Comparison Of Conventional And Pratt Methods To Measure Variable Importance In Multiple Linear Regression

Abstract

The objective of this research is to compare various methods in determining variable importance in multiple linear regression. In multiple linear regression analysis, it is of interest to rank order and scale predictors in terms of their importance to dependent variable. In one conventional method, variables are ranked based on their standardized coefficients obtained from regression model, which is regarded as their relative importance. In other method, partial correlation between the predictors and dependent variable is used as a measure of variable importance. Pratt in 1987 proposed different method to determine variable importance within several assumptions that the variables have to met. Specifically, this method gives an estimation to the importance measure. This research reviews three methods, namely the standardized coefficient, partial correlation, and Pratt method. Two sets of data with specific variable importance parameters were generated. One set was generated under multicollinearity condition, while the other was without it. Three kind of regression models were constructed from the data with each contained two, five and eight variables, respectively. Each model was then simulated in 50 turns, in each of which importance measures were obtained using the three methods. The measures' averages were then compared to the importance parameters to determine their performance. The result shows that under no multicollinearity condition Pratt method gives better estimate to variable importance parameter in regression model with 5 and 8 variables, compared to conventional methods. Meanwhile, under multicollinearity condition the three methods performance are about the same. Pratt method also consistently produces smaller variance than the other two, indicating that this method is more stable in measuring the variable importance.