Generalized Correlation Coefficient Based on Log Likelihood Ratio Test Statistic

Department of Informatics and Biomedical Engineering, Asia University, Taichung 41354, Taiwan, ROC
Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung 40306, Taiwan

^a Corresponding author: lhc@asia.edu.tw

Abstract

In this paper, I point out that both Joe’s and Ding’s strength statistics can only be used for testing the pair-wise independence, and I propose a novel G-square based strength statistic, called Liu’s generalized correlation coefficient, it can be used to detect and compare the strength of not only the pair-wise independence but also the mutual independence of any multivariate variables. Furthermore, I proved that only Liu’s generalized correlation coefficient is strictly increasing on its number of variables, it is more sensitive and useful than Cramer’s V coefficient, in other words, Liu generalized correlation coefficient is not only the G-square based strength statistic, but also an improved statistic for detecting and comparing the strengths of deferent associations of any two or more sets of multivariate variables, moreover, this new strength statistic can also be tested by G².