Nonlinear Regression with R (eBook)

Preface 7
Contents 9
1 Introduction 12
1.1 A stock-recruitment model 13
1.2 Competition between plant biotypes 14
1.3 Grouped dose-response data 15
2 Getting Started 18
2.1 Background 18
2.2 Getting started with nls () 19
2.3 Generalised linear models 29
Exercises 31
3 Starting Values and Self-starters 33
3.1 Finding starting values 33
3.2 Using self-starter functions 39
Exercises 45
4 More on nls () 47
4.1 Arguments and methods 47
4.2 Supplying gradient information 48
4.3 Conditionally linear parameters 51
4.4 Fitting models with several predictor variables 55
4.5 Error messages 60
4.6 Controlling 62
Exercises 63
5 Model Diagnostics 65
5.1 Model assumptions 65
5.2 Checking the mean structure 66
5.3 Variance homogeneity 75
5.4 Normal distribution 76
5.5 Independence 79
Exercises 80
6 Remedies for Model Violations 82
6.1 Variance modelling 82
6.2 Transformations 87
6.3 Sandwich estimators 92
6.4 Weighting 94
Exercises 100
7 Uncertainty, Hypothesis Testing, and Model Selection 101
7.1 Profile likelihood 102
7.2 Bootstrap 104
7.3 Wald confidence intervals 107
7.4 Estimating derived parameters 108
7.5 Nested models 109
7.6 Non-nested models 113
Exercises 116
8 Grouped Data 117
8.1 Fitting grouped data models 117
8.2 Model reduction and parameter models 122
8.3 Common control 126
8.4 Prediction 129
8.5 Nonlinear mixed models 131
Exercises 139
Appendix A: Datasets and Models 140
Appendix B: Self-starter Functions 142
Appendix C: Packages and Functions 143
References 145
Index 149