Statistical tools for nonlinear regression : a practical guide with S-PLUS and R examples / S. Huet ... [and others].

Format:

Book

Author/Creator:

Huet, S. (Sylvie)

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Springer series in statistics

Language:

English

Subjects (All):

Regression analysis.

Nonlinear theories.

Parameter estimation.

Physical Description:

xiv, 232 pages : illustrations ; 24 cm.

Edition:

Second edition.

Place of Publication:

New York : Springer, [2004]

Summary:

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 nonlinear 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.

This book is aimed at scientists who are not familiar with statistical theory, but have a basic knowledge of statistical concepts. It includes methods based on classical nonlinear regression theory and more modern methods, such as bootstrap, which have proved effective in practice. The additional chapters of the second edition assume some practical experience in data analysis using generalized linear models. The book will be of interest both to practitioners as a guide and reference book, and to students as a tutorial book.

Contents:

1 Nonlinear Regression Model and Parameter Estimation 1

1.1.1 Pasture Regrowth: Estimating a Growth Curve 1

1.1.2 Radioimmunological Assay of Cortisol: Estimating a Calibration Curve 2

1.1.3 Antibodies Anticoronavirus Assayed by an ELISA Test: Comparing Several Response Curves 6

1.1.4 Comparison of Immature and Mature Goat Ovocytes: Comparing Parameters 8

1.1.5 Isomerization: More than One Independent Variable 9

1.2 The Parametric Nonlinear Regression Model 10

1.3 Estimation 11

1.4 Applications 13

1.4.1 Pasture Regrowth: Parameter Estimation and Graph of Observed and Adjusted Response Values 13

1.4.2 Cortisol Assay: Parameter Estimation and Graph of Observed and Adjusted Response Values 13

1.4.3 ELISA Test: Parameter Estimation and Graph of Observed and Adjusted Curves for May and June 14

1.4.4 Ovocytes: Parameter Estimation and Graph of Observed and Adjusted Volume of Mature and Immature Ovocytes in Propane-Diol 15

