Linear Models
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Linear Models In Statistics
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Author : Alvin C. Rencher
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-07
Linear Models In Statistics written by Alvin C. Rencher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-07 with Mathematics categories.
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.
Generalized Linear Models With Examples In R
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Author : Peter K. Dunn
language : en
Publisher: Springer
Release Date : 2018-11-10
Generalized Linear Models With Examples In R written by Peter K. Dunn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-10 with Mathematics categories.
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
Partially Linear Models
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Author : Wolfgang Härdle
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-09-14
Partially Linear Models written by Wolfgang Härdle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-14 with Business & Economics categories.
In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Linear Models And Generalizations
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Author : C. Radhakrishna Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-15
Linear Models And Generalizations written by C. Radhakrishna Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-15 with Mathematics categories.
Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.
Generalized Linear Models Second Edition
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Author : P. McCullagh
language : en
Publisher: CRC Press
Release Date : 1989-08-01
Generalized Linear Models Second Edition written by P. McCullagh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-01 with Mathematics categories.
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.
Foundations Of Linear And Generalized Linear Models
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Author : Alan Agresti
language : en
Publisher: John Wiley & Sons
Release Date : 2015-02-23
Foundations Of Linear And Generalized Linear Models written by Alan Agresti and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-23 with Mathematics categories.
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.
Applying Generalized Linear Models
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Author : James K. Lindsey
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-15
Applying Generalized Linear Models written by James K. Lindsey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-15 with Mathematics categories.
Applying Generalized Linear Models describes how generalized linear modelling procedures can be used for statistical modelling in many different fields, without becoming lost in problems of statistical inference. Many students, even in relatively advanced statistics courses, do not have an overview whereby they can see that the three areas - linear normal, categorical, and survival models - have much in common. The author shows the unity of many of the commonly used models and provides the reader with a taste of many different areas, such as survival models, time series, and spatial analysis. This book should appeal to applied statisticians and to scientists with a basic grounding in modern statistics. With the many exercises included at the ends of chapters, it will be an excellent text for teaching the fundamental uses of statistical modelling. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, and should be familiar at least with the analysis of the simpler normal linear models, regression and ANOVA. The author is professor in the biostatistics department at Limburgs University, Diepenbeek, in the social science department at the University of Liège, and in medical statistics at DeMontfort University, Leicester. He is the author of nine other books.
Visualizing Linear Models
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Author : W. D. Brinda
language : en
Publisher: Springer Nature
Release Date : 2021-02-24
Visualizing Linear Models written by W. D. Brinda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-24 with Mathematics categories.
This book provides a visual and intuitive coverage of the core theory of linear models. Designed to develop fluency with the underlying mathematics and to build a deep understanding of the principles, it's an excellent basis for a one-semester course on statistical theory and linear modeling for intermediate undergraduates or graduate students. Three chapters gradually develop the essentials of linear model theory. They are each preceded by a review chapter that covers a foundational prerequisite topic. This classroom-tested work explores two distinct and complementary types of visualization: the “observations picture” and the “variables picture.” To improve retention of material, this book is supplemented by a bank of ready-made practice exercises for students. These are available for digital or print use.
Linear Model Theory
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Author : Dale L. Zimmerman
language : en
Publisher: Springer Nature
Release Date : 2020-11-02
Linear Model Theory written by Dale L. Zimmerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Mathematics categories.
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.
Linear Models With Python
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Author : Julian J. Faraway
language : en
Publisher: CRC Press
Release Date : 2021-01-08
Linear Models With Python written by Julian J. Faraway and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-08 with Business & Economics categories.
Praise for Linear Models with R: This book is a must-have tool for anyone interested in understanding and applying linear models. The logical ordering of the chapters is well thought out and portrays Faraway’s wealth of experience in teaching and using linear models. ... It lays down the material in a logical and intricate manner and makes linear modeling appealing to researchers from virtually all fields of study. -Biometrical Journal Throughout, it gives plenty of insight ... with comments that even the seasoned practitioner will appreciate. Interspersed with R code and the output that it produces one can find many little gems of what I think is sound statistical advice, well epitomized with the examples chosen...I read it with delight and think that the same will be true with anyone who is engaged in the use or teaching of linear models. -Journal of the Royal Statistical Society Like its widely praised, best-selling companion version, Linear Models with R, this book replaces R with Python to seamlessly give a coherent exposition of the practice of linear modeling. Linear Models with Python 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 Python. Features: Python is a powerful, open source programming language increasingly being used in data science, machine learning and computer science. Python and R are similar, but R was designed for statistics, while Python is multi-talented. This version replaces R with Python to make it accessible to a greater number of users outside of statistics, including those from Machine Learning. A reader coming to this book from an ML background will learn new statistical perspectives on learning from data. Topics include Model Selection, Shrinkage, Experiments with Blocks and Missing Data. Includes an Appendix on Python for beginners. Linear Models with Python explains how to use linear models in physical science, engineering, social science and business applications. It is ideal as a textbook for linear models or linear regression courses.