Statistical Tools for Nonlinear Regression

A Practical Guide With S-PLUS and R Examples
2. Auflage 2004
ISBN: 978-0-387-40081-5
Verlag: Springer

Buch, Englisch, 234 Seiten, Format (B × H): 157 mm x 240 mm, Gewicht: 1170 g

Reihe: Springer Series in Statistics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Huet, Sylvie

Jolivet, Emmanuel

Bouvier, Anne

Poursat, Marie-Anne

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizinische Mathematik & Informatik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software

Inhaltsverzeichnis

Nonlinear Regression Model and Parameter Estimation.- Accuracy of Estimators, Confidence Intervals and Tests.- Variance Estimation.- Diagnostics of Model Misspecification.- Calibration and Prediction.- Binomial Nonlinear Models.- Multinomial and Poisson Nonlinear Models.