In several previous chapters, we have considered a number of models for different types of responses. We have generalized the linear model by allowing different links and distributions (generalized linear models) and by estimating nonlinear transformations of the explanatory variables (generalized additive models). In all of these models, the explanatory variables, or transformations of these variables, are combined linearly to form a linear predictor. In this chapter, we will consider more complex, nonlinear models and methods for estimating their parameters. Here, the mean of the (continuous) response variable is modeled as a nonlinear function of explanatory variables. As in the linear model, the response is typically assumed to have a normal distribution and a constant variance. In addition to nonlinear models, we will also consider maximum likelihood estimation in situations when the likelihood equations cannot be solved analytically, because the same S-PLUS functions are often involved.
KeywordsNonlinear Model Onset Data Bootstrap Approach Bootstrap Distribution Iterative Numerical Method
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