Foundations of Linear and Generalized Linear Models

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 1118730038

Category: Mathematics

Page: 444

View: 2422

DOWNLOAD NOW »
"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"--

Generalized Linear Mixed Models

Author: Charles E. McCulloch

Publisher: IMS

ISBN: 9780940600546

Category: Mathematics

Page: 84

View: 681

DOWNLOAD NOW »
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

Linear models in statistics

Author: Alvin C. Rencher

Publisher: Wiley-Interscience

ISBN: 9780471315643

Category: Mathematics

Page: 578

View: 6786

DOWNLOAD NOW »
* Graphs, charts, and tables as well as extensive references

Linear Models

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

Publisher: John Wiley & Sons

ISBN: 1118952855

Category: Mathematics

Page: 696

View: 3444

DOWNLOAD NOW »
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.

Introduction to Linear Regression Analysis

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

Publisher: John Wiley & Sons

ISBN: 1119180171

Category: Mathematics

Page: 672

View: 3601

DOWNLOAD NOW »
Praise for the Fourth Edition "As with previous editions, the authors have produced a leadingtextbook on regression." —Journal of the American Statistical Association A comprehensive and up-to-date introduction to thefundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Editioncontinues to present both the conventional and less common uses oflinear regression in today’s cutting-edge scientificresearch. The authors blend both theory and application to equipreaders with an understanding of the basic principles needed toapply regression model-building techniques in various fields ofstudy, including engineering, management, and the healthsciences. Following a general introduction to regression modeling,including typical applications, a host of technical tools areoutlined such as basic inference procedures, introductory aspectsof model adequacy checking, and polynomial regression models andtheir variations. The book then discusses how transformations andweighted least squares can be used to resolve problems of modelinadequacy and also how to deal with influential observations. TheFifth Edition features numerous newly added topics,including: A chapter on regression analysis of time series data thatpresents the Durbin-Watson test and other techniques for detectingautocorrelation as well as parameter estimation in time seriesregression models Regression models with random effects in addition to adiscussion on subsampling and the importance of the mixedmodel Tests on individual regression coefficients and subsets ofcoefficients Examples of current uses of simple linear regression models andthe use of multiple regression models for understanding patientsatisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors haveincorporated JMP and the freely available R software to illustratethe discussed techniques and procedures in this new edition.Numerous exercises have been added throughout, allowing readers totest their understanding of the material. Introduction to Linear Regression Analysis, Fifth Editionis an excellent book for statistics and engineering courses onregression at the upper-undergraduate and graduate levels. The bookalso serves as a valuable, robust resource for professionals in thefields of engineering, life and biological sciences, and the socialsciences.

Applied Linear Regression

Author: Sanford Weisberg

Publisher: John Wiley & Sons

ISBN: 1118594851

Category: Mathematics

Page: 368

View: 3815

DOWNLOAD NOW »
Praise for the Third Edition "...this is an excellent book which could easily be used as acourse text..." —International Statistical Institute The Fourth Edition of Applied LinearRegression provides a thorough update of the basic theoryand methodology of linear regression modeling. Demonstrating thepractical applications of linear regression analysis techniques,the Fourth Edition uses interesting, real-worldexercises and examples. Stressing central concepts such as model building, understandingparameters, assessing fit and reliability, and drawing conclusions,the new edition illustrates how to develop estimation, confidence,and testing procedures primarily through the use of least squaresregression. While maintaining the accessible appeal of eachprevious edition,Applied Linear Regression, FourthEdition features: Graphical methods stressed in the initial exploratory phase,analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple andcomplex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, andvariance assumptions Updated methodology, such as bootstrapping, cross-validationbinomial and Poisson regression, and modern model selectionmethods Applied Linear Regression, Fourth Edition is anexcellent textbook for upper-undergraduate and graduate-levelstudents, as well as an appropriate reference guide forpractitioners and applied statisticians in engineering, businessadministration, economics, and the social sciences.

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: 3489

DOWNLOAD NOW »
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.

