A new method for choosing the biasing parameter in ridge estimator for generalized linear model

Abstract

Multicollinearity problem arises frequently in several modern applications, such as chemometrics, biology, and other scientific fields. The common feature of the multicollinearity problem is that a large number of predictors are highly correlated. Generalized linear model is a powerful and a popular approach for modeling a large variety of regression data. It is well known that the existence of multicollinearity can inflate the variance of the maximum likelihood estimator. To reduce the effects of multicollinearity, the ridge estimator has been efficiently demonstrated to be an attractive method. However, the choice of the biasing parameter of the ridge estimator is critical. Our aim is to efficiently estimate such a biasing parameter. Towards this aim, a kidney-inspired algorithm, which is a population-based algorithm inspiring by the kidney process in the human body, is proposed. Extensive comparisons with different classical biasing parameter estimating methods are conducted through simulation and real data application. The results demonstrate that our proposed approach is able to find the best biasing parameter value with high prediction accuracy. Further, the results indicate that the performance of our proposed approach is superior to that of other competitor methods.