Analysis of Variance Design and Regression

Author: Ronald Christensen
Publisher: CRC Press
ISBN: 1498730191
Format: PDF, ePub, Docs

Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition presents linear structures for modeling data with an emphasis on how to incorporate specific ideas (hypotheses) about the structure of the data into a linear model for the data. The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data. New to the Second Edition Reorganized to focus on unbalanced data Reworked balanced analyses using methods for unbalanced data Introductions to nonparametric and lasso regression Introductions to general additive and generalized additive models Examination of homologous factors Unbalanced split plot analyses Extensions to generalized linear models R, Minitab®, and SAS code on the author’s website The text can be used in a variety of courses, including a yearlong graduate course on regression and ANOVA or a data analysis course for upper-division statistics students and graduate students from other fields. It places a strong emphasis on interpreting the range of computer output encountered when dealing with unbalanced data.

Analysis of Variance Design and Regression

Author: Ronald Christensen
Publisher: CRC Press
ISBN: 9780412062919
Format: PDF, Kindle

This text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful.

Modern Data Science with R

Author: Benjamin S. Baumer
Publisher: CRC Press
ISBN: 1498724493
Format: PDF, ePub

Modern Data Science with R is a comprehensive data science textbook for undergraduates that incorporates statistical and computational thinking to solve real-world problems with data. Rather than focus exclusively on case studies or programming syntax, this book illustrates how statistical programming in the state-of-the-art R/RStudio computing environment can be leveraged to extract meaningful information from a variety of data in the service of addressing compelling statistical questions. Contemporary data science requires a tight integration of knowledge from statistics, computer science, mathematics, and a domain of application. This book will help readers with some background in statistics and modest prior experience with coding develop and practice the appropriate skills to tackle complex data science projects. The book features a number of exercises and has a flexible organization conducive to teaching a variety of semester courses.

Discrete Data Analysis with R

Author: Michael Friendly
Publisher: CRC Press
ISBN: 1498725856
Format: PDF, Kindle

An Applied Treatment of Modern Graphical Methods for Analyzing Categorical Data Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data presents an applied treatment of modern methods for the analysis of categorical data, both discrete response data and frequency data. It explains how to use graphical methods for exploring data, spotting unusual features, visualizing fitted models, and presenting results. The book is designed for advanced undergraduate and graduate students in the social and health sciences, epidemiology, economics, business, statistics, and biostatistics as well as researchers, methodologists, and consultants who can use the methods with their own data and analyses. Along with describing the necessary statistical theory, the authors illustrate the practical application of the techniques to a large number of substantive problems, including how to organize data, conduct an analysis, produce informative graphs, and evaluate what the graphs reveal about the data. The first part of the book contains introductory material on graphical methods for discrete data, basic R skills, and methods for fitting and visualizing one-way discrete distributions. The second part focuses on simple, traditional nonparametric tests and exploratory methods for visualizing patterns of association in two-way and larger frequency tables. The final part of the text discusses model-based methods for the analysis of discrete data. Web Resource The data sets and R software used, including the authors’ own vcd and vcdExtra packages, are available at http://cran.r-project.org.

Modeling and Analysis of Stochastic Systems Third Edition

Publisher: CRC Press
ISBN: 149875662X
Format: PDF

Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.

Linear Models and the Relevant Distributions and Matrix Algebra

Author: David A. Harville
Publisher: CRC Press
ISBN: 1351264672
Format: PDF, Docs

Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance. Features: Provides coverage of matrix algebra that is extensive and relatively self-contained and does so in a meaningful context Provides thorough coverage of the relevant statistical distributions, including spherically and elliptically symmetric distributions Includes extensive coverage of multiple-comparison procedures (and of simultaneous confidence intervals), including procedures for controlling the k-FWER and the FDR Provides thorough coverage (complete with detailed and highly accessible proofs) of results on the properties of various linear-model procedures, including those of least squares estimators and those of the F test. Features the use of real data sets for illustrative purposes Includes many exercises David Harville served for 10 years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson AFB, Ohio, 20 years as a full professor in Iowa State University’s Department of Statistics where he now has emeritus status, and seven years as a research staff member of the Mathematical Sciences Department of IBM’s T.J. Watson Research Center. He has considerable relevant experience, having taught M.S. and Ph.D. level courses in linear models, been the thesis advisor of 10 Ph.D. graduates, and authored or co-authored two books and more than 80 research articles. His work has been recognized through his election as a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and as a member of the International Statistical Institute.

Linear Model Methodology

Author: Andre I. Khuri
Publisher: CRC Press
ISBN: 9781420010442
Format: PDF, ePub, Docs

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.

Fitting Linear Models

Author: A. McIntosh
Publisher: Springer Science & Business Media
ISBN: 1461257522
Format: PDF, ePub, Mobi

The increasing power and decreasing price of smalI computers, especialIy "personal" computers, has made them increasingly popular in statistical analysis. The day may not be too far off when every statistician has on his or her desktop computing power on a par with the large mainframe computers of 15 or 20 years ago. These same factors make it relatively easy to acquire and manipulate large quantities of data, and statisticians can expect a corresponding increase in the size of the datasets that they must analyze. Unfortunately, because of constraints imposed by architecture, size or price, these smalI computers do not possess the main memory of their large cousins. Thus, there is a growing need for algorithms that are sufficiently economical of space to permit statistical analysis on smalI computers. One area of analysis where there is a need for algorithms that are economical of space is in the fitting of linear models.

Statistical Design and Analysis of Experiments

Author: Robert L. Mason
Publisher: Wiley-Interscience
ISBN: 9780471372165
Format: PDF, ePub, Mobi

Emphasizes the strategy of experimentation, data analysis, and the interpretation of experimental results. Features numerous examples using actual engineering and scientific studies. Presents statistics as an integral component of experimentation from the planning stage to the presentation of the conclusions. Deep and concentrated experimental design coverage, with equivalent but separate emphasis on the analysis of data from the various designs. Topics can be implemented by practitioners and do not require a high level of training in statistics. New edition includes new and updated material and computer output.