Distance Correlation

In credit analytics, identifying meaningful relationships among customer attributes is essential for building robust risk models and gaining insight into borrower behavior. Traditional measures such as Pearson’s correlation coefficient detect only linear relationships and potentially ignore important nonlinear dependencies that can exist within financial data.

Distance Correlation is a more versatile metric that detects any form of statistical dependence between variables (linear or nonlinear). Unlike Pearson’s correlation, distance correlation equals zero if and only if the variables are statistically independent. Therefore, distance correlation is an effective tool for uncovering complex interactions in multidimensional datasets.

This case study uses bankloan.sav, a sample dataset that contains financial and demographic information for 850 individuals. To demonstrate the value of distance correlation, the focus is on the following selected subset of four key variables:
  • Age in years
  • Years with current employer
  • Household income (in thousands)
  • Debt-to-income ratio (×100)

These variables are commonly used in credit risk assessment and financial profiling. Pairwise distance correlations are computed among the variables to identify the strength and nature of inter-variable relationships. The objective is to detect both linear and nonlinear associations that might be influential but not readily observable through conventional techniques.

By isolating the strongest dependencies among these core variables, this analysis aims to provide deeper insight into borrower characteristics that might affect creditworthiness and loan decision-making.

Conceptual Overview of Distance Correlation

In statistical analysis, understanding the relationship between two variables is fundamental. Traditional methods, such as Pearson’s correlation coefficient, are limited to capturing linear associations. However, real-world data, especially in the context of financial behavior, often exhibit nonlinear or complex dependencies that linear methods might fail to detect.

Distance Correlation is a more generalized statistical measure that is designed to address this limitation. Unlike Pearson’s correlation, which quantifies only linear association, distance correlation can detect both linear and nonlinear relationships between two variables or multivariate data structures. This makes it valuable when you analyze behavioral or demographic variables where patterns may not follow a straight-line relationship.

At a conceptual level, the process involves the following steps:
Pairwise comparison of observations
Distance correlation begins by computing the pairwise distances between all observations within each variable. This quantifies how different each case is from every other case, based on the variable in question.
Assessment of joint variability
The method then examines whether pairs of observations that are similar (or dissimilar) in one variable also tend to be similarly related in the second variable. This step captures the essence of statistical dependence, regardless of the form it takes.
Derivation of a dependency score
The resulting value, ranging from 0 to 1, reflects the strength of association. A value of 0 indicates complete independence, while a value closer to 1 implies strong dependency of any kind (not restricted to linear).

In summary, distance correlation serves as a comprehensive measure of dependence, capable of identifying relationships that otherwise remain undetected using traditional correlation approaches. In financial datasets such as bankloan.sav, where variables like income, debt, and credit rating might interact in complex ways, this method provides a more robust foundation for understanding inter-variable dynamics.