Statistical Tools for Nonlinear Regression

Transcription

1 S. Huet A. Bouvier M.-A. Poursat E. Jolivet Statistical Tools for Nonlinear Regression A Practical Guide With S-PLUS and R Examples Second Edition Springer

2 Preface to the Second Edition Preface to the First Edition XI XIII 1 Nonlinear Regression Model and Parameter Estimation Examples Pasture Regrowth: Estimating a Growth Curve Radioimmunological Assay of Cortisol: Estimating a Calibration Curve Antibodies Anticoronavirus Assayed by an ELISA Test: Comparing Several Response Curves Comparison of Immature and Mature Goat Ovocytes: Comparing Parameters Isomerization: More than One Independent Variable The Parametric Nonlinear Regression Model Estimation Applications Pasture Regrowth: Parameter Estimation and Graph of Observed and Adjusted Response Values Cortisol Assay: Parameter Estimation and Graph of Observed and Adjusted Response Values ELISA Test: Parameter Estimation and Graph of Observed and Adjusted Curves for May and June Ovocytes: Parameter Estimation and Graph of Observed and Adjusted Volume of Mature and Immature Ovocytes in Propane-Diol Isomerization: Parameter Estimation and Graph of Adjusted versus Observed Values Conclusion and References Using nls2 18

3 Accuracy of Estimators, Confidence Intervals and Tests Examples Problem Formulation Solutions Classical Asymptotic Results Asymptotic Confidence Intervals for A Asymptotic Tests of A = Ao against A ^ Ao Asymptotic Tests of A6 = Lo against AO ^ L Bootstrap Estimations Applications Pasture Regrowth: Calculation of a Confidence Interval for the Maximum Yield Cortisol Assay: Estimation of the Accuracy of the Estimated Dose D ELISA Test: Comparison of Curves Ovocytes: Calculation of Confidence Regions Isomerization: An Awkward Example Pasture Regrowth: Calculation of a Confidence Interval for A = exp Conclusion Using nls2 49 Variance Estimation Examples Growth of Winter Wheat Tillers: Few Replications Solubility of Peptides in Trichloacetic Acid Solutions: No Replications Parametric Modeling of the Variance Estimation Maximum Likelihood Estimation Quasi-Likelihood Estimation Three-Step Estimation Tests and Confidence Regions The Wald Test The Likelihood Ratio Test Bootstrap Estimations Links Between Testing Procedures and Confidence Region Computations Confidence Regions Applications Growth of Winter Wheat Tillers Solubility of Peptides in Trichloacetic Acid Solutions Using nls2 83

4 VII Diagnostics of Model Misspecification Problem Formulation Diagnostics of Model Misspecincations with Graphics Pasture Regrowth Example: Estimation Using a Concave-Shaped Curve and Plot for Diagnostics Isomerization Example: Graphics for Diagnostic Peptides Example: Graphics for Diagnostic Cortisol Assay Example: How to Choose the Variance Function Using Replications Trajectory of Roots of Maize: How to Detect Correlations in Errors What Can We Say About the Experimental Design? Diagnostics of Model Misspecincations with Tests RIA of Cortisol: Comparison of Nested Models Tests Using Replications Cortisol Assay Example: Misspecification Tests Using Replications Ovocytes Example: Graphics of Residuais and Misspecification Tests Using Replications Numerical Troubles During the Estimation Process: Peptides Example Peptides Example: Concluded Using nls2 119 Calibration and Prediction Examples Problem Formulation Confidence Intervals Prediction of a Response Calibration with Constant Variances Calibration with Nonconstant Variances Applications Pasture Regrowth Example: Prediction of the Yield at Time x 0 = Cortisol Assay Example Nasturtium Assay Example i References Using nls2 145 Binomial Nonlinear Models Examples Assay of an Insecticide with a Synergist: A Binomial Nonlinear Model Vaso-Constriction in the Skin of the Digits: The Case of Binary Response Data 155

5 VIII Contents Mortality of Confused Flour Beetles: The Choice of a Link Function in a Binomial Linear Model Mortality of Confused Flour Beetles 2: Survival Analysis Using a Binomial Nonlinear Model Germination of Orobranche: Overdispersion The Parametric Binomial Nonlinear Model Overdispersion, Underdispersion Estimation Case of Binomial Nonlinear Models Case of Overdispersion or Underdispersion Tests and Confidence Regions Applications Assay of an Insecticide with a Synergist: Estimating the Parameters Vaso-Constriction in the Skin of the Digits: Estimation and Test of Nested Models Mortality of Confused Flour Beetles: Estimating the Link Function and Calculating Confidence Intervals for the LD Mortality of Confused Flour Beetles 2: Comparison of Curves and Confidence Intervals for the ED Germination of Orobranche: Estimating Overdispersion Using the Quasi-Likelihood Estimation Method Using nls Multinomial and Poisson Nonlinear Models Multinomial Model Pneumoconiosis among Coal Miners: An Example of Multicategory Response Data A Cheese Tasting Experiment The Parametric Multinomial Model Estimation in the Multinomial Model Tests and Confidence Intervals Pneumoconiosis among Coal Miners: The Multinomial Logit Model Cheese Tasting Example: Model Based on Cumulative Probabilities Using nls Poisson Model The Parametric Poisson Model Estimation in the Poisson Model Cortisol Assay Example: The Poisson Nonlinear Model Using nls2 225

6 IX References 227 Index 231 \