The estimated parameter of logistic regression model by Markov Chain Monte Carlo method with multicollinearity

Abstract

Markov Chain Monte Carlo (MCMC) method has been a popular method for getting information about probability distribution for estimating posterior distribution by Gibbs sampling. So far, the standard methods such as maximum likelihood and logistic ridge regression methods have represented to compare with MCMC. The maximum likelihood method is the classical method to estimate the parameter on the logistic regression model by differential the loglikelihood function on the estimator. The logistic ridge regression depends on the choice of ridge parameter by using crossvalidation for computing estimator on penalty function. This paper provides maximum likelihood, logistic ridge regression, and MCMC to estimate parameter on logit function and transforms into a probability. The logistic regression model predicts the probability to observe a phenomenon. The prediction accuracy evaluates in terms of the percentage with correct predictions of a binary event. A simulation study conducts a binary response variable by using 2, 4, and 6 explanatory variables, which are generated from multivariate normal distribution on the positive and negative correlation coefficient or called multicollinearity problem. The criterion of these methods is to compare by a maximum of predictive accuracy. The outcomes find that MCMC satisfies all situations.