Asymmetric versus symmetric binary regresion: a new proposal with applications

Abstract

The classical logit and probit models allow to explain a dichotomous dependent variable as a function of factors or covariates which can influence the response variable. This paper introduces a new skew-logit link for item response theory by considering the arctan transformation over the scobit logit model, yielding a very flexible link function from a new class of generalized distribution. This approach assumes an asymmetric model, which reduces to the standard logit model for a special case of the parameters that control the distribution’s symmetry. The model proposed is simple and allows us to estimate the parameters without using Bayesian methods, which requires implementing Markov Chain Monte Carlo methods. Furthermore, no special function appears in the formulation of the model. We compared the proposed model with the classical logit specification using three datasets. The first one deals with the well-known data collection widely studied in the statistical literature, concerning with mortality of adult beetle after exposure to gaseous carbon disulphide, the second one considers an automobile insurance portfolio. Finally, the third dataset examines touristic data related to tourist expenditure. For these examples, the results illustrate that the new model changes the significance level of some explanatory variables and the marginal effects. For the latter example, we have also modified the definition of the intercept in the linear predictor to prevent confounding.