Regularized Structural Equation Modeling with Both Factors and Components

Integrated generalized structured component analysis (IGSCA) has been recently developed to estimate structural equation models that incorporate both factors and components. In this paper, we propose integrating regularization into IGSCA to address the issues of multicollinearity and variable selection. The proposed method, termed regularized IGSCA, enables the imposition of <i>L</i>₁ (ridge) or <i>L</i>₂ (lasso) penalty on loadings and path coefficients separately. We seek to minimize a penalized least squares objective function for parameter estimation. We evaluate the performance of the method through a simulation study and illustrate its empirical applicability using real data.