Sensitivity Analysis in Linear Regression

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470317426

Category: Mathematics

Page: 315

View: 636

DOWNLOAD NOW »
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

an introduction

Author: Irwin Guttman

Publisher: Krieger Pub Co

ISBN: N.A

Category: Mathematics

Page: 358

View: 5073

DOWNLOAD NOW »

Linear Statistical Models

Author: James H. Stapleton

Publisher: John Wiley & Sons

ISBN: 0470317760

Category: Mathematics

Page: 472

View: 7401

DOWNLOAD NOW »
Linear Statistical Models Developed and refined over a period of twenty years, the material in this book offers an especially lucid presentation of linear statistical models. These models lead to what is usually called "multiple regression" or "analysis of variance" methodology, which, in turn, opens up a wide range of applications to the physical, biological, and social sciences, as well as to business, agriculture, and engineering. Unlike similar books on this topic, Linear Statistical Models emphasizes the geometry of vector spaces because of the intuitive insights this approach brings to an understanding of the theory. While the focus is on theory, examples of applications, using the SAS and S-Plus packages, are included. Prerequisites include some familiarity with linear algebra, and probability and statistics at the postcalculus level. Major topics covered include: * Methods of study of random vectors, including the multivariate normal, chi-square, t and F distributions, central and noncentral * The linear model and the basic theory of regression analysis and the analysis of variance * Multiple regression methods, including transformations, analysis of residuals, and asymptotic theory for regression analysis. Separate sections are devoted to robust methods and to the bootstrap. * Simultaneous confidence intervals: Bonferroni, Scheffe, Tukey, and Bechhofer * Analysis of variance, with two- and three-way analysis of variance * Random component models, nested designs, and balanced incomplete block designs * Analysis of frequency data through log-linear models, with emphasis on vector space viewpoint. This chapter alone is sufficient for a course on the analysis of frequency data.

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: 2859

DOWNLOAD NOW »
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.

Generalized Linear Models

with Applications in Engineering and the Sciences

Author: Raymond H. Myers,Douglas C. Montgomery,G. Geoffrey Vining,Timothy J. Robinson

Publisher: John Wiley & Sons

ISBN: 0470556978

Category: Mathematics

Page: 544

View: 3531

DOWNLOAD NOW »
Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities." —Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences. This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of GLMs and providing an overview of the basic, related concepts such as multiple linear regression, nonlinear regression, least squares, and the maximum likelihood estimation procedure. Incorporating the latest developments, new features of this Second Edition include: A new chapter on random effects and designs for GLMs A thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersion A new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression models Expanded discussion of weighted least squares, including examples that illustrate how to estimate the weights Illustrations of R code to perform GLM analysis The authors demonstrate the diverse applications of GLMs through numerous examples, from classical applications in the fields of biology and biopharmaceuticals to more modern examples related to engineering and quality assurance. The Second Edition has been designed to demonstrate the growing computational nature of GLMs, as SAS®, Minitab®, JMP®, and R software packages are used throughout the book to demonstrate fitting and analysis of generalized linear models, perform inference, and conduct diagnostic checking. Numerous figures and screen shots illustrating computer output are provided, and a related FTP site houses supplementary material, including computer commands and additional data sets. Generalized Linear Models, Second Edition is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate level. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work.

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: 4033

DOWNLOAD NOW »
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.

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: 9681

DOWNLOAD NOW »
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.

Applied Mixed Models in Medicine

Author: Helen Brown,Robin Prescott

Publisher: John Wiley & Sons

ISBN: 1118778243

Category: Medical

Page: 536

View: 3857

DOWNLOAD NOW »
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 Regression Analysis

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

Publisher: John Wiley & Sons

ISBN: 1118274423

Category: Mathematics

Page: 582

View: 1299

DOWNLOAD NOW »
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 and Time-Series Analysis

Regression, ANOVA, ARMA and GARCH

Author: Marc S. Paolella

Publisher: Wiley

ISBN: 1119431905

Category: Mathematics

Page: 896

View: 8838

DOWNLOAD NOW »
A comprehensive and timely edition on an emerging new trend in time series Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author's previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation. The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedicated to it. With respect to the subject/technology, many chapters in Linear Models and Time-Series Analysis cover firmly entrenched topics (regression and ARMA). Several others are dedicated to very modern methods, as used in empirical finance, asset pricing, risk management, and portfolio optimization, in order to address the severe change in performance of many pension funds, and changes in how fund managers work. Covers traditional time series analysis with new guidelines Provides access to cutting edge topics that are at the forefront of financial econometrics and industry Includes latest developments and topics such as financial returns data, notably also in a multivariate context Written by a leading expert in time series analysis Extensively classroom tested Includes a tutorial on SAS Supplemented with a companion website containing numerous Matlab programs Solutions to most exercises are provided in the book Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH is suitable for advanced masters students in statistics and quantitative finance, as well as doctoral students in economics and finance. It is also useful for quantitative financial practitioners in large financial institutions and smaller finance outlets.