9780387400815

Statistical Tools for Nonlinear Regression, Second Edition, presents methods for analyzing data using parametric nonlinear regression models. The new edition has been expanded to include binomial, multinomial and Poisson non-linear models. Using examples from experiments in agronomy and biochemistry, it shows how to apply these methods. It concentrates on presenting the methods in an intuitive way rather than developing the theoretical backgrounds. The examples are analyzed with the free software nls2 updated to deal with the new models included in the second edition. The nls2 package is implemented in S-PLUS and R. Its main advantages are to make the model building, estimation and validation tasks, easy to do. More precisely, Complex models can be easily described using a symbolic syntax. The regression function as well as the variance function can be defined explicitly as functions of independent variables and of unknown parameters or they can be defined as the solution to a system of differential equations. Moreover, constraints on the parameters can easily be added to the model. It is thus possible to test nested hypotheses and to compare several data sets. Several additional tools are included in the package for calculating confidence regions for functions of parameters or calibration intervals, using classical methodology or bootstrap. Some graphical tools are proposed for visualizing the fitted curves, the residuals, the confidence regions, and the numerical estimation procedure.

Sylvie Huet and Emmanuel Jolivet are senior researchers and Annie Bouvier is a computing engineer at INRA, National Institute of Agronomical Research, France Marie-Anne Poursat is an associate professor of statistics at the University Paris XI

Preface to the Second Edition

XI

Preface to the First Edition

XIII

1 Nonlinear Regression Model and Parameter Estimation

1

(28)

1.1 Examples

1

(9)

1.1.1 Pasture Regrowth: Estimating a Growth Curve

1

(1)

1.1.2 Radioimmunological Assay of Cortisol: Estimating a Calibration Curve

2

(4)

1.1.3 Antibodies Anticoronavirus Assayed by an ELISA Test: Comparing Several Response Curves

6

(2)

1.1.4 Comparison of Immature and Mature Goat Ovocytes: Comparing Parameters

8

(1)

1.1.5 Isomerization: More than One Independent Variable

9

(1)

1.2 The Parametric Nonlinear Regression Model

10

(1)

1.3 Estimation

11

(2)

1.4 Applications

13

(4)

1.4.1 Pasture Regrowth: Parameter Estimation and Graph of Observed and Adjusted Response Values

13

(1)

1.4.2 Cortisol Assay: Parameter Estimation and Graph of Observed and Adjusted Response Values

13

(1)

1.4.3 ELISA Test: Parameter Estimation and Graph of Observed and Adjusted Curves for May and June

14

(1)

1.4.4 Ovocytes: Parameter Estimation and Graph of Observed and Adjusted Volume of Mature and Immature Ovocytes in Propane-Diol

15

(1)

1.4.5 Isomerization: Parameter Estimation and Graph of Adjusted versus Observed Values

16

(1)

1.5 Conclusion and References

17

(1)

1.6 Using nls2

18

(11)

2 Accuracy of Estimators, Confidence Intervals and Tests

29

(32)

2.1 Examples

29

(1)

2.2 Problem Formulation

30

(1)

2.3 Solutions

30

(8)

2.3.1 Classical Asymptotic Results

30

(2)

2.3.2 Asymptotic Confidence Intervals for Λ

32

(1)

2.3.3 Asymptotic Tests of &Lambda = Λomicron against Λ not equal Λ omicron

33

(1)

2.3.4 Asymptotic Tests of Λ θ = Λ omicron against Λ Omicron L omicron

34

(1)

2.3.5 Bootstrap Estimations

35

(3)

2.4 Applications

38

(11)

2.4.1 Pasture Regrowth: Calculation of a Confidence Interval for the Maximum Yield

38

(1)

2.4.2 Cortisol Assay: Estimation of the Accuracy of the Estimated Dose D

39

(1)

2.4.3 ELISA Test: Comparison of Curves

40

(2)

2.4.4 Ovocytes: Calculation of Confidence Regions

42

(1)

2.4.5 Isomerization: An Awkward Example

43

(4)

2.4.6 Pasture Regrowth: Calculation of a Confidence Interval for A = exp θ 3

47

(2)

2.5 Conclusion

49

(1)

2.6 Using nls2

49

(12)

3 Variance Estimation

61

(32)

3.1 Examples

61

(4)

3.1.1 Growth of Winter Wheat Tillers: Few Replications

61

(2)

3.1.2 Solubility of Peptides in Trichloacetic Acid Solutions: No Replications

63

(2)

3.2 Parametric Modeling of the Variance

65

(1)

3.3 Estimation

66

(3)

3.3.1 Maximum Likelihood Estimation

66

(1)

3.3.2 Quasi-Likelihood Estimation

67

(2)

3.3.3 Three-Step Estimation

69

(1)

3.4 Tests and Confidence Regions

69

(5)

3.4.1 The Wald Test

69

(1)

3.4.2 The Likelihood Ratio Test

70

(1)

3.4.3 Bootstrap Estimations

71

(1)

3.4.4 Links Between Testing Procedures and Confidence Region Computations

72

(1)

3.4.5 Confidence Regions

73

(1)

3.5 Applications

74

(9)

3.5.1 Growth of Winter Wheat Tillers

74

(4)

3.5.2 Solubility of Peptides in Trichloacetic Acid Solutions

78

(5)

3.6 Using nls2

83

(10)

4 Diagnostics of Model Misspecification

93

(42)

4.1 Problem Formulation

93

(1)

4.2 Diagnostics of Model Misspecifications with Graphics

94

(16)

