Regularized Matrix Decomposition Structural Equation Modeling

Matrix Decomposition Structural Equation Modeling (MDSEM) provides a data-matrix-based alternative to conventional SEM procedures. MDSEM is shown to be highly vulnerable to multicollinearity among latent variables, often resulting in biased and unstable estimates of parameters. This study proposes Regularized Matrix Decomposition Structural Equation Modeling (RMDSEM), an extension of MDSEM that introduces explicit L2 regularization. RMDSEM addresses the multicollinearity issue by regularizing the path coefficient matrix while preserving the matrix-decomposition framework. An iterative estimation algorithm and a K-fold cross-validation procedure for tuning multiple regularization parameters are derived. Simulation results show that MDSEM and maximum-likelihood SEM yield inflated bias and standard errors under moderate to strong multicollinearity, whereas RMDSEM achieves stable estimation with substantially reduced mean squared errors. Empirical applications further demonstrate that RMDSEM suppresses unreasonable estimates and yields interpretable structural relations.