Linear Models

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Author: William R. Moser
Publisher: Elsevier
ISBN: 9780080510293
Size: 24.38 MB
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Linear Models by William R. Moser

Original Title: Linear Models

Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory. Provides a versatile format for investigating linear model theory, using the mean model Uses examples that are familiar to the student: Design of experiments, analysis of variance, regression, and normal distribution theory Includes a review of relevant linear algebra concepts Contains fully worked examples which follow the theorem/proof presentation

Generalized Linear Models Second Edition

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Author: P. McCullagh
Publisher: CRC Press
ISBN: 9780412317606
Size: 74.68 MB
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Generalized Linear Models Second Edition by P. McCullagh

Original Title: Generalized Linear Models Second Edition

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables. The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions. Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

A First Course In Linear Model Theory

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Author: Nalini Ravishanker
Publisher: CRC Press
ISBN: 9781584882473
Size: 42.85 MB
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A First Course In Linear Model Theory by Nalini Ravishanker

Original Title: A First Course In Linear Model Theory

This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

Linear Models With R Second Edition

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Author: Julian J. Faraway
Publisher: CRC Press
ISBN: 1439887330
Size: 23.96 MB
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Linear Models With R Second Edition by Julian J. Faraway

Original Title: Linear Models With R Second Edition

A Hands-On Way to Learning Data Analysis Part 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 in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Linear Models

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Author: Debasis Sengupta
Publisher: World Scientific
ISBN: 9789812564900
Size: 39.34 MB
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Linear Models by Debasis Sengupta

Original Title: Linear Models

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.

Linear Model Methodology

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Author: Andre I. Khuri
Publisher: CRC Press
ISBN: 9781420010442
Size: 30.30 MB
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Linear Model Methodology by Andre I. Khuri

Original Title: Linear Model Methodology

Given the importance of linear models in statistical theory and experimental research, a good understanding of their fundamental principles and theory is essential. Supported by a large number of examples, Linear Model Methodology provides a strong foundation in the theory of linear models and explores the latest developments in data analysis. After presenting the historical evolution of certain methods and techniques used in linear models, the book reviews vector spaces and linear transformations and discusses the basic concepts and results of matrix algebra that are relevant to the study of linear models. Although mainly focused on classical linear models, the next several chapters also explore recent techniques for solving well-known problems that pertain to the distribution and independence of quadratic forms, the analysis of estimable linear functions and contrasts, and the general treatment of balanced random and mixed-effects models. The author then covers more contemporary topics in linear models, including the adequacy of Satterthwaite’s approximation, unbalanced fixed- and mixed-effects models, heteroscedastic linear models, response surface models with random effects, and linear multiresponse models. The final chapter introduces generalized linear models, which represent an extension of classical linear models. Linear models provide the groundwork for analysis of variance, regression analysis, response surface methodology, variance components analysis, and more, making it necessary to understand the theory behind linear modeling. Reflecting advances made in the last thirty years, this book offers a rigorous development of the theory underlying linear models.

Linear Algebra And Linear Models

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Author: Ravindra B. Bapat
Publisher: Springer Science & Business Media
ISBN: 1447127382
Size: 52.14 MB
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Linear Algebra And Linear Models by Ravindra B. Bapat

Original Title: Linear Algebra And Linear Models

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include: coverage of topics such as rank additivity, inequalities for eigenvalues and singular values; a new chapter on linear mixed models; over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices. This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.

Advanced Log Linear Models Using Sas

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Author: Daniel Zelterman
Publisher: SAS Institute
ISBN: 9781590470800
Size: 24.17 MB
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Advanced Log Linear Models Using Sas by Daniel Zelterman

Original Title: Advanced Log Linear Models Using Sas

Daniel Zelterman applies his extensive SAS knowledge and biostatistics experience to illustrate how to use the GENMOD procedure to analyze log-linear models for categorical data. The discussion of each model and method emphasizes statistical aspects, such as interpretation of results, rather than programming skills. Statisticians who have a basic understanding both of SAS and of the analysis of categorical data will greatly benefit from this book.

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