The three remaining chapters of this book are concerned with probability models. Just like regression models – indeed like any econometric model – these models determine the probability density function of the dependent variable; the difference lies in the role of the random variation. In regression models this is cursorily treated by the introduction of the disturbance, which is a nuisance variable characterized by nuisance parameters; to eliminate it, and let y take its expected value, is the ideal, or at any rate the standard, case for interpretation and discussion. The interest of the analysis lies precisely in this expected value, which is the “systematic component” of the model, and much ingenuity is spent on its design. In probability models, in contrast, the random variation is the essential phenomenon, and in the construction of the model it is the probability mechanism rather than the systematic component that is elaborated. Probability models are designed to describe individual variation, and they have no immediate bearing on aggregate data. Since they usually account fully for the observed variation there is no need to allow explicitly for neglected factors or other imperfections.

These general characteristics will be demonstrated in the sequel. Like the regression model, most probability models have their origin in biology and in medical research. Numerous studies of transport choice, of the demand for durables, and of occupational choice reflect a lively interest in their application to microeconomic data.