The qualitative response model or discrete variables model is the statistical model that specifies the probability distribution of one or more discrete depend­ent variables as a function of independent variables. It is analogous to a regression model in that it characterizes a relationship between two sets
of variables, but differs from a regression model in that not all of the information of the model is fully captured by specifying conditional means and variances of the dependent variables, given the independent variables. The same remark holds for the models of the subsequent two sections.

The qualitative response model originated in the biometric field, where it was used to analyze phenomena such as whether a patient was cured by a medical treatment, or whether insects died after the administration of an insecticide. Recently the model has gained great popularity among econometricians, as extensive sample survey data describing the behavior of individuals have become available. Many of these data are discrete. The following are some examples: whether or not a consumer buys a car in a given year, whether or not a worker is unemployed at a given time, how many cars a household owns, what type of occupation a person’s job is considered, and by what mode of transportation during what time interval a commuter travels to his workplace. The first two examples are binary; the next two, multinomial; and the last, multivariate.

In this book we consider only models that involve a single dependent variable. In Section 13.5.1 we examine the binary model, where the de­pendent variable takes two values, and in Section 13.5.2 we look at the multinomial model, where the dependent variable takes more than two values. The multivariate model, as well as many other issues not dealt with here, are discussed at an introductory level in Amemiya (1981) and at a more advanced level in Amemiya (1985, chapter 9).

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