Advanced Regression and Alternatives

Abstract

Linear regression models are not the only curve-fitting methods in wide use. Also, these methods are not useful for analyzing data for categorical responses. In this chapter, so-called “kriging” models, “artificial neural nets” (ANNs), and logistic regression methods are briefly described. ANNs and logistic regression methods are relevant for categorical responses. Each of the modeling methods described here offers advantages in specific contexts. However, all of these alternatives have a practical disadvantage in that formal optimization must be used in their fitting process.

Section 2 discusses generic curve fitting and the role of optimization. Section 3 briefly describes kriging models, which are considered particularly relevant for analyzing deterministic computer experiments and in the context of global optimization methods. In Section 3, one type of neural net is presented. Section 4 defines logistic regression models including so-called “discrete choice” models. In Section 5, examples illustrate logit and probit discrete choice models.