Particle swarm optimization based ridge logistic estimator

Abstract

Logistic regression is a commonly used method when the dependent variable is dichotomous. However, it is known that the presence of multicollinearity significantly affects maximum likelihood estimations in logistic regression models. In this case, unstable estimates, in other words, parameter estimates with high variances, are obtained. To deal with this problem, a ridge-type estimator was proposed by Schaefer et al. Ridge regression shrinks the maximum likelihood estimation vector of regression coefficients, allowing a bias but providing a smaller variance. However, the selection of shrinkage parameter λ in ridge logistic regression is an important matter. In this study, a new alternative approach based on particle swarm optimization is introduced to obtain an optimal shrinkage parameter. The performance of the new approach is evaluated by simulation studies and a real dataset application.