Discrete regression models

Abstract

This chapter begins with an analysis of a single explanatory variable that is observed as a dichotomous variable. We discuss the linear probability model and its relationship to the linear discriminant function. We next discuss the logit and probit models and their estimation by maximum likelihood methods based on individual data and minimum χ 2 methods based on grouped data. We next consider the unordered polychotomous variable and the multinomial logit model. We then consider polychotomous variables for ordered and sequential responses. For the analysis of polychotomous variables that are not categorized, we consider the Poisson regression model. Finally, we consider estimation of logit models with randomized data and logit and probit models with panel data. The discussion of the multinomial logit model is continued in Chapter 3. The discussion of discriminant analysis is continued in Chapter 4. The extension of the analysis presented in this chapter to the case of several qualitative (categorical) variables is contained in Chapter 5. What are discrete regression models? By discrete regression models we mean those models in which the dependent variable assumes discrete values. The simplest of these models is that in which the dependent variable y is binary (it can assume only two values, which for convenience and without any loss of generality, we denote by 0 and 1). Numerous examples of this were considered in Chapter 1.