Relative Importance and Value

Abstract

Three axioms provide a formal definition of relative importance in a statistical or econometric model by identifying the likelihood that any ordering of independent variables is correctly ordered with respect to their relative importance. The expected contribution to model performance of independent variables with respect to this distribution is the proportional marginal decomposition of model performance with respect to the performance measure. Decomposition components are shown to be equal to the proportional value (Ortmann (2000), Feldman (1999, 2002)) of an appropriately constructed cooperative game. Also addressed are admissibility criteria for measures of relative importance, other measures of relative importance, the entropy of cooperative games and extensions and limitations.

Keywords: Attribution, joint effects, random order model, relative importance, Shapley value, proportional value and variance decomposition

JEL Classification: C10, C52, C71, D00, D81, G11