Improved Ridge Regression Estimators For The Logistic Regression Model

In the multiple linear regression model, we usually assume that the explanatoryvariables are independent and the dependent variables are continuous. However, inpractice, there may be multicollinearity between the independent variables and thedependent variables are dichotomous discrete. For the problem of multicollinearity,ridge estimation is the most popular method. And Logistic regression model is awell-known method for dichotomous data. This article will apply the ridgeestimator to the Logistic regression model, it has strong research significance intheory and important value in practice.This paper mainly studies the binary Logistic regression model, and proposedthree Logistic regression parameter estimators: unrestricted estimator, restrictedestimator and preliminary test estimator when linear regression parameters may besome constraints. Ridge estimators are combined with three Logistic regressionestimators because of multicollinearity, correspondingly we propose three Logisticridge regression parameter estimation methods: unrestricted ridge estimator,restricted ridge estimator and preliminary test ridge estimator. Furthermore, thispaper studies the asymptotic properties of the three ridge estimation on the secondbias, and gives three ridge estimator mean square error matrix and quadratic riskfunction.In this paper, three ridge estimate methods are compared in numerical formbased on the risk function. The first compared is between three ridge regressionestimators and three regression estimators, mainly takes on the the risk function ofridge regression estimator with respect to the partial derivative of ridge parameterapproach. Ultimately determine the range of ridge parameters and in which Logisticregression estimators are superior to Logistic regression estimators. The secondcompared is among three kinds of ridge regression estimates. The main method is tomake the subtraction between the ridge estimators. And the ridge estimator having asmall function is more excellent, and we get the optimal estimator range of threeridge estimators. According to data about liver from India, combining with SASsoftware, the Logistic ridge estimation is simulated. Finally, we find the right ridgeparameters, make Logistic ridge estimation is superior to the Logistic estimationwhen independent variables are with multicollinearity.