Exploring and Comparing Pairwise Nonlinear Association Measures for Continuous

There are many linear and nonlinear measures of association between two continuous pairwise variables. They are used to indicate the strength of the relationship between the two variables. The question thus arises as to which of these measures should be used to explore relationships between two variables in general. The identification of linear and/or nonlinear relationship between two variables can help to avoid problems within a regression framework. The objective of this paper is to examine alternative measures of association that could be employed as a replacement or in conjunction with, standard linear correlation coefficients. The results lead us to conclude that the maximum correlation measure is particularly useful, and capable of detecting linear and nonlinear associations between two continuous variables, while also being relatively computationally efficient. It can be utilized in exploratory analysis and in a modern regression framework.