Quantifying the Relative Importance of Predictors in Multiple Linear Regression Analyses for Public Health Studies

Abstract

Multiple linear regression analysis is widely used in many scientific fields, including public health, to evaluate how an outcome or response variable is related to a set of predictors. As a result, researchers often need to assess “relative importance” of a predictor by comparing the contributions made by other individual predictors in a particular regression model. Hence, development of valid statistical methods to estimate the relative importance of a set of predictors is of great interest. In this research, the authors considered the relative importance of a predictor when defined by that portion of the squared multiple correlation explained by the contribution of each predictor in the final model of interest. Here, a number of suggested relative importance indices motivated by this definition are reviewed, including the squared zero-order correlation, squared semipartial correlation, Product Measure (i.e., Pratt's Index), General Dominance Index, and Johnson's Relative Weight. The authors compared these indices using data sets from an occupational health study in which human inhalation exposure to styrene was measured and from a laboratory animal study on risk factors for atherosclerosis, and statistical properties using bootstrap methods were examined. The analysis suggests that the General Dominance Index and Johnson's Relative Weight are preferred methods for quantifying the relative importance of predictors in a multiple linear regression model. Johnson's Relative Weight involves significantly less computational burden than the General Dominance Index when the number of predictors in the final model is large.

Keywords:

• General Dominance Index
• Johnson's Relative Weight
• multiple linear regression analysis
• Pratt's Index
• predictor
• relative importance

ACKNOWLEDGMENTS

The authors gratefully appreciate Dr. Lawrence L. Rudel for providing us with the data set from the animal study, which was supported by NIH grants HL-49373 and HL-24736. This work was partially supported by grants from NIEHS (P42-ES05948 and T32-ES07018). The authors declare that they have no competing financial interests.

Notes

^A The value of the relative importance index estimated from the original data set.

^B The rank is determined by comparing the estimated relative importance values. The rank of 1 indicates the most important predictor, the rank of 2 indicates the second most important predictor, etc.

^A The single value above the 95% CI is the value of the relative importance index estimated from the original data set.

^B The 95% bootstrap confidence interval for the corresponding relative importance index.

^A The value of the relative importance index estimated from the original data set.

^B The rank is determined by comparing the estimated relative importance values. The rank of 1 indicates the most important predictor, the rank of 2 indicates the second most important predictor, etc.

^A The single value above the 95% CI is the value of the relative importance index estimated from the original data set.

^B The 95% bootstrap confidence interval for the corresponding relative importance index.