Generalized Structured Component Analysis with Latent Interactions

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling. In practice, researchers may often be interested in examining the interaction effects of latent variables. However, GSCA has been geared only for the specification and testing of the main effects of variables. Thus, an extension of GSCA is proposed to effectively deal with various types of interactions among latent variables. In the proposed method, a latent interaction is defined as a product of interacting latent variables. As a result, this method does not require the construction of additional indicators for latent interactions. Moreover, it can easily accommodate both exogenous and endogenous latent interactions. An alternating least-squares algorithm is developed to minimize a single optimization criterion for parameter estimation. A Monte Carlo simulation study is conducted to investigate the parameter recovery capability of the proposed method. An application is also presented to demonstrate the empirical usefulness of the proposed method.