Three-Way Generalized Structured Component Analysis

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling, where components of observed variables are used as proxies for latent variables. GSCA has thus far focused on analyzing two-way (e.g., subjects by variables) data. In this paper, GSCA is extended to deal with three-way data that contain three different types of entities (e.g., subjects, variables, and occasions) simultaneously. The proposed method, called three-way GSCA, permits each latent variable to be loaded on two types of entities, such as variables and occasions, in the measurement model. This enables to investigate how these entities are associated with the latent variable. The method aims to minimize a single least squares criterion to estimate parameters. An alternating least squares algorithm is developed to minimize this criterion. We conduct a simulation study to evaluate the performance of three-way GSCA. We also apply three-way GSCA to real data to demonstrate its empirical usefulness.