plane answers to complex questions the theory of linear models springer texts in statistics

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Plane Answers To Complex Questions

Author : Ronald Christensen
ISBN : 9781475724776
Genre : Mathematics
File Size : 25. 54 MB
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The second edition of Plane Answers has many additions and a couple of deletions. New material includes additional illustrative examples in Ap pendices A and B and Chapters 2 and 3, as well as discussions of Bayesian estimation, near replicate lack of fit tests, testing the independence assump tion, testing variance components, the interblock analysis for balanced in complete block designs, nonestimable constraints, analysis of unreplicated experiments using normal plots, tensors, and properties of Kronecker prod ucts and Vee operators. The book contains an improved discussion of the relation between ANOVA and regression, and an improved presentation of general Gauss-Markov models. The primary material that has been deleted are the discussions of weighted means and of log-linear models. The mate rial on log-linear models was included in Christensen (1990b), so it became redundant here. Generally, I have tried to clean up the presentation of ideas wherever it seemed obscure to me. Much of the work on the second edition was done while on sabbatical at the University of Canterbury in Christchurch, New Zealand. I would par ticularly like to thank John Deely for arranging my sabbatical. Through their comments and criticisms, four people were particularly helpful in con structing this new edition. I would like to thank Wes Johnson, Snehalata Huzurbazar, Ron Butler, and Vance Berger.

Plane Answers To Complex Questions

Author : Ronald Christensen
ISBN : 9781441998163
Genre : Mathematics
File Size : 23. 54 MB
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This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill’s generalization of Tukey’s one degree of freedom for nonadditivity test.

Plane Answers To Complex Questions

Author : Ronald Christensen
ISBN : 0387953612
Genre : Mathematics
File Size : 37. 15 MB
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This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes discussion of identifiability and its relationship to estimability, different approaches to the theories of testing parametric hypotheses and analysis of covariance, additional discussion of the geometry of least squares estimation and testing, new discussion of models for experiments with factorial treatment structures, and a new appendix on possible causes for getting test statistics that are so small as to be suspicious. Ronald Christensen is a Professor of Statistics at the University of New Mexico. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.

Advanced Linear Modeling

Author : Ronald Christensen
ISBN : 0387952969
Genre : Mathematics
File Size : 45. 34 MB
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This book introduces several topics related to linear model theory: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. The second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subject and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure. He is the author of numerous technical articles and several books and he is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. Also Available: Christensen, Ronald. Plane Answers to Complex Questions: The Theory of Linear Models, Second Edition (1996). New York: Springer-Verlag New York, Inc. Christensen, Ronald. Log-Linear Models and Logistic Regression, Second Edition (1997). New York: Springer-Verlag New York, Inc.

A Primer On Linear Models

Author : John F. Monahan
ISBN : 1420062042
Genre : Mathematics
File Size : 72. 99 MB
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A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Linear Models For Multivariate Time Series And Spatial Data

Author : Ronald Christensen
ISBN : 9781475741032
Genre : Mathematics
File Size : 27. 64 MB
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This is a self-contained companion volume to the authors book "Plane Answers to Complex Questions: The Theory of Linear Models". It provides introductions to several topics related to linear model theory: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis (geostatistics). The purpose of this volume is to use the three fundamental ideas of best linear prediction, projections, and Mahalanobis' distance to exploit their properties in examining multivariate, time series and spatial data. Ronald Christensen is Professor of Statistics at the University of New Mexico, and is recognised internationally as an expert in the theory and application of linear models.

Log Linear Models

Author : Ronald Christensen
ISBN : 9781475741117
Genre : Mathematics
File Size : 84. 1 MB
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This book examines log-linear models for contingency tables. Logistic re gression and logistic discrimination are treated as special cases and gener alized linear models (in the GLIM sense) are also discussed. The book is designed to fill a niche between basic introductory books such as Fienberg (1980) and Everitt (1977) and advanced books such as Bishop, Fienberg, and Holland (1975), Haberman (1974), and Santner and Duffy (1989). lt is primarily directed at advanced Masters degree students in Statistics but it can be used at both higher and lower levels. The primary theme of the book is using previous knowledge of analysis of variance and regression to motivate and explicate the use of log-linear models. Of course, both the analogies and the distinctions between the different methods must be kept in mind. The book is written at several levels. A basic introductory course would take material from Chapters I, II (deemphasizing Section II. 4), III, Sec tions IV. 1 through IV. 5 (eliminating the material on graphical models), Section IV. lü, Chapter VII, and Chapter IX. The advanced modeling ma terial at the end of Sections VII. 1, VII. 2, and possibly the material in Section IX. 2 should be deleted in a basic introductory course. For Mas ters degree students in Statistics, all the material in Chapters I through V, VII, IX, and X should be accessible. For an applied Ph. D.

Methods And Applications Of Linear Models

Author : Ronald R. Hocking
ISBN : 9781118593028
Genre : Mathematics
File Size : 65. 79 MB
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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.

Theory Of Linear Models

Author : Bent Jorgensen
ISBN : 0412042614
Genre : Mathematics
File Size : 29. 61 MB
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This book provides a self-contained exposition of the theory of linear models, including practical aspects of residuals and data analysis.

An Introduction To Statistical Learning

Author : Gareth James
ISBN : 9781461471387
Genre : Mathematics
File Size : 28. 84 MB
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An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

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