Nonlinear regression with R

Preface

1. Introduction

1.1. A stock-recruitment model

1.2. Competition between plant biotypes

1.3. Grouped dose-response data

2. Getting Started

2.1. Background

2.2. Getting started with nls()

2.2.1. Introducing the data example

2.2.2. Model fitting

2.2.3. Prediction

2.2.4. Making plots

2.2.5. Illustrating the estimation

2.3. Generalised linear models

Exercises

3. Starting Values and Self-starters

3.1. Finding starting values

3.1.1. Graphical exploration

3.1.2. Searching a grid

3.2. Using self-starter functions

3.2.1. Built-in self-starter functions for nls()

3.2.2. Defining a self-starter function for nls()

Exercises

4. More on nls()

4.1. Arguments and methods

4.2. Supplying gradient information

4.2.1. Manual supply

4.2.2. Automatic supply

4.3. Conditionally linear parameters

4.3.1. nls() using the "plinear" algorithm

4.3.2. A pedestrian approach

4.4. Fitting models with several predictor variables

4.4.1. Two-dimensional predictor

4.4.2. General least-squares minimisation

4.5. Error messages

4.6. Controlling nls()

Exercises

5. Model Diagnostics

5.1. Model assumptions

5.2. Checking the mean structure

5.2.1. Plot of the fitted regression curve

5.2.2. Residual plots

5.2.3. Lack-of-fit tests

5.3. Variance homogeneity

5.3.1. Absolute residuals

5.3.2. Levene's test

5.4. Normal distribution

5.4.1. QQ plot

5.4.2. Shapiro-Wilk test

5.5. Independence

Exercises

6. Remedies for Model Violations

6.1. Variance modelling

6.1.1. Power-of-the-mean variance model

6.1.2. Other variance models

6.2. Transformations

6.2.1. Transform-both-sides approach

6.2.2. Finding an appropriate transformation

6.3. Sandwich estimators

6.4. Weighting

6.4.1. Decline in nitrogen content in soil

Exercises

7. Uncertainty, Hypothesis Testing, and Model Selection

7.1. Profile likelihood

7.2. Bootstrap

7.3. Wald confidence intervals

7.4. Estimating derived parameters

7.5. Nested models

7.5.1. Using t-tests

7.5.2. Using F-tests

7.6. Non-nested models

Exercises

8. Grouped Data

8.1. Fitting grouped data models

8.1.1. Using nls()

8.1.2. Using gnls()

8.1.3. Using nlsList()

8.2. Model reduction and parameter models

8.2.1. Comparison of entire groups

8.2.2. Comparison of specific parameters

8.3. Common control

8.4. Prediction

8.5. Nonlinear mixed models

Exercises

Appendix A. Datasets and Models

Appendix B. Self-starter Functions

Appendix C. Packages and Functions

References

Index