Mixed Effects (Step Back) Attribution
The mixed effects model is a variation of the scalloping approach to attribution that breaks the variation into the effects of each individual input, and then a component that represents a mixed effect from the inputs.Regression Example
The mixed effects model is most prominently used when running an OLS Regression. When regressing multiple variables, it is often asked what the contribution of each regressor is to the total R squared.The standard practice is to run the regression for the full set of regressors and not the R squared. Next, run the regression with all the regressors, but excluding one. Subtract the resulting R squared from the full R squared. This becomes the amount of R squared due to the missing regressor.
When all regressors have been attributed, there will be a portion of the toal R squared that is unexplained. That is, summing the individual R squares will be less than the total. The residual R squared amount is then attributed as a mixed effect.