Quantifying direct associations between variables

Correctly quantifying the direct association between variables based on observed data is a valuable topic to study. On the one hand, many traditional methods can only measure the linear direct association. On the other hand, certain existing measures of direct association between two variables suffer an instability problem when a parent variable has a strong influence on both variables. To solve these issues, we propose a measure, namely the independent conditional mutual information (ICMI), to quantify the direct association between two variables in a three-variable network. Additionally, we use simulation data to numerically compare the stability and reliability of the ICMI with those of other measures of direct association under different conditions. The numerical results show that ICMI performs more stably in many cases than the known measures such as unique information, conditional mutual information, and partial correlation. The statistical power results show that ICMI is more reliable for different forms of function. We further use our measure to analyze a network consisting of family finance, social security, and the residence of senior citizens.