Addressing multicollinearity in general linear model: A novel approach for ridge parameter with performance comparison

The problem of ill-conditioned data or multicollinearity is common in regression modelling. The problem results in imprecise parameter estimation which leads to inability of gauging true impact of explanatory variables on the response. Also, due to strong multicollinearity, standard errors of parameter estimates get inflated leading to wider confidence intervals and hence increased risk of type-II error. To handle the problem, different approaches have been proposed in literature. Primarily, such techniques penalize the coefficient estimates in one way or other. Ridge regression is one of the most applied among such techniques. In ridge regression, a penalty term is added in the objective function of the general linear model. That penalty term introduces a small amount of bias in parameter estimates with an objective to decrease the mean square error. In the current article, some new choices for ridge constant are proposed. The performance of proposed ridge choices are compared through Monte Carlo simulations under different scenarios, using mean square error as measure of performance. The simulation results indicate that the proposed ridge estimator performs better than existing ridge constants, in most cases catering for severity of multicollinearity, number of explanatory variables, sample size and error variance structure. The simulation results were further corroborated by comparing performance of proposed ridge penalties using two real-life applications.