Interpreting Johnson's Relative Weights Analysis: Insights from New Formulae and Computational Tools
Abstract
Relative weights and dominance analysis offer two promising relative importance methods for multiple regression. Whereas dominance analysis offers more statistically interpretable solutions, calculating such solutions is computationally burdensome. Conversely, although relative weights are computationally simpler, interpreting said weights is more difficult. This paper presents a new relative weights derivation and formula that is both computationally efficient and clarifies relative weights statistical interpretation. Specifically, the derivation contained herein suggests two new relative weights interpretations drawing from (1) principal components analysis (PCA) and (2) generalized least squares (GLS) regression. This new method is then translated into the R language while also explicitly clarifying the relationship between mathematical formulae and computer code. The new method contains two key advantages over existing computational implementations in that the new method (1) avoids matrix inversion entirely and (2) is better suited for modern missing data methods (e.g., full information maximum likelihood). The inferential and computational benefits of this new method notwithstanding, caution is ultimately warranted in that the new method makes clear certain relative weights matrix choices are, in current practice, arbitrary.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 2021
- Accession Number
- AD1139429
Entities
People
- Garett N. Howardson
Organizations
- U.S. Army Research Institute for the Behavioral and Social Sciences