Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes

Abstract

Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all indicators and components, however, it could not utilize information on the indicators’ scale in parameter estimation. Consequently, its component scores could just show the relative standing of each individual for a component, rather than the individual’s absolute standing in terms of the original indicators’ measurement scales. In the paper, we propose a new version of GSCA, named convex GSCA, which can produce a new type of unstandardized components, termed convex components, which can be intuitively interpreted in terms of the original indicators’ scales. We investigate the empirical performance of the proposed method through the analyses of simulated and real data.