ABSTRACT
In this chapter we build on the introduction to parametric modelling presented in Section 4 of Chapter 1. As well as providing a historical overview, much of the material presented here serves as an underpinning to the parametric analyses presented in later chapters. Our overarching framework is likelihood. We have seen in Chapter 3 that, in the likelihood setting, the missing at random (MAR) assumption, together with parameter separability, is a sufficient condition for ignorability of the missing data mechanism. One implication of this is that, under the MAR assumption, likelihood-based analyses can proceed in a conventional way, and so fall into the much broader category of model construction in a general sense. The main implications of missing data then lie with models that incorporate NMAR mechanisms and the focus in this chapter is on such settings. In one form or another, such models jointly represent both the outcome and the missing value process. In practice, such models tend to be used as part of a sensitivity analysis in which they parameterize departures from the MAR assumption (see for example Part V of this volume). A key to their success therefore lies in their ability to represent such departures in a substantively meaningful and transparent
there has been much methodological development of such models, not all reflects this important need.
