Nonlinear Regression With R
by Ritz, ChristianEdition: 1st
Format: Paperback
Pub. Date: 2008-12-15
Publisher(s): Springer Verlag
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Summary
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. Currently, R offers a wide range of functionality for nonlinear regression analysis, but the relevant functions, packages and documentation are scattered across the R environment. This book provides a coherent and unified treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology. R. Subsequent chapters explain the salient features of the main fitting function nls (), the use of model diagnostics, how to deal with various model departures, and carry out hypothesis testing. In the final chapter grouped-data structures, including an example of a nonlinear mixed-effects regression model, are considered.
Author Biography
Christian Ritz has a PhD in biostatistics from the Royal Veterinary and Agricultural University Jens Carl Streibig is a professor in weed science at the University of Copenhagen
Table of Contents
| Preface | p. VII |
| Introduction | p. 1 |
| A stock-recruitment model | p. 2 |
| Competition between plant biotypes | p. 3 |
| Grouped dose-response data | p. 4 |
| Getting Started | p. 7 |
| Background | p. 7 |
| Getting started with nls() | p. 8 |
| Introducing the data example | p. 9 |
| Model fitting | p. 9 |
| Prediction | p. 13 |
| Making plots | p. 15 |
| Illustrating the estimation | p. 16 |
| Generalised linear models | p. 18 |
| Exercises | p. 20 |
| Starting Values and Self-starters | p. 23 |
| Finding starting values | p. 23 |
| Graphical exploration | p. 23 |
| Searching a grid | p. 27 |
| Using self-starter functions | p. 29 |
| Built-in self-starter functions for nls() | p. 30 |
| Defining a self-starter function for nls() | p. 31 |
| Exercises | p. 35 |
| More on nls() | p. 37 |
| Arguments and methods | p. 37 |
| Supplying gradient information | p. 38 |
| Manual supply | p. 39 |
| Automatic supply | p. 40 |
| Conditionally linear parameters | p. 41 |
| nls() using the "plinear" algorithm | p. 42 |
| A pedestrian approach | p. 43 |
| Fitting models with several predictor variables | p. 45 |
| Two-dimensional predictor | p. 45 |
| General least-squares minimisation | p. 48 |
| Error messages | p. 50 |
| Controlling nls() | p. 52 |
| Exercises | p. 53 |
| Model Diagnostics | p. 55 |
| Model assumptions | p. 55 |
| Checking the mean structure | p. 56 |
| Plot of the fitted regression curve | p. 56 |
| Residual plots | p. 59 |
| Lack-of-fit tests | p. 60 |
| Variance homogeneity | p. 65 |
| Absolute residuals | p. 65 |
| Levene's test | p. 65 |
| Normal distribution | p. 66 |
| QQ plot | p. 67 |
| Shapiro-Wilk test | p. 69 |
| Independence | p. 69 |
| Exercises | p. 70 |
| Remedies for Model Violations | p. 73 |
| Variance modelling | p. 73 |
| Power-of-the-mean variance model | p. 74 |
| Other variance models | p. 77 |
| Transformations | p. 78 |
| Transform-both-sides approach | p. 78 |
| Finding an appropriate transformation | p. 81 |
| Sandwich estimators | p. 83 |
| Weighting | p. 85 |
| Decline in nitrogen content in soil | p. 87 |
| Exercises | p. 91 |
| Uncertainty, Hypothesis Testing, and Model Selection | p. 93 |
| Profile likelihood | p. 94 |
| Bootstrap | p. 96 |
| Wald confidence intervals | p. 99 |
| Estimating derived parameters | p. 100 |
| Nested models | p. 101 |
| Using t-tests | p. 102 |
| Using F-tests | p. 103 |
| Non-nested models | p. 105 |
| Exercises | p. 108 |
| Grouped Data | p. 109 |
| Fitting grouped data models | p. 109 |
| Using nls() | p. 111 |
| Using gnls() | p. 112 |
| Using nlsList() | p. 113 |
| Model reduction and parameter models | p. 114 |
| Comparison of entire groups | p. 114 |
| Comparison of specific parameters | p. 115 |
| Common control | p. 118 |
| Prediction | p. 121 |
| Nonlinear mixed models | p. 123 |
| Exercises | p. 131 |
| Datasets and Models | p. 133 |
| Self-starter Functions | p. 135 |
| Packages and Functions | p. 137 |
| References | p. 139 |
| Index | p. 143 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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