A Bayesian approach on multicollinearity problem with an Informative Prior

Abstract

Abstract Multicollinearity is a severe problem in multiple regression. High collinearity in some explanatory variables leads to the high standard error estimates. It becomes a problem for the hypothesis test on the slope of regression. The ridge regression is the most popular method used to minimize the standard error estimates. However, the hypothesis testing in regression model has been not solved yet. It does not provide the statistical hypothesis test. Therefore, the alternative method is needed. The method must be able to obtain the parameter estimates with a high level of precision and also facilitates the hypothesis test of regression parameters simultaneously. We proposed the Bayesian method with an informative prior as an alternative solution. The Monte Carlo simulation concludes the Bayesian method outperformed to ridge regression in term of Bias, Mean Square Error and power of the test. Based on the simulation result, the Bayesian method can be used to solve hypothesis testing in regression analysis with multicollinearity problem effectively.