Logit, Probit and Tobit

Two convenient classifications for variables which are not amenable to treatment by the principal tool of econometrics, regression analysis, are quantal responses and limited responses. In the quantal response (all or nothing) category are dichotomous, qualitative and categorical outcomes, and the methods of analysis identified as probit and logit are appropriate for these variables. Illustrative applications include decisions to own or rent, choice of travel mode, and choice of professions. The limited response category covers variables which take on mixtures of discrete and continuous outcomes, and the prototypical model and analysis technique is identified as tobit. Examples are samples with both zero and positive expenditures on durable goods, and models of markets with price ceilings including data with both limit and non-limit prices. While the tobit model evolved out of the probit model and the limited and quantal response methods share many properties and characteristics, they are sufficiently different to make separate treatment more convenient.