Introduction

In Chapters 4 and 5, we presented a selection of case studies with the goals of emphasizing the application and of illustrating higher order approximations as an adjunct to inference. The selection of our case studies was informed by these twin goals – we used relatively small data sets, and our discussion was sometimes rather remote from the original application.

In this chapter we present more detailed analyses of data collected to address particular scientific problems, with emphasis on the modelling and the conclusions. While we use higher order methods as an adjunct to the analysis, the main focus is on the data analysis rather than the inference methods. These case studies are a subset of examples that have crossed our desks in collaborative work. In Chapter 7 we take the opposite approach, and illustrate a selection of inference problems that are amenable to higher order approximation.

Sections 6.2 and 6.3 present slightly non-standard analysis of binary data; in the first case a natural model leads to the complementary log–log link, and in the second we consider conditional assessment of the binary model, eliminating the parameters in the binary regression by conditioning on the sufficient statistic. In Section 6.4 we present detailed analysis of a published set of herbicide data, with particular emphasis on the nlreg package of the hoa bundle. This package provides an extensive set of diagnostics and plots that are a useful adjunct to first order analysis, as well as providing an implementation of higher order approximations.