A Theory of Dichotomous Valuation with Applications to Variable Selection

An econometric or statistical model may undergo a marginal gain when a new variable is admitted, and a marginal loss if an existing variable is removed. The value of a variable to the model is quantified by its expected marginal gain and marginal loss. Assuming the equality of opportunity, we derive a few formulas which evaluate the overall performance in potential modeling scenarios. However, the value is not symmetric to marginal gain and marginal loss; thus, we introduce an unbiased solution. Simulation studies show that our new approaches significantly outperform a few practice-used variable selection methods.