
Statistical Tools for Nonlinear Regression
A Practical Guide With S-PLUS and R Examples
By: Sylvie Huet, Anne Bouvier, Marie-Anne Poursat
Hardcover | 12 September 2003 | Edition Number 2
At a Glance
252 Pages
Revised
18.42 x 15.88 x 1.91
Hardcover
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Industry Reviews
From the reviews of the second edition:
"Users of S-PLUS or R who do nonlinear estimation would certainly want a copy of this book. The wealth of applications and code for using the specialized software transcends the limitation of the applications to medicine and biology." Technometrics, May 2004
"In this second edition to the first edition published in 1996, the authors present a comprehensive overview of nonlinear regression methods. With an emphasis on learning the basics of how to perform analyses using S-PLUS or R and understand and present the results, the book provides a valuable resource for those interested in learning this material...The book is easy to read, and the inclusion of S-PLUS output, graphs, and source code makes picking up the book and getting started much easier. For those working with data best modeled by nonlinear relationships, this book will be a valuable addition to your shelf of resources." Journal of the American Statistical Association, September 2004
"As the title suggests, the book deals with non-linear regression analysis ... . The real strength of the book lies in a careful and detailed discussion of a number of examples ... . Anyone who is interested in actually analysing data using non-linear models will benefit from working through these examples ... . the book would make an excellent secondary source for a course in non-linear models. ... A number of excellent references are available that provide the necessary theoretical background ... ." (Christopher Cox, Statistics in Medicine, Vol. 24 (13), 2005)
"This second edition provides a comprehensive overview of the field of parametric nonlinear regression models in data analysis. The book aims especially at students, as a tutorial book, and at the scientists applying statistical methods in different practical domains. Each chapter begins with a set of different concrete examples, followed by the corresponding statistical issues and solutions. Inaddition, where necessary, a very simple theoretical background is provided." (Florin Gorunescu, Zentralblatt MATH, Vol. 1041 (16), 2004)
"The first 5 chapters of this book discuss normal distribution models where the mean is described with a nonlinear model. Chapter six discusses a nonlinear model with a binomial distribution, chapter seven uses a Poisson and multinomial distribution. ... The large amount of examples ... makes this book a valuable contribution to the every day statistical practice." (J. van den Broek, Kwantitatieve Methoden, Issue 72B34, 2004)
"This book describes itself as a 'cookbook' for non-linear regression and is supported by the nls2 software ... . The chapters are reasonably and logically laid out ... . There are 42 references, many of which are to other text-books on modeling ... . The back cover suggests that it may be of use to students as a tutorial book. It is certainly a valuable complement to the nls2 software ... ." (Paul Hewson, Journal of the Royal Statistical Society, Vol. 198 (1), 2005)
| Preface to the Second Edition | p. XI |
| Preface to the First Edition | p. XIII |
| Nonlinear Regression Model and Parameter Estimation | p. 1 |
| Examples | p. 1 |
| Pasture Regrowth: Estimating a Growth Curve | p. 1 |
| Radioimmunological Assay of Cortisol: Estimating a Calibration Curve | p. 2 |
| Antibodies Anticoronavirus Assayed by an ELISA Test: Comparing Several Response Curves | p. 6 |
| Comparison of Immature and Mature Goat Ovocytes: Comparing Parameters | p. 8 |
| Isomerization: More than One Independent Variable | p. 9 |
| The Parametric Nonlinear Regression Model | p. 10 |
| Estimation | p. 11 |
| Applications | p. 13 |
| Pasture Regrowth: Parameter Estimation and Graph of Observed and Adjusted Response Values | p. 13 |
| Cortisol Assay: Parameter Estimation and Graph of Observed and Adjusted Response Values | p. 13 |
| ELISA Test: Parameter Estimation and Graph of Observed and Adjusted Curves for May and June | p. 14 |
| Ovocytes: Parameter Estimation and Graph of Observed and Adjusted Volume of Mature and Immature Ovocytes in Propane-Diol | p. 15 |
| Isomerization: Parameter Estimation and Graph of Adjusted versus Observed Values | p. 16 |
| Conclusion and References | p. 17 |
| Using nls2 | p. 18 |
| Accuracy of Estimators, Confidence Intervals and Tests | p. 29 |
| Examples | p. 29 |
| Problem Formulation | p. 30 |
| Solutions | p. 30 |
| Classical Asymptotic Results | p. 30 |
| Asymptotic Confidence Intervals for [lambda] | p. 32 |
| Asymptotic Tests of [lambda] = [lambda subscript 0] against [lambda not equal lambda subscript 0] | p. 33 |
| Asymptotic Tests of [Lambda theta] = L[subscript 0] against [Lambda theta not equal] L[subscript 0] | p. 34 |
| Bootstrap Estimations | p. 35 |
| Applications | p. 38 |
| Pasture Regrowth: Calculation of a Confidence Interval for the Maximum Yield | p. 38 |
