The Comparison of Classical and Bayesian Bivariate Binary Logistic Regression Prediction for Unbalanced Response (Case Study: Customers of Antivirus Software 'X' Company)

Abstract

The purpose of this study was to compare the performance of classical bivariate binary logistic regression and Bayesian bivariate binary logistic regression. The sizes of sample used in research were small and large sample. The size of the small sample was 200 and the large sample was 10000 samples. Parameter estimation method that often used in logistic regression modeling is maximum likelihood which is called the classical approach. However, using a maximum likelihood parameter estimation has several weaknesses. When the number of sample is small and the dependent variable is unbalanced, bias parameters are frequently obtained. Nevertheless, when the sample size is too large, it has propensity to reject H0. As the solution, the use of Bayesian approach to overcome the small sample size problem and unbalanced dependent variable is suggested. The case study carried out in this research was customer loyalty of 'X' Company. This study used two dependent variables, i.e. Customer Defections and Contract Answer. Initial information on the number of consumers who defected and not defected was unbalanced, likewise for the Contract Answers. Based on the comparison of classical and Bayesian bivariate binary logistic regression prediction, Bayesian method was evidenced to yield better performance compared to classical method.