Inferential Procedures for Dominance Analysis Measures in Multiple Regression

Abstract

In order to better interpret a selected multiple regression model, researchers are often interested in whether a predictor is significantly more important than another or not. This study investigates the performance of the Normal-Theory based (asymptotic) confidence interval and bootstrap confidence intervals for predictors' dominance relationships using both normal and non-normal data. The results show that asymptotic confidence interval method is adequate to make inferences for comparing two general dominance measures when the distribution is multivariate normal or slightly non-normal and when the effect size is no less than 0.15 and the sample size is at least 100. However, the bootstrap confidence interval methods are preferred over the asymptotic confidence interval when the data are considerably non-normal (e.g., skew > 0.75, or |kurtosis| > 1.2). The choice among standardized, percentile and bias-corrected bootstrap confidence intervals is based on the properties of the real data set, like sample size and distribution. An empirical demonstration and appropriate interpretation are also provided.