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 R2 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 loglinear 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.