GL⁺ and GL^- regressions

Regression analysis for which the dependent variable is binary has typically been modelled by the Logit and the Probit models. We propose two new regression models GL⁺ and GL^- regressions based on the function of [5, 6] and the function of [4] for binary dependent variables. These models allow for possible asymmetries in the underlying mechanisms governing the binary output variable and make allowance for the independent variables to determine its shape. Our simulation results of the univariate regression indicate that the expected average mean square error is smallest for the GL⁺ model than the Logit or the Probit models. On the other hand, the expected correlation between the outcome and the predicted probabilities is greatest for the GL^- model than the Logit and Probit models. Therefore, the GL⁺ having higher predictive power over the Logit and Probit, should be more useful to researchers, economists and scientists that rely on the Logit and Probit models for their work.