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The probit and logit models are regression models for situations in which the dependent variable is a discrete outcome, such as a “yes” or “no” decision. For example, an analyst might be interested in examining the effect of 8th grade math achievement on graduation from high school. The probit model examines the effects of a set of independent variables (Xs) on the probability of success or failure on the dependent variable, P(Y). The observed occurrence of a given choice (i.e., success or failure) is taken as an indicator of an underlying, unobservable continuous variable, which may be called “propensity to choose a given alternative.” Such a variable is characterized by the existence of a threshold defining the position at which one switches from one alternative to another. For example, a student’s propensity to graduate from high school may be directly related to his or her 8th grade math achievement, which in turn may depend on family background and motivation factors. Whether a student graduates is likely to depend on whether his or her 8th grade math achievement does or does not exceed his or her threshold. This threshold, which differs across students with the same family background and motivation factors plays the role of a random disturbance.
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