| Description |
1 online resource (241 pages) |
| Series |
Chapman and Hall/CRC Interdisciplinary Statistics Ser |
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Chapman and Hall/CRC Interdisciplinary Statistics Ser
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| Contents |
Cover; Half Title; Series Page; Title Page; Copyright Page; Dedication; Contents; Preface; 1. Generalized Linear Models; 1.1 Introduction; 1.2 Mathematics of the general linear model; 1.3 Towards the generalized linear model; 1.4 Generalized linear models; 1.5 Estimating the values of the model parameters; 2. Background Material; 2.1 Introduction; 2.2 Maximisation or minimisation of a function; 2.2.1 A function of one variable; 2.2.2 A function of more than one variable; 2.3 Restrictions on independent variables; 2.4 Constrained optimisation in R; 2.4.1 The function constrOptim |
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2.4.2 Additional features of constrOptim2.4.3 Constrained optimisation without constrOptim; 2.4.4 Notes and examples; 2.4.5 Using the function optim; 2.4.6 Initial values for optimisations; 2.5 Numerical integration; 2.6 Conclusion; 3. The Theory Underlying Design; 3.1 Introduction; 3.2 Notation; 3.3 Designing an experiment; 3.3.1 Exact and approximate designs; 3.3.2 Constructing an exact design from an approximate design; 3.3.3 Constructing an exact design directly; 3.4 Selecting the support points; 3.4.1 Thinking about criteria for selection; 3.4.2 The standardised variance |
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3.5 Generalized linear models3.5.1 Theory; 3.5.2 Example: a simple logistic regression; 3.6 Difficulties caused by small samples; 3.7 Optimality; 3.7.1 Number of support points; 3.7.2 Optimality criteria; 3.7.3 A-optimality; 3.7.4 D-optimality; 3.7.5 Ds-optimality; 3.7.6 E-optimality; 3.7.7 G-optimality; 3.8 Example; 3.8.1 Using constrOptim; 3.8.2 Using optim; 3.8.3 How to be sure that you have the right design; 3.9 The general equivalence theorem; 3.10 Where next?; 4. The Binomial Distribution; 4.1 Introduction; 4.2 Notation; 4.3 Link functions; 4.3.1 The logit link function |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Linear models
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Experimental design.
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binomial distribution.
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linear mixed models.
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linear models.
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mixture experiments.
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Poisson distribution.
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R software.
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Experimental design.
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| Form |
Electronic book
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| ISBN |
9780429615627 |
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0429615620 |
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9780429614415 |
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0429614411 |
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9780429613203 |
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0429613202 |
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9780429057489 |
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0429057482 |
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