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Logistic and probit models are the most popular regression models for binary outcomes. A simple robust alternative is the robit model, which replaces the underlying normal distribution in the probit model with a Student’s t distribution. The heavier tails of the t distribution (compared with the normal distribution) mean that model outliers are less influential. Robit regression models can be fit as generalized linear models with the link function defined as the inverse cumulative t distribution function with a specified number of degrees of freedom; they have been advocated as being particularly suitable for estimating inverse-probability weights and propensity scoring more generally. Here we describe a new command, robit , that implements robit regression in Stata.
Newson et al. (Fri,) studied this question.