Decision making by variable contribution in discriminant, logit, and regression analyses

Comparative contribution of predictors in multivariate statistical models is widely used for decision making on the importance of the variables for the aims of analysis and prediction. However, the analysis can be made difficult because of the predictors' multicollinearity that distorts estimates for coefficients in-the linear aggregate. To solve the problem of the robust evaluation of the predictors' contribution, we apply the Shapley Value regression analysis that provides consistent results in the presence of multicollinearity both for regression and discriminant functions. We also show how the linear discriminant function can be constructed as a multiple regression, and how the logistic regression can be approximated by linear regression that helps to obtain the variables contribution in the linear aggregate.