Design of Experiments for Generalized Linear Models
Design of Experiments for Generalized Linear Models

Author: Kenneth G. Russell

Publisher: CRC Press

Published: 2018-12-14

Total Pages: 260

ISBN-13: 0429614411

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Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM, little information is available on how to collect the data that are to be analysed in this way. This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level, and without any information on computation. This book explains the motivation behind various techniques, reduces the difficulty of the mathematics, or moves it to one side if it cannot be avoided, and gives examples of how to write and run computer programs using R. Features The generalisation of the linear model to GLMs Background mathematics, and the use of constrained optimisation in R Coverage of the theory behind the optimality of a design Individual chapters on designs for data that have Binomial or Poisson distributions Bayesian experimental design An online resource contains R programs used in the book This book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra, and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided.

Bayesian Estimation and Experimental Design in Linear Regression Models
Bayesian Estimation and Experimental Design in Linear Regression Models

Author: Jürgen Pilz

Publisher:

Published: 1991-07-09

Total Pages: 316

ISBN-13:

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Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.

Design of Experiments for Generalized Linear Models
Design of Experiments for Generalized Linear Models

Author: Kenneth G. Russell

Publisher: CRC Press

Published: 2018-12-14

Total Pages: 241

ISBN-13: 0429615620

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Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM, little information is available on how to collect the data that are to be analysed in this way. This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level, and without any information on computation. This book explains the motivation behind various techniques, reduces the difficulty of the mathematics, or moves it to one side if it cannot be avoided, and gives examples of how to write and run computer programs using R. Features The generalisation of the linear model to GLMs Background mathematics, and the use of constrained optimisation in R Coverage of the theory behind the optimality of a design Individual chapters on designs for data that have Binomial or Poisson distributions Bayesian experimental design An online resource contains R programs used in the book This book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra, and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided.

Handbook of Design and Analysis of Experiments
Handbook of Design and Analysis of Experiments

Author: Angela Dean

Publisher: CRC Press

Published: 2015-06-26

Total Pages: 946

ISBN-13: 146650434X

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This carefully edited collection synthesizes the state of the art in the theory and applications of designed experiments and their analyses. It provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook covers many recent advances in the field, including designs for nonlinear models and algorithms applicable to a wide variety of design problems. It also explores the extensive use of experimental designs in marketing, the pharmaceutical industry, engineering and other areas.

Optimal Mixture Experiments
Optimal Mixture Experiments

Author: B.K. Sinha

Publisher: Springer

Published: 2014-05-24

Total Pages: 213

ISBN-13: 8132217861

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​The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.

Linear Models in Statistics
Linear Models in Statistics

Author: Alvin C. Rencher

Publisher: John Wiley & Sons

Published: 2008-01-07

Total Pages: 690

ISBN-13: 0470192607

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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.

Sequential Analysis and Optimal Design
Sequential Analysis and Optimal Design

Author: Herman Chernoff

Publisher: SIAM

Published: 1972-01-01

Total Pages: 124

ISBN-13: 9781611970593

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An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.

Optimal Design of Experiments
Optimal Design of Experiments

Author: Friedrich Pukelsheim

Publisher: SIAM

Published: 2006-04-01

Total Pages: 527

ISBN-13: 0898716047

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Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.

New Statistics for Design Researchers
New Statistics for Design Researchers

Author: Martin Schmettow

Publisher: Springer

Published: 2022-07-15

Total Pages: 0

ISBN-13: 9783030463823

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Design Research uses scientific methods to evaluate designs and build design theories. This book starts with recognizable questions in Design Research, such as A/B testing, how users learn to operate a device and why computer-generated faces are eerie. Using a broad range of examples, efficient research designs are presented together with statistical models and many visualizations. With the tidy R approach, producing publication-ready statistical reports is straight-forward and even non-programmers can learn this in just one day. Hundreds of illustrations, tables, simulations and models are presented with full R code and data included. Using Bayesian linear models, multi-level models and generalized linear models, an extensive statistical framework is introduced, covering a huge variety of research situations and yet, building on only a handful of basic concepts. Unique solutions to recurring problems are presented, such as psychometric multi-level models, beta regression for rating scales and ExGaussian regression for response times. A “think-first” approach is promoted for model building, as much as the quantitative interpretation of results, stimulating readers to think about data generating processes, as well as rational decision making. New Statistics for Design Researchers: A Bayesian Workflow in Tidy R targets scientists, industrial researchers and students in a range of disciplines, such as Human Factors, Applied Psychology, Communication Science, Industrial Design, Computer Science and Social Robotics. Statistical concepts are introduced in a problem-oriented way and with minimal formalism. Included primers on R and Bayesian statistics provide entry point for all backgrounds. A dedicated chapter on model criticism and comparison is a valuable addition for the seasoned scientist.