Comparison of link functions for the estimation of logistic ridge regression: an application to urine data

Abstract

The logistic regression model is applied in situations when the response variable is of binary nature and follows the Bernoulli distribution. The maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the logistic regression. However, in the presence of multicollinearity, MLE is not a reliable estimation method due to its large variance and high standard errors. To overcome this problem, we consider the logistic ridge regression estimator (LRRE) under different link functions. Moreover, we also propose some ridge parameters for the LRRE and compare the performance of these ridge parameters with the available best ones. A Monte Carlo simulation study and a real dataset are considered for the evaluation of LRRE using scalar mean squared error as performance evaluation criteria. The simulation results indicate the superiority of the LRRE with a specified link function over the MLE in the presence of multicollinearity. From the simulation and real data application results, it is observed that the LRRE with ridge parameters k_8 and k_9 under logit and probit link functions is superior to the other ridge parameters with other link functions.

Keywords:

• Link functions
• Logistic regression
• Logistic ridge regression estimator
• MLE
• Multicollinearity