Quantifying the relative importance of predictors in multiple linear regression analyses for public health studies

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.