![]() The logic of the weights of 1/3, 1/6, 1/6, and 1/3, is that we equally weight the regressions based on the number of possible models. Thus, we can say that the average effect of adding A to a model is that it improves the R-squared statistic by. 2 when added to the regression with B and C. ![]() 2 when added to B (i.e., model A and B minus model B) 4 when added on its own (i.e., the A-only model minus the No Predictors model). For each predictor we compute the average improvement that is created when adding that variable to a model. This would lead to the conclusion that A is twice as important as B, which is twice as important as C.īack to Shapley. No predictors (other than the intercept R ²: 0)īefore looking at the computations of Shapley, take a second to think about a simple approach to computing importance, which is to compare the regressions with a single predictor.For example, if we have three predictors - A, B, and C - then eight linear regressions are estimated with the following combinations of predictors (hypothetical R-squared statistics are shown in brackets): The first step with Shapley Value regression is to compute linear regressions using all possible combinations of predictors, with the R-squared statistic being computed for each regression. ![]() Shapley Value regression is also known as Shapley regression, Shapley Value analysis, LMG, Kruskal analysis, and dominance analysis, and incremental R-squared analysis. Its principal application is to resolve a weakness of linear regression, which is that it is not reliable when predicted variables are moderately to highly correlated. Shapley Value regression is a technique for working out the relative importance of predictor variables in linear regression.
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