Recursive Random Binning to Detect and Display Pairwise Dependence

ABSTRACT Random binnings generated via recursive binary splits are introduced as a way to detect, measure the strength of, and to display the pattern of association between any two variates, whether one or both are continuous or categorical. This provides a single approach to ordering large numbers of variate pairs by their measure of dependence and then to examine any pattern of dependence via a common display, the departure display (coloring bins by a standardized Pearson residual). Continuous variates are first ranked and their rank pairs binned. The Pearson's goodness of fit statistic is applicable but the classic approximation to its null distribution is not. Theoretical and empirical investigations motivate several approximations, including a simple approximation with real‐valued, yet intuitive, degrees of freedom. Alternatively, applying an inverse probability transform from the ranks before binning returns a simple Pearson statistic with the classic degrees of freedom. Recursive random binning with different approximations is compared to recent grid‐based methods on a variety of non‐null dependence patterns; the method with any of th