Linear Models

Author : Alvin C. Rencher,G. Bruce Schaalje
Publisher : John Wiley & Sons
Page : 690 pages
File Size : 52,9 Mb
Release : 2008-01-07
Category : Mathematics
ISBN : 9780470192603

Get Book

Linear Models in Statistics by Alvin C. Rencher,G. Bruce Schaalje Pdf

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.

Author : Paul Roback,Julie Legler
Publisher : CRC Press
Page : 436 pages
File Size : 46,7 Mb
Release : 2021-01-14
Category : Mathematics
ISBN : 9781439885406

Get Book

Beyond Multiple Linear Regression by Paul Roback,Julie Legler Pdf

Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR)

Author : Shayle R. Searle
Publisher : John Wiley & Sons
Page : 565 pages
File Size : 54,9 Mb
Release : 1997-03-28
Category : Mathematics
ISBN : 9780471184997

Get Book

Linear Models by Shayle R. Searle Pdf

This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

Author : P. McCullagh
Publisher : Routledge
Page : 361 pages
File Size : 44,5 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351445849

Get Book

Generalized Linear Models by P. McCullagh Pdf

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 ot

Author : Peter K. Dunn,Gordon K. Smyth
Publisher : Springer
Page : 562 pages
File Size : 54,8 Mb
Release : 2018-11-10
Category : Mathematics
ISBN : 9781441901187

Get Book

Generalized Linear Models With Examples in R by Peter K. Dunn,Gordon K. Smyth Pdf

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

Author : Anthony S. Bryk,Dr Stephen W Raudenbush
Publisher : SAGE Publications, Incorporated
Page : 296 pages
File Size : 49,6 Mb
Release : 1992
Category : Social Science
ISBN : STANFORD:36105006022078

Get Book

Hierarchical Linear Models by Anthony S. Bryk,Dr Stephen W Raudenbush Pdf

Hierarchical Linear Models launches a new Sage series, Advanced Quantitative Techniques in the Social Sciences. This introductory text explicates the theory and use of hierarchical linear models (HLM) through rich, illustrative examples and lucid explanations. The presentation remains reasonably nontechnical by focusing on three general research purposes - improved estimation of effects within an individual unit, estimating and testing hypotheses about cross-level effects, and partitioning of variance and covariance components among levels. This innovative volume describes use of both two and three level models in organizational research, studies of individual development and meta-analysis applications, and concludes with a formal derivation of the statistical methods used in the book.

Author : Julian J. Faraway
Publisher : CRC Press
Page : 284 pages
File Size : 50,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439887349

Get Book

Linear Models with R by Julian J. Faraway Pdf

A Hands-On Way to Learning Data AnalysisPart 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

Author : Ronald R. Hocking
Publisher : Thomson Brooks/Cole
Page : 414 pages
File Size : 53,9 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015015719936

Get Book

The Analysis of Linear Models by Ronald R. Hocking Pdf

Author : Dale L. Zimmerman
Publisher : Springer Nature
Page : 504 pages
File Size : 41,9 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9783030520632

Get Book

Linear Model Theory by Dale L. Zimmerman Pdf

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.

Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 47,5 Mb
Release : 2008-01-18
Category : Mathematics
ISBN : 9780387226019

Get Book

Linear Algebra and Linear Models by Ravindra B. Bapat Pdf

This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.

Author : C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 53,7 Mb
Release : 2007-10-15
Category : Mathematics
ISBN : 9783540742272

Get Book

Linear Models and Generalizations by C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann Pdf

Revised and updated with the latest results, this Third Edition explores the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights of coverage include sensitivity analysis and model selection, an analysis of incomplete data, an analysis of categorical data based on a unified presentation of generalized linear models, and an extensive appendix on matrix theory.

Author : Alan Agresti
Publisher : John Wiley & Sons
Page : 471 pages
File Size : 53,6 Mb
Release : 2015-02-23
Category : Mathematics
ISBN : 9781118730034

Get Book

Foundations of Linear and Generalized Linear Models by Alan Agresti Pdf

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.

Author : Richard B. Darlington,Andrew F. Hayes
Publisher : Guilford Publications
Page : 689 pages
File Size : 43,9 Mb
Release : 2016-08-22
Category : Social Science
ISBN : 9781462527984

Get Book

Regression Analysis and Linear Models by Richard B. Darlington,Andrew F. Hayes Pdf

Emphasizing conceptual understanding over mathematics, this user-friendly text introduces linear regression analysis to students and researchers across the social, behavioral, consumer, and health sciences. Coverage includes model construction and estimation, quantification and measurement of multivariate and partial associations, statistical control, group comparisons, moderation analysis, mediation and path analysis, and regression diagnostics, among other important topics. Engaging worked-through examples demonstrate each technique, accompanied by helpful advice and cautions. The use of SPSS, SAS, and STATA is emphasized, with an appendix on regression analysis using R. The companion website (www.afhayes.com) provides datasets for the book's examples as well as the RLM macro for SPSS and SAS. Pedagogical Features: *Chapters include SPSS, SAS, or STATA code pertinent to the analyses described, with each distinctively formatted for easy identification. *An appendix documents the RLM macro, which facilitates computations for estimating and probing interactions, dominance analysis, heteroscedasticity-consistent standard errors, and linear spline regression, among other analyses. *Students are guided to practice what they learn in each chapter using datasets provided online. *Addresses topics not usually covered, such as ways to measure a variable’s importance, coding systems for representing categorical variables, causation, and myths about testing interaction.

Author : Jonathon D. Brown
Publisher : Springer
Page : 536 pages
File Size : 47,5 Mb
Release : 2015-01-21
Category : Social Science
ISBN : 9783319117348

Get Book

Linear Models in Matrix Form by Jonathon D. Brown Pdf

This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.

Author : James K. Lindsey
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 55,5 Mb
Release : 2008-01-15
Category : Mathematics
ISBN : 9780387227306

Get Book

Applying Generalized Linear Models by James K. Lindsey Pdf

This book describes how generalised linear modelling procedures can be used in many different fields, without becoming entangled in problems of statistical inference. The author shows the unity of many of the commonly used models and provides readers with a taste of many different areas, such as survival models, time series, and spatial analysis, and of their unity. As such, this book will appeal to applied statisticians and to scientists having a basic grounding in modern statistics. With many exercises at the end of each chapter, it will equally constitute an excellent text for teaching applied statistics students and non- statistics majors. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, being familiar at least with the analysis of the simpler normal linear models, regression and ANOVA.