A Theory of Dichotomous Valuation with Applications to Variable Selection

TL;DR

This paper introduces a new valuation framework for variable selection based on expected marginal gains and losses, addressing asymmetry and outperforming existing methods.

Contribution

It develops a novel dichotomous valuation approach with three unbiased solutions, enhancing variable selection techniques in econometrics and statistics.

Findings

Outperforms popular variable selection methods

Reveals new properties of the Shapley value

Provides unbiased solutions for valuation asymmetry

Abstract

An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables, we derive a valuation framework by the expected marginal gain and marginal loss in all potential modeling scenarios. However, marginal gain and loss are not symmetric; thus, we introduce three unbiased solutions. When used in variable selection, our new approaches significantly outperform several popular methods used in practice. The results also explore some novel traits of the Shapley value.