TABLE OF CONTENTS Mainstream models developed over the years in various scientific and engineering disciplines were introduced in Chapter 2. All models had monotone convex/concave relationship with the response. In Chapter 3 we elaborated in further detail on three of the models, and derived important observations that are valid for all.
First, a particular classification has emerged of the components of variation shared by the models. These include two components of random variation, represented by two error terms, and a component of systematic variation, transmitted to the response via the linear predictor. With regard to the former components, earlier related to as the dual-error structure, it has become clear that one error term is associated with the linear predictor (and characterized as an additive error term), and another is directly associated with the response. The latter error can be assumed to exist irrespective of whether the linear predictor (with its associated additive random error) varies or is constant. Furthermore, current engineering and scientific models, reviewed in Chapter 2, seem to regard this error (either explicitly or implicitly) as additive in the original scale of the response or as additive in the log-transformed scale. As will be shown later in this chapter, most often these two seemingly different definitions of the error are approximately equivalent.
Secondly, a particular hierarchical classification has emerged of the functions that relate the linear predictor (with the associated additive random error) to the response. This classification has been captured by the "Ladder of fundamental uniformly convex/concave functions".
