Hierarchical Partitioning

Many users of regression methods are attracted to the notion that it would be valuable to determine the relative importance of independent variables.This article demonstrates a method based on hierarchies that builds on previous efforts to decompose R 2 through incremental partitioning.The standard method of incremental partitioning has been to follow one order among the many possible orders available.By taking a hierarchical approach in which all orders of variables are used, the average independent contribution of a variable is obtained and an exact partitioning results.Much the same logic is used to divide the joint effect of a variable.The method is general and applicable to all regression methods, including ordinary least squares, logistic, probit, and log-linear regression.A validation test demonstrates that the algorithm is sensitive to the relationships in the data rather than the proportion of variability accounted for by the statistical model used.