Generalized Structured Component Analysis with Uniqueness Terms for Accommodating Measurement Error

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM), where latent variables are approximated by weighted composites of indicators. It has no formal mechanism to incorporate errors in indicators, which in turn renders components prone to the errors as well. We propose to extend GSCA to account for errors in indicators explicitly. This extension, called GSCAM, considers both common and unique parts of indicators, as postulated in common factor analysis, and estimates a weighted composite of indicators with their unique parts removed. Adding such unique parts or uniqueness terms serves to account for measurement errors in indicators in a manner similar to common factor analysis. Simulation studies are conducted to compare parameter recovery of GSCAM and existing methods. These methods are also applied to fit a substantively well-established model to real data.