Determination of the final estimators and their distributions proposed in the ridge regresion

Multicollinearity problem is one of the most common problems in regression analysis. There are many ways to solve this problem. Principal Components Regression and Ridge Regression (RR) method are some of the most commonly used methods. There are many studies in the literature using the RR method. In this study, the effects of the multicollinearity problem on the Maximum Likelihood Estimator (MLE) were analyzed using a binary logistic regression model. Here, the aim is to estimate the optimal Ridge parameter that gives the smallest Mean Square Error (MSE) with different sample size, different degrees of multicollinearity, and different number of independent variables. In the study, 15 different Ridge parameter estimators mentioned in the literature were included and a Monte Carlo simulation study was designed to evaluate their performance. As a performance criterion, not only the MLE, but also the conformity of the produced parameter values to the normal distribution and the criteria for producing values between 0-10 were considered for a total of 175 different situations. With the results obtained, the most effective ridge parameter estimators were determined in the binary logistic regression analysis.