qad: An R-package to detect asymmetric and directed dependence in bivariate samples

Abstract

Correlations belong to the standard repertoire of ecologists for quantifying the strength of dependence between two random variables. Classical dependence measures are usually not capable of detecting non-monotonic or non-functional dependencies. Furthermore, they completely fail to detect asymmetry and direction in dependence, which exist in many situations and should not be ignored. In this paper, we present qad (short for quantification of asymmetric dependence), a nonparametric statistical method to quantify directed and asymmetric dependence of bivariate samples. Qad is applicable in general (e.g. linear, non-linear, or non-monotonic) situations, is sensitive to noise in data, exhibits a good small sample performance, detects asymmetry in dependence, shows high power in testing for independence, requires no assumptions regarding the underlying distribution of the data and reliably quantifies the information gain/predictability of quantity Y given knowledge of quantity X, and vice versa (i.e. q(X,Y) (Formula presented.) q(Y,X)). Here, we briefly recall the methodology underlying qad, introduce the functions of the R-package qad, which returns estimates for the measures (Formula presented.) denoting the directed dependence of (Formula presented.) on (Formula presented.) (or, equivalently, the influence of (Formula presented.) on (Formula presented.)), (Formula presented.) the directed dependence of (Formula presented.) on (Formula presented.), (Formula presented.) the asymmetry in dependence. Furthermore, qad can be used to predict Y given knowledge of X, and vice versa. Additionally, we compare empirical performance of qad with that of seven other well established measures and demonstrate the applicability of qad on ecological datasets. We illustrate that direction and asymmetry in dependence are universal properties of bivariate associations. Qad thus provides additional information gain and avoids model bias and will therefore advance and facilitate the understanding of ecological systems.