An Approach to Structural Equation Modeling With Both Factors and Components: Integrated Generalized Structured Component Analysis

In this article, we propose integrated generalized structured component analysis (IGSCA), which is a general statistical approach for analyzing data with both components and factors in the same model, simultaneously. This approach combines generalized structured component analysis (GSCA) and generalized structured component analysis with measurement errors incorporated (GSCAM) in a unified manner and can estimate both factor- and component-model parameters, including component and factor loadings, component and factor path coefficients, and path coefficients connecting factors and components. We conduct 2 simulation studies to investigate the performance of IGSCA under models with both factors and components. The first simulation study assesses how existing approaches for structural equation modeling and IGSCA recover parameters. This study shows that only consistent partial least squares (PLSc) and IGSCA yield unbiased estimates of all parameters, whereas the other approaches always provided biased estimates of several parameters. As such, we conduct a second, extensive simulation study to evaluate the relative performance of the 2 competitors (PLSc and IGSCA), considering a variety of experimental factors (model specification, sample size, the number of indicators per factor/component, and exogenous factor/component correlation). IGSCA exhibits better performance than PLSc under most conditions. We also present a real data application of IGSCA to the study of genes and their influence on depression. Finally, we discuss the implications and limitations of this approach, and recommendations for future research.