A first-order approximated jackknifed ridge estimator in binary logistic regression

The purpose of this paper is to solve the problem of multicollinearity that affects the estimation of logistic regression model by introducing first-order approximated jackknifed ridge logistic estimator which is more efficient than the first-order approximated maximum likelihood estimator and has smaller variance than the first-order approximated jackknife ridge logistic estimator. Comparisons of the first-order approximated jackknifed ridge logistic estimator to the first-order approximated maximum likelihood, first-order approximated ridge, first-order approximated r-k class and principal components logistic regression estimators according to the bias, covariance and mean square error criteria are done. Three different estimators for the ridge parameter are also proposed. A real data set is used to see the performance of the first-order approximated jackknifed ridge logistic estimator over the first-order approximated maximum likelihood, first-order approximated ridge logistic, first-order approximated r-k class and first-order approximated principal components logistic regression estimators. Finally, two simulation studies are conducted in order to show the performance of the first-order approximated jackknife ridge logistic estimator.