New estimators for the probit regression model with multicollinearity

Abstract

The probit regression model (PRORM) aims to model a binary response with one or more explanatory variables. The parameter of the PRORM is estimated using an estimation method called the maximum likelihood (ML), like a logistic model. When multicollinearity exists, ML performance suffers. In this case, we propose two estimators (the probit modified ridge and probit Dawoud−Kibria estimators) for the PRORM. To assess the proposed estimators' superiority, we have some theoretical comparisons of the proposed probit Dawoud−Kibria estimator with the ML, probit ridge, probit Liu, and probit modified ridge estimators via the mean squared error. A simulation study is offered with several criteria for examining the effectiveness of the suggested estimators' efficiency. In addition, a real-life application is applied to confirm the proposed estimators’ efficiency. The results of the simulation and application indicated that the proposed estimators outperformed ML and probit ridge estimators, especially when there was a strong correlation between the explanatory variables.

Keywords

• Probit model
• Probit Dawoud−Kibria estimator
• Probit Ridge estimator
• Probit Liu estimator