians, engineers, and scientists who use multiple regression or analysis of variance in their work. SHAYLE R. SEARLE, PhD, was Professor Emeritus of Biometry at Cornell University. He was the author of the first edition of Linear Models, Linear Models for Unbalanced Data, and Generalized, Linear, and Mixed Models (with Charles E. McCulloch), all from Wiley. The first edition of Linear Models appears in the Wiley Classics Library. MARVIN H. J. GRUBER, PhD, is Professor Emeritus at Rochester Institute of Technology, School of Mathematical Sciences. Dr. Gruber has written a number of papers and has given numerous presentations at professional meetings during his tenure as a professor at RIT. His fields of interest include regression estimators and the improvement of their efficiency using shrinkage estimators. He has written and published two books on this topic. Another of his books, Matrix Algebra for Linear Models, also published by Wiley, provides good preparation for studying Linear Models. He is a member of the American Mathematical Society, the Institute of Mathematical Statistics and the American Statistical Association.

Linear Model Theory

Univariate, Multivariate, and Mixed Models

Author: Keith E. Muller,Paul W. Stewart

Publisher: John Wiley & Sons

ISBN: 0470052139

Category: Mathematics

Page: 480

View: 8304

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A precise and accessible presentation of linear model theory, illustrated with data examples Statisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas Linear Model Theory: Univariate, Multivariate, and Mixed Models presents a unified treatment in order to make clear the distinctions among the three classes of models. Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sample size. Substantial sets of excercises of varying difficulty serve instructors for their classes, as well as help students to test their own knowledge. The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective. Topics covered include: A review of matrix algebra for linear models The general linear univariate model The general linear multivariate model Generalizations of the multivariate linear model The linear mixed model Multivariate distribution theory Estimation in linear models Tests in Gaussian linear models Choosing a sample size in Gaussian linear models Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, Linear Model Theory: Univariate, Multivariate, and Mixed Models centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation.

Applied Mixed Models in Medicine

Author: Helen Brown,Robin Prescott

Publisher: John Wiley & Sons

ISBN: 1118778243

Category: Medical

Page: 536

View: 2802

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A fully updated edition of this key text on mixed models,focusing on applications in medical research The application of mixed models is an increasingly popular wayof analysing medical data, particularly in the pharmaceuticalindustry. A mixed model allows the incorporation of both fixed andrandom variables within a statistical analysis, enabling efficientinferences and more information to be gained from the data. Therehave been many recent advances in mixed modelling, particularlyregarding the software and applications. This third edition ofBrown and Prescott’s groundbreaking text provides an updateon the latest developments, and includes guidance on the use ofcurrent SAS techniques across a wide range of applications. Presents an overview of the theory and applications of mixedmodels in medical research, including the latest developments andnew sections on incomplete block designs and the analysis ofbilateral data. Easily accessible to practitioners in any area where mixedmodels are used, including medical statisticians andeconomists. Includes numerous examples using real data from medical andhealth research, and epidemiology, illustrated with SAS code andoutput. Features the new version of SAS, including new graphics formodel diagnostics and the procedure PROC MCMC. Supported by a website featuring computer code, data sets, andfurther material. This third edition will appeal to applied statisticians workingin medical research and the pharmaceutical industry, as well asteachers and students of statistics courses in mixed models. Thebook will also be of great value to a broad range of scientists,particularly those working in the medical and pharmaceuticalareas.

Linear models

an introduction

Author: Irwin Guttman

Publisher: Krieger Pub Co

ISBN: N.A

Category: Mathematics

Page: 358

View: 2956

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Bayesian estimation and experimental design in linear regression models

Author: Jürgen Pilz

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 296

View: 1862

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Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.

Nonparametric methods in general linear models

Author: Madan Lal Puri,Pranab Kumar Sen

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 399

View: 6315

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Presents a systematic account of the theory of rank order statistics as applied to the problems of general linear models. Offers a unified approach to general multivariate linear models with an emphasis on nonparametrics. Includes an extensive, up-to-date bibliograpy.

Introduction to Linear Regression Analysis, Fifth Edition Set

Author: Douglas C. Montgomery

Publisher: Wiley

ISBN: 9781118780572

Category: Mathematics

Page: 836

View: 1865

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This set includes Introduction to Linear Regression Analysis, 5th Edition & Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition. Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.

Linear Models

An Integrated Approach

Author: Debasis Sengupta,S. Rao Jammalamadaka

Publisher: World Scientific

ISBN: 9789812564900

Category: Mathematics

Page: 644

View: 8824

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Linear Models: An Integrated Approach aims to provide a clearand deep understanding of the general linear model using simplestatistical ideas. Elegant geometric arguments are also invoked asneeded and a review of vector spaces and matrices is provided to makethe treatment self-contained.

Methods and Applications of Linear Models

Regression and the Analysis of Variance

Author: Ronald R. Hocking

Publisher: John Wiley & Sons

ISBN: 1118593022

Category: Mathematics

Page: 720

View: 7998

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Praise for the Second Edition "An essential desktop reference book . . . it should definitely be on your bookshelf." —Technometrics A thoroughly updated book, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition features innovative approaches to understanding and working with models and theory of linear regression. The Third Edition provides readers with the necessary theoretical concepts, which are presented using intuitive ideas rather than complicated proofs, to describe the inference that is appropriate for the methods being discussed. The book presents a unique discussion that combines coverage of mathematical theory of linear models with analysis of variance models, providing readers with a comprehensive understanding of both the theoretical and technical aspects of linear models. With a new focus on fixed effects models, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition also features: Newly added topics including least squares, the cell means model, and graphical inspection of data in the AVE method Frequent conceptual and numerical examples for clarifying the statistical analyses and demonstrating potential pitfalls Graphics and computations developed using JMP® software to accompany the concepts and techniques presented Numerous exercises presented to test readers and deepen their understanding of the material An ideal book for courses on linear models and linear regression at the undergraduate and graduate levels, the Third Edition of Methods and Applications of Linear Models: Regression and the Analysis of Variance is also a valuable reference for applied statisticians and researchers who utilize linear model methodology.

Linear Regression Analysis

Author: George A. F. Seber,Alan J. Lee

Publisher: John Wiley & Sons

ISBN: 1118274423

Category: Mathematics

Page: 582

View: 9618

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Concise, mathematically clear, and comprehensive treatment of thesubject. * Expanded coverage of diagnostics and methods of modelfitting. * Requires no specialized knowledge beyond a good grasp of matrixalgebra and some acquaintance with straight-line regression andsimple analysis of variance models. * More than 200 problems throughout the book plus outline solutionsfor the exercises. * This revision has been extensively class-tested.

Linear Models

The Theory and Application of Analysis of Variance

Author: Brenton R. Clarke

Publisher: John Wiley & Sons

ISBN: 9780470377970

Category: Mathematics

Page: 288

View: 9059

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An insightful approach to the analysis of variance in the study of linear models Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. The author begins with a presentation of the classic fixed-effects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of least-squares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical two-way and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include: Vector space theory The theory of least squares estimation Gauss-Markov theorem Kronecker products Diagnostic and robust methods for linear models Likelihood approaches to estimation A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.