Shapley Value And Biased-estimate Estimate Relative Importance Of Independent Variables In Multivariate Linear Regression Model

Objectives1) analysis the homoorganicity between estimation of relative importance ofvariables or shares of influence that independent variables contributed to the linear regressionmodel and measure the “value” of playing a particular role in an n-person game. Based on thishomoorganicity, we established another method by using average the partial R2in submodel toestimate the relative importance of variables, and using a medical example to compare the resultsof Shapley value, traditional methods and recommending methods.2) Due to the highlycorrelated or multicollinear of the independent variables in the real data, Multicollinearity hasseveral detrimental effects in the analysis of the variables’ influence on the depedent variable, evencould lead to the regression model distortion. Therefore, we should adjust the model firstly whenthe independent variables has highly correlated. Additionally, product measure and relative weightwere estimated the relative importance of independent variables.Methods The relative importance of independent variables was estimated via using the gametheory Shapley value. Meanwhile, product measure and relative weight method was also used toestimate the relative importance of independent variables in the partial-estimated linear regressionmodel when the independent variables has multicollinear. The method of simulated data is MonteClaro. All results were performed by SAS9.2implementation.Results The estimation results of relative importance of independent variables between thedominance analysis and Shapley value are same. According to the principle of dominance analysis,relative weight and product measure, the dominance analysis couldn’t use to analyse the relativeimportance of independent variables in biased-estimated linear regression model. Then, The idea ofrelative weight was showed that the result of analysis is unreasonable. Therefore, we considered touse product measure to estimate the relative importance of independent variables in biased-estimated linear regressin model. However, product measure owned an undesirable defect was thatthe estimation results could product negative value in ordinary least squares linear regressionmodel. At last, lots of simulated data was to check wether negative values were still exist in biased-estimation. The simulation results showed that negative values were still existed. Furthmore, with the numbers of independent variables increased, the numbers of negative values were quicklyincreased in same sample size.Conclusions In ordinary least squares regression, the Shapley value approach with severaladvantages was to estimate the relative importance of independent variable. This approachprovided a solution that was closer to the actual modeling for any complex process. because itcompared and averaged all possible subsets of independent variables in the model. So thisapproach could be used to estimate the relative importance of independent variables in ordinaryleast squares regression. Moreover, because of negative value in this approach estimation results,the product measure was not suited to estimate the relative importance of independent variables inbiased-estimated linear regression model.