Foundations of Linear and Generalized Linear Models

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 1118730038

Category: Mathematics

Page: 472

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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"--

Statistical Tests for Mixed Linear Models

Author: André I. Khuri,Thomas Mathew,Bimal K. Sinha

Publisher: John Wiley & Sons

ISBN: 1118164857

Category: Mathematics

Page: 384

View: 7187

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An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models at an advanced level. Statistical Tests for Mixed Linear Models: Combines analysis and testing in one self-contained volume. Describes analysis of variance (ANOVA) procedures in balanced and unbalanced data situations. Examines methods for determining the effect of imbalance on data analysis. Explains exact and optimum tests and methods for their derivation. Summarizes test procedures for multivariate mixed and random models. Enables novice readers to skip the derivations and discussions on optimum tests. Offers plentiful examples and exercises, many of which are numerical in flavor. Provides solutions to selected exercises. Statistical Tests for Mixed Linear Models is an accessible reference for researchers in analysis of variance, experimental design, variance component analysis, and linear mixed models. It is also an important text for graduate students interested in mixed models.

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: 8228

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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.

Linear models in statistics

Author: Alvin C. Rencher

Publisher: Wiley-Interscience

ISBN: 9780471315643

Category: Mathematics

Page: 578

View: 6355

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

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: 544

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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.

Linear Statistical Models

Author: James H. Stapleton

Publisher: John Wiley & Sons

ISBN: 0470317760

Category: Mathematics

Page: 472

View: 2959

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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.

Applied Regression Analysis

Author: Norman R. Draper,Harry Smith

Publisher: John Wiley & Sons

ISBN: 1118625684

Category: Mathematics

Page: 736

View: 8252

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An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concepts and applications, offers a complete, easily accessible introduction to the fundamentals of regression analysis. Assuming only a basic knowledge of elementary statistics, Applied Regression Analysis, Third Edition focuses on the fitting and checking of both linear and nonlinear regression models, using small and large data sets, with pocket calculators or computers. This Third Edition features separate chapters on multicollinearity, generalized linear models, mixture ingredients, geometry of regression, robust regression, and resampling procedures. Extensive support materials include sets of carefully designed exercises with full or partial solutions and a series of true/false questions with answers. All data sets used in both the text and the exercises can be found on the companion disk at the back of the book. For analysts, researchers, and students in university, industrial, and government courses on regression, this text is an excellent introduction to the subject and an efficient means of learning how to use a valuable analytical tool. It will also prove an invaluable reference resource for applied scientists and statisticians.

Applied Linear Regression

Author: Sanford Weisberg

Publisher: John Wiley & Sons

ISBN: 1118594851

Category: Mathematics

Page: 384

View: 7381

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Praise for the Third Edition "...this is an excellent book which could easily be used as a course text..." —International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, 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 squares regression. While maintaining the accessible appeal of each previous edition,Applied Linear Regression, Fourth Edition 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 and complex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, and variance assumptions Updated methodology, such as bootstrapping, cross-validation binomial and Poisson regression, and modern model selection methods Applied Linear Regression, Fourth Edition is an excellent textbook for upper-undergraduate and graduate-level students, as well as an appropriate reference guide for practitioners and applied statisticians in engineering, business administration, economics, and the social sciences.

Categorical Data Analysis

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 1118710940

Category: Mathematics

Page: 744

View: 2784

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Praise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis." —Statistics in Medicine "It is a total delight reading this book." —Pharmaceutical Research "If you do any analysis of categorical data, this is an essential desktop reference." —Technometrics The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis. Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features: An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections introducing the Bayesian approach for methods in that chapter More than 100 analyses of data sets and over 600 exercises Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.

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: 2863

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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: 2933

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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.

Models for Probability and Statistical Inference

Theory and Applications

Author: James H. Stapleton

Publisher: John Wiley & Sons

ISBN: 9780470183403

Category: Mathematics

Page: 512

View: 882

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This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.

Robust Statistics

Theory and Methods (with R)

Author: Ricardo A. Maronna,R. Douglas Martin,Victor J. Yohai,Matías Salibián-Barrera

Publisher: John Wiley & Sons

ISBN: 1119214661

Category: Mathematics

Page: 464

View: 8048

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A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Sensitivity Analysis in Linear Regression

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470317426

Category: Mathematics

Page: 315

View: 6605

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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.

Regression Analysis by Example

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470055456

Category: Mathematics

Page: 416

View: 5473

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The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Mixed Models

Theory and Applications with R

Author: Eugene Demidenko

Publisher: John Wiley & Sons

ISBN: 1118091574

Category: Mathematics

Page: 717

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Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. The new edition includes significant updating, over 300 exercises, stimulating chapter projects and model simulations, inclusion of R subroutines, and a revised text format. The target audience continues to be graduate students and researchers. An author-maintained web site is available with solutions to exercises and a compendium of relevant data sets.

Bayesian Modeling Using WinBUGS

Author: Ioannis Ntzoufras

Publisher: John Wiley & Sons

ISBN: 1118210352

Category: Mathematics

Page: 520

View: 4744

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A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all data sets and code are available on the book's related Web site. Requiring only a working knowledge of probability theory and statistics, Bayesian Modeling Using WinBUGS serves as an excellent book for courses on Bayesian statistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of statistics, actuarial science, medicine, and the social sciences who use WinBUGS in their everyday work.