1.4.5 Isomerization: Parameter Estimation and Graph of Adjusted versus Observed Values 16

1.6 Using nls2 18

2 Accuracy of Estimators, Confidence Intervals and Tests 29

2.2 Problem Formulation 30

2.3 Solutions 30

2.3.1 Classical Asymptotic Results 30

2.3.2 Asymptotic Confidence Intervals for [lambda] 32

2.3.3 Asymptotic Tests of [lambda] = [lambda subscript 0] against [lambda not equal lambda subscript 0] 33

2.3.4 Asymptotic Tests of [Lambda theta] = L[subscript 0] against [Lambda theta not equal] L[subscript 0] 34

2.3.5 Bootstrap Estimations 35

2.4 Applications 38

2.4.1 Pasture Regrowth: Calculation of a Confidence Interval for the Maximum Yield 38

2.4.2 Cortisol Assay: Estimation of the Accuracy of the Estimated Dose D 39

2.4.3 ELISA Test: Comparison of Curves 40

2.4.4 Ovocytes: Calculation of Confidence Regions 42

2.4.5 Isomerization: An Awkward Example 43

2.4.6 Pasture Regrowth: Calculation of a Confidence Interval for [lambda] = exp[theta subscript 3] 47

3 Variance Estimation 61

3.1.1 Growth of Winter Wheat Tillers: Few Replications 61

3.1.2 Solubility of Peptides in Trichloacetic Acid Solutions: No Replications 63

3.2 Parametric Modeling of the Variance 65

3.3 Estimation 66

3.3.1 Maximum Likelihood Estimation 66

3.3.2 Quasi-Likelihood Estimation 67

3.3.3 Three-Step Estimation 69

3.4 Tests and Confidence Regions 69

3.4.1 The Wald Test 69

3.4.2 The Likelihood Ratio Test 70

3.4.3 Bootstrap Estimations 71

3.4.4 Links Between Testing Procedures and Confidence Region Computations 72

3.4.5 Confidence Regions 73

3.5 Applications 74

3.5.1 Growth of Winter Wheat Tillers 74

3.5.2 Solubility of Peptides in Trichloacetic Acid Solutions 78

4 Diagnostics of Model Misspecification 93

4.1 Problem Formulation 93

4.2 Diagnostics of Model Misspecifications with Graphics 94

4.2.1 Pasture Regrowth Example: Estimation Using a Concave-Shaped Curve and Plot for Diagnostics 95

4.2.2 Isomerization Example: Graphics for Diagnostic 95

4.2.3 Peptides Example: Graphics for Diagnostic 97

4.2.4 Cortisol Assay Example: How to Choose the Variance Function Using Replications 99

4.2.5 Trajectory of Roots of Maize: How to Detect Correlations in Errors 103

4.2.6 What Can We Say About the Experimental Design? 107

4.3 Diagnostics of Model Misspecifications with Tests 110

4.3.1 RIA of Cortisol: Comparison of Nested Models 110

4.3.2 Tests Using Replications 110

4.3.3 Cortisol Assay Example: Misspecification Tests Using Replications 112

4.3.4 Ovocytes Example: Graphics of Residuals and Misspecification Tests Using Replications 112

4.4 Numerical Troubles During the Estimation Process: Peptides Example 114

4.5 Peptides Example: Concluded 118

5 Calibration and Prediction 135

5.2 Problem Formulation 137

5.3 Confidence Intervals 137

5.3.1 Prediction of a Response 137

5.3.2 Calibration with Constant Variances 139

5.3.3 Calibration with Nonconstant Variances 141

5.4 Applications 142

5.4.1 Pasture Regrowth Example: Prediction of the Yield at Time x[subscript 0] = 50 142

5.4.2 Cortisol Assay Example 143

5.4.3 Nasturtium Assay Example 144

6 Binomial Nonlinear Models 153

6.1.1 Assay of an Insecticide with a Synergist: A Binomial Nonlinear Model 153

6.1.2 Vaso-Constriction in the Skin of the Digits: The Case of Binary Response Data 155

6.1.3 Mortality of Confused Flour Beetles: The Choice of a Link Function in a Binomial Linear Model 156

6.1.4 Mortality of Confused Flour Beetles 2: Survival Analysis Using a Binomial Nonlinear Model 158

6.1.5 Germination of Orobranche: Overdispersion 159

6.2 The Parametric Binomial Nonlinear Model 160

6.3 Overdispersion, Underdispersion 161

6.4 Estimation 162

6.4.1 Case of Binomial Nonlinear Models 162

6.4.2 Case of Overdispersion or Underdispersion 164

6.5 Tests and Confidence Regions 165

6.6 Applications 167

6.6.1 Assay of an Insecticide with a Synergist: Estimating the Parameters 167

6.6.2 Vaso-Constriction in the Skin of the Digits: Estimation and Test of Nested Models 171

6.6.3 Mortality of Confused Flour Beetles: Estimating the Link Function and Calculating Confidence Intervals for the LD90 172

6.6.4 Mortality of Confused Flour Beetles 2: Comparison of Curves and Confidence Intervals for the ED50 174

6.6.5 Germination of Orobranche: Estimating Overdispersion Using the Quasi-Likelihood Estimation Method 177

7 Multinomial and Poisson Nonlinear Models 199

7.1 Multinomial Model 199

7.1.1 Pneumoconiosis among Coal Miners: An Example of Multicategory Response Data 200

7.1.2 A Cheese Tasting Experiment 200

7.1.3 The Parametric Multinomial Model 201

7.1.4 Estimation in the Multinomial Model 204

7.1.5 Tests and Confidence Intervals 206

7.1.6 Pneumoconiosis among Coal Miners: The Multinomial Logit Model 208

7.1.7 Cheese Tasting Example: Model Based on Cumulative Probabilities 210

7.2 Poisson Model 221

7.2.1 The Parametric Poisson Model 222

7.2.2 Estimation in the Poisson Model 222

7.2.3 Cortisol Assay Example: The Poisson Nonlinear Model 223.

Notes:

Includes bibliographical references (pages [227]-229) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0387400818

OCLC:

52092090