The random utility model described in Chapter 1 is one of two essential building blocks that form the foundation for modeling ordered choices. The second fundamental pillar is the model for binary choices. The ordered choice model that will be the focus of the rest of this book is an extension of a model used to analyze the situation of a choice between two alternatives – whether the individual takes an action or does not, or chooses one of two elemental alternatives, and so on. This chapter will develop the standard model for binary choices in considerable detail. Many of the results analyzed in the chapters to follow will then be straightforward extensions.

There are numerous surveys available, including Amemiya (1981), Greene (2008a, Ch. 23) and several book-length treatments such as Cox (1970) and Collett (1991). Our interest here is in the aspects of binary choice modeling that are likely to reappear in the analysis of ordered choices. We have therefore bypassed several topics that do appear in other treatments, notably semiparametric and nonparametric approaches, but whose counterparts have not yet made significant inroads in ordered choice modeling. (Chapter 12 does contain some description of a few early entrants to this nascent literature.) This chapter also contains a long list of topics related to binary choice modeling, such as fit measures, multiple equation models, sample selection, and many others, that are useful as components or building blocks in the analysis of ordered choices. Our intent with this chapter is to extend beyond conventional binary choice modeling, and provide a bridge to the somewhat more involved models for ordered choices.