Huet S. et al. Statistical Tools for Nonlinear Regression: A Practical Guide With S-PLUS and R Examples

2nd edition. — Springer, 2004. — 248 p. — (Springer Series in Statistics).This second edition contains two additional chapters dealing with binomial, multinomial and Poisson models. If you have to analyze data sets where the response variable is a count or the distribution of individuals in categories, you will be interested in these chapters. Generalized linear models are usually used for modeling these data. They assume that the expected response is linked to a linear predictor through a one-to-one known transformation. We consider extensions of these models by taking into account the cases where such a linearizing transformation does not exist. We call these models generalized nonlinear models. Although they do not fall strictly within the definition of nonlinear regression models, the underlying principles and methods are very similar. In Chapter 6 we consider binomial variables, and in Chapter 7 multinomial and Poisson variables. It is fairly straightforward to extend the method to other distributions such as exponential distribution or gamma distribution.
Maintaining the approach of the first edition, we start by presenting practical examples, and we describe the statistical problems posed by these examples, focusing on those that cannot be analyzed within the framework of generalized linear models. We demonstrate how to solve these problems using nls
2. It should be noted that we do not review the statistical problems related to generalized linear models that have been discussed extensively in the literature. Rather, we postulate that you have some practical experience with data analysis using generalized linear models, and we base our demonstrations on the link between the generalized nonlinear model and the heteroscedastic nonlinear regression model dealt with in Chapter
3. For that purpose, the estimation method based on the quasi-likelihood equations is introduced in Section 3_
3. The use of the nls2’s facilities for analyzing data modeled with generalized nonlinear models is the main contribution of the second edition.
The modifications to Chapters 1 to 5 are minor except for the bootstrap method. Indeed, we propose an extension of the bootstrap method to heteroscedastic models in Section 3_4, and we apply it to calculating prediction and calibration confidence intervals.