A new Bayesian ridge estimator for logistic regression in the presence of multicollinearity

Abstract

This research introduces the Bayesian schemes for estimating logistic regression parameters in the presence of multicollinearity. The Bayesian schemes involve the introduction of a prior together with the likelihood which resulted in the posterior distribution that is not tractable, hence the use of a numerical method i.e Gibbs sampler. Different levels of multicollinearity were chosen to be p = 0.80‚0.85‚0.90‚0.95‚0.99and 0.999to accommodate severe, very severe and nearly perfect state of multicollinearity with sample sizes taken as 10,20,30,50,100,200,300 and 500.Different ridge parameters k were introduced to remedy the effect of multicollinearity .The explanatory variables used were 3 and 7. Model estimation was carried out using Bayesian approach via the Gibbs sampler of Markov Chain Monte Carlo Simulation. The means square error MSE of Bayesian logistic regression estimation was compared with the frequentist methods of the estimation. The result shows a minimum mean square error with the Bayesian scheme compared to the frequentist method.