Dominance Analysis with Model Uncertainty
Dominance analysis (DA), first proposed by Budescu (1993), is a statistical method used to compare the relative importance of predictors in various statistical models. In the dominance analysis of p predictors, a predictor Xi is said to dominate another variable Xj" , if the additional contribution of Xi to the prediction of the criterion that is evaluated by semi-partial correlation is higher than that of Xj" in (2p-2) possible subset models. Ranking of p predictors is then achieved by p(p-1)/2 pairwise comparisons among p predictors. Azen and Budescu (2003) developed DA inference method based on bootstrapping techniques in which the dominance analysis was applied based on the full regression model for each bootstrap sample, under an implicit assumption that the full model is “the correct” model. This approach, although natural and sensible, especially in a scenario where the verification of a structure of a model is prioritized, may not be appropriate when the model uncertainty is taken into account. In the present study, I developed a new inference method of dominance analysis in which the DA is conducted on the best fitting model (BFM) of each specific bootstrapped resample. A simulation study was conducted to examine the effectiveness of the BFM DA and explore how its effectiveness is influenced by the model uncertainty which was reflected by the diversity of BFMs in the bootstrap samples. Results showed that the BFM approach overall performed as well as the traditional DA inference method, and in simulation conditions of high BFM diversity, it led to more accurate approximation of the population dominance structure. A real data illustration was included for the purpose of providing prototypes of how the traditional and the new bootstrapping inference method of dominance analysis can be applied to a real data set, namely, what types of key results and supplemental results can be presented when one needs to make inference about the dominance analysis results using either one of the inference methods. Recommendations on the choice of appropriate DA inference method and other applications of the methodology developed by the current study were listed.
Quantitative psychology|Systematic biology|Biostatistics
Han, Ying, "Dominance Analysis with Model Uncertainty" (2023). ETD Collection for Fordham University. AAI30490954.