A simple nonparametric index of bivariate association for environmental data exploration. (October 2017) - Vetrova, Varvara; Bardsley, Earl
Abstract: A purely data-based index for detecting bivariate association is proposed for preliminary data exploration when seeking to model a dependent variable, associated with a possibly large number of independent variables. No particular form of association between the dependent and independent variables is assumed. The proposed bivariate association index is the valuep, which is the probability that a scatter plot created by an X -randomization will generate a smaller mean nearest neighbour distance. The rationale is that randomizing an existing X-Y association will result in a scatter plot which will usually have a greater mean nearest neighbour distance. The process is then repeated for all other independent variables to give a specificp for each one. A subset of potentially informative independent variables is then obtained by noting all those with lowp values, but just how smallp should be is left to the user. Highlights: A purely nonparametric index is proposed for general bivariate association. The index reflects nearest neighbour distances increasing if an existing association is disrupted by randomization. No estimation of marginal distributions or other continuous functions are required. No assumption is made concerning physical or stochastic processes giving rise to the data.