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. We quantify the value of a variable to the model by its expected marginal gain and expected marginal loss in all modeling scenarios. Assuming the equality of opportunity among all candidate variables, we derive a few formulas which evaluate the overall performance of each variable 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 bias-adjusted approaches significantly outperform a few variable selection methods used in practice. The tools employed are concepts from cooperative game theory, and the results explore several novel features of the Shapley value . We even bridge the Shapley value and the Banzhaf value with binomial distributions .
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 few evaluation methodologies by the expected marginal gain and marginal loss in all potential modeling scenarios. However, marginal gain and loss are not symmetric ; thus, we introduce several unbiased solutions . Simulation studies show that our approaches significantly outperform a few variable selection methods used in practice. The results also explore several novel features of the Shapley value .
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We quantify the value of a variable to the model by its expected marginal gain and expected marginal loss in all modeling scenarios. Assuming the
Assuming
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formulas which evaluate the overall performance of each variable in
evaluation methodologies by the expected marginal gain and marginal loss in all
D
the value is not symmetric to
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marginal loss
loss are not symmetric
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an unbiased solution
several unbiased solutions
D
bias-adjusted
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tools employed are concepts from cooperative game theory, and the results
results also
D
. We even bridge the Shapley value and the Banzhaf value with binomial distributions