A2091
Title: On the relative importance of explanatory variables for the multivariate regression model
Authors: Chao-Ting Yu - National Chengchi University (Taiwan) [presenting]
Tsung-Chi Cheng - National Chengchi University (Taiwan)
Abstract: Assessing the relative importance of explanatory variables is a central issue in regression analysis. Existing methods, such as the Lindeman-Merenda-Gold (LMG) method, proportional marginal variance decomposition (PMVD), dominance analysis (DA), and relative weights analysis (RWA), were mainly developed for models with a single response variable. However, many empirical studies involve multiple correlated outcomes that are better represented by multivariate linear regression. Relative importance analysis is extended to the multivariate setting by defining overall model fit as a scalar function of the residual and explained SSCP matrices. Trace-based and determinant-based $R^2$- and $P^2$-type criteria are considered, and multivariate versions of LMG and PMVD are derived. A unified matrix-based framework is proposed to decompose multivariate model fit into predictor-specific contributions. The proposed methods allow explanatory power to be allocated coherently under different fit criteria while accounting for correlations among response variables. Simulation results and a real-data application illustrate the statistical behavior, interpretability, and practical usefulness of the proposed methods compared with existing approaches.
