Scobit: An Alternative Estimator to Logit and Probit

Abstract

Logit and probit, the two most common techniques for estimation of models with a dichotomous dependent variable, impose the assumption that individuals with a probability of .5 of choosing either of two alternatives are most sensitive to changes in independent variables. This assumption is imposed by the estimation technique because both the logistic and normal density functions are symmetric about zero. Rather than let methodology dictate substantive assumptions, I propose an alternative distribution for the disturbances to the normal or logistic distribution. The resulting estimator developed here, scobit (or skewed-logit), is shown to be appropriate where individuals with any initial probability of choosing either of two alternatives are most sensitive to changes in independent variables. I then demonstrate that voters with initial probability of voting of less than .5 are most sensitive to changes in independent variables. And I examine whether individuals with low levels of education or high levels of education are most sensitive to changes in voting laws with respect to their probability of voting.