4.2.1 Pasture Regrowth Example: Estimation Using a Concave-Shaped Curve and Plot for Diagnostics

95

(1)

4.2.2 Isomerization Example: Graphics for Diagnostic

95

(2)

4.2.3 Peptides Example: Graphics for Diagnostic

97

(2)

4.2.4 Cortisol Assay Example: How to Choose the Variance Function Using Replications

99

(4)

4.2.5 Trajectory of Roots of Maize: How to Detect Correlations in Errors

103

(4)

4.2.6 What Can We Say About the Experimental Design?

107

(3)

4.3 Diagnostics of Model Misspecifications with Tests

110

(4)

4.3.1 RIA of Cortisol: Comparison of Nested Models

110

(1)

4.3.2 Tests Using Replications

110

(2)

4.3.3 Cortisol Assay Example: Misspecification Tests Using Replications

112

(1)

4.3.4 Ovocytes Example: Graphics of Residuals and Misspecification Tests Using Replications

112

(2)

4.4 Numerical Troubles During the Estimation Process: Peptides Example

114

(4)

4.5 Peptides Example: Concluded

118

(1)

4.6 Using nls2

119

(16)

5 Calibration and Prediction

135

(18)

5.1 Examples

135

(2)

5.2 Problem Formulation

137

(1)

5.3 Confidence Intervals

137

(5)

5.3.1 Prediction of a Response

137

(2)

5.3.2 Calibration with Constant Variances

139

(2)

5.3.3 Calibration with Nonconstant Variances

141

(1)

5.4 Applications

142

(3)

5.4.1 Pasture Regrowth Example: Prediction of the Yield at Time χ omicron = 50

142

(1)

5.4.2 Cortisol Assay Example

143

(1)

5.4.3 Nasturtium Assay Example

144

(1)

5.5 References

145

(1)

5.6 Using nls2

145

(8)

6 Binomial Nonlinear Models

153

(46)

6.1 Examples

153

(7)

6.1.1 Assay of an Insecticide with a Synergist: A Binomial Nonlinear Model

153

(2)

6.1.2 Vaso-Constriction in the Skin of the Digits: The Case of Binary Response Data

155

(1)

6.1.3 Mortality of Confused Flour Beetles: The Choice of a Link Function in a Binomial Linear Model

156

(2)

6.1.4 Mortality of Confused Flour Beetles 2: Survival Analysis Using a Binomial Nonlinear Model

158

(1)

6.1.5 Germination of Orobranche: Overdispersion

159

(1)

6.2 The Parametric Binomial Nonlinear Model

160

(1)

6.3 Overdispersion, Underdispersion

161

(1)

6.4 Estimation

162

(3)

6.4.1 Case of Binomial Nonlinear Models

162

(2)

6.4.2 Case of Overdispersion or Underdispersion

164

(1)

6.5 Tests and Confidence Regions

165

(2)

6.6 Applications

167

(13)

6.6.1 Assay of an Insecticide with a Synergist: Estimating the Parameters

167

(4)

6.6.2 Vaso-Constriction in the Skin of the Digits: Estimation and Test of Nested Models

171

(1)

6.6.3 Mortality of Confused Flour Beetles: Estimating the Link Function and Calculating Confidence Intervals for the LD90

172

(2)

6.6.4 Mortality of Confused Flour Beetles 2: Comparison of Curves and Confidence Intervals for the ED50

174

(3)

6.6.5 Germination of Orobranche: Estimating Overdispersion Using the Quasi-Likelihood Estimation Method

177

(3)

6.7 Using nls2

180

(19)

7 Multinomial and Poisson Nonlinear Models

199

(28)

7.1 Multinomial Model

199

(22)

7.1.1 Pneumoconiosis among Coal Miners: An Example of Multicategory Response Data

200

(1)

7.1.2 A Cheese Tasting Experiment

200

(1)

7.1.3 The Parametric Multinomial Model

201

(3)

7.1.4 Estimation in the Multinomial Model

204

(2)

7.1.5 Tests and Confidence Intervals

206

(2)

7.1.6 Pneumoconiosis among Coal Miners: The Multinomial Logit Model

208

(2)

7.1.7 Cheese Tasting Example: Mode Based on Cumulative Probabilities

210

(3)

7.1.8 Using nls2

213

(8)

7.2 Poisson Model

221

(6)

7.2.1 The Parametric Poisson Model

222

(1)

7.2.2 Estimation in the Poisson Mode

222

(1)

7.2.3 Cortisol Assay Example: The Poisson Nonlinear Mode

223

(2)

7.2.4 Using nls2

225

(2)

References

227

(4)

Index

231

0415944805

ACKNOWLEDGMENTS

IX

1 INTRODUCTION: CELEBRITY TALK, LESBIAN STYLE

1

(10)

2 VISIBILITY NOW! THE SEXUAL POLITICS OF SEEING

11

(34)

3 CELESTIAL CONFIGURATIONS: ASPECTS OF LESBIAN STARDOM

45

(36)

4 GOING PUBLIC: STAR WARS IN THE LIBERATION MOVEMENTS

81

(34)

5 IN RETROSPECT: LEGENDS OF MERCEDES DE ACOSTA AND COMPANY

115

(42)

6 POPULAR MECHANICS: ADVANCED TECHNOLOGIES OF LESBIAN CELEBRITY

157

(34)

7 AFTERWORD

191

(8)

NOTES

199

(14)

BIBLIOGRAPHY

213

(12)

INDEX

225

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Statistical Tools for Nonlinear Regression

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