| Cortisol Assay: Estimation of the Accuracy of the Estimated Dose D | p. 39 |
| ELISA Test: Comparison of Curves | p. 40 |
| Ovocytes: Calculation of Confidence Regions | p. 42 |
| Isomerization: An Awkward Example | p. 43 |
| Pasture Regrowth: Calculation of a Confidence Interval for [lambda] = exp[theta subscript 3] | p. 47 |
| Conclusion | p. 49 |
| Using nls2 | p. 49 |
| Variance Estimation | p. 61 |
| Examples | p. 61 |
| Growth of Winter Wheat Tillers: Few Replications | p. 61 |
| Solubility of Peptides in Trichloacetic Acid Solutions: No Replications | p. 63 |
| Parametric Modeling of the Variance | p. 65 |
| Estimation | p. 66 |
| Maximum Likelihood Estimation | p. 66 |
| Quasi-Likelihood Estimation | p. 67 |
| Three-Step Estimation | p. 69 |
| Tests and Confidence Regions | p. 69 |
| The Wald Test | p. 69 |
| The Likelihood Ratio Test | p. 70 |
| Bootstrap Estimations | p. 71 |
| Links Between Testing Procedures and Confidence Region Computations | p. 72 |
| Confidence Regions | p. 73 |
| Applications | p. 74 |
| Growth of Winter Wheat Tillers | p. 74 |
| Solubility of Peptides in Trichloacetic Acid Solutions | p. 78 |
| Using nls2 | p. 83 |
| Diagnostics of Model Misspecification | p. 93 |
| Problem Formulation | p. 93 |
| Diagnostics of Model Misspecifications with Graphics | p. 94 |
| Pasture Regrowth Example: Estimation Using a Concave-Shaped Curve and Plot for Diagnostics | p. 95 |
| Isomerization Example: Graphics for Diagnostic | p. 95 |
| Peptides Example: Graphics for Diagnostic | p. 97 |
| Cortisol Assay Example: How to Choose the Variance Function Using Replications | p. 99 |
| Trajectory of Roots of Maize: How to Detect Correlations in Errors | p. 103 |
| What Can We Say About the Experimental Design? | p. 107 |
| Diagnostics of Model Misspecifications with Tests | p. 110 |
| RIA of Cortisol: Comparison of Nested Models | p. 110 |
| Tests Using Replications | p. 110 |
| Cortisol Assay Example: Misspecification Tests Using Replications | p. 112 |
| Ovocytes Example: Graphics of Residuals and Misspecification Tests Using Replications | p. 112 |
| Numerical Troubles During the Estimation Process: Peptides Example | p. 114 |
| Peptides Example: Concluded | p. 118 |
| Using nls2 | p. 119 |
| Calibration and Prediction | p. 135 |
| Examples | p. 135 |
| Problem Formulation | p. 137 |
| Confidence Intervals | p. 137 |
| Prediction of a Response | p. 137 |
| Calibration with Constant Variances | p. 139 |
| Calibration with Nonconstant Variances | p. 141 |
| Applications | p. 142 |
| Pasture Regrowth Example: Prediction of the Yield at Time x[subscript 0] = 50 | p. 142 |
| Cortisol Assay Example | p. 143 |
| Nasturtium Assay Example | p. 144 |
| References | p. 145 |
| Using nls2 | p. 145 |
| Binomial Nonlinear Models | p. 153 |
| Examples | p. 153 |
| Assay of an Insecticide with a Synergist: A Binomial Nonlinear Model | p. 153 |
| Vaso-Constriction in the Skin of the Digits: The Case of Binary Response Data | p. 155 |
| Mortality of Confused Flour Beetles: The Choice of a Link Function in a Binomial Linear Model | p. 156 |
| Mortality of Confused Flour Beetles 2: Survival Analysis Using a Binomial Nonlinear Model | p. 158 |
| Germination of Orobranche: Overdispersion | p. 159 |
| The Parametric Binomial Nonlinear Model | p. 160 |
| Overdispersion, Underdispersion | p. 161 |
| Estimation | p. 162 |
| Case of Binomial Nonlinear Models | p. 162 |
| Case of Overdispersion or Underdispersion | p. 164 |
| Tests and Confidence Regions | p. 165 |
| Applications | p. 167 |
| Assay of an Insecticide with a Synergist: Estimating the Parameters | p. 167 |
| Vaso-Constriction in the Skin of the Digits: Estimation and Test of Nested Models | p. 171 |
| Mortality of Confused Flour Beetles: Estimating the Link Function and Calculating Confidence Intervals for the LD90 | p. 172 |
| Mortality of Confused Flour Beetles 2: Comparison of Curves and Confidence Intervals for the ED50 | p. 174 |
| Germination of Orobranche: Estimating Overdispersion Using the Quasi-Likelihood Estimation Method | p. 177 |
| Using nls2 | p. 180 |
| Multinomial and Poisson Nonlinear Models | p. 199 |
| Multinomial Model | p. 199 |
| Pneumoconiosis among Coal Miners: An Example of Multicategory Response Data | p. 200 |
| A Cheese Tasting Experiment | p. 200 |
| The Parametric Multinomial Model | p. 201 |
| Estimation in the Multinomial Model | p. 204 |
| Tests and Confidence Intervals | p. 206 |
| Pneumoconiosis among Coal Miners: The Multinomial Logit Model | p. 208 |
| Cheese Tasting Example: Model Based on Cumulative Probabilities | p. 210 |
| Using nls2 | p. 213 |
| Poisson Model | p. 221 |
| The Parametric Poisson Model | p. 222 |
| Estimation in the Poisson Model | p. 222 |
| Cortisol Assay Example: The Poisson Nonlinear Model | p. 223 |
| Using nls2 | p. 225 |
| References | p. 227 |
| Index | p. 231 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387400815
ISBN-10: 0387400818
Series: Springer Series in Statistics
Published: 12th September 2003
Format: Hardcover
Language: English
Number of Pages: 252
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 18.42 x 15.88 x 1.91
Weight (kg): 0.5
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