Structural equation modeling with factors and composites within the framework of the basic design

In this paper, we study structural equation modeling with factors and composites within the framework of the basic design. The PLS approach (i.e. PLS-SEM based on PLS-PM, PLSc and the composite model) used to estimate this model has many limitations, including lack of theoretical foundations and the use of iterative algorithms with no guaranteed convergence. To address these shortcomings, we introduce a novel method, SVD-SEM, which corrects these issues. Indeed, SVD-SEM relies on a non-iterative SVD-based algorithm for parameter estimation, producing consistent and asymptotically normal estimators, offering a statistically and computationally sound alternative to PLS-SEM. Additionally, we present the restricted maximum-likelihood approach (RML-SEM) for the basic design with factors and composites. SVD-SEM can serve as an initial solution for RML-SEM. To illustrate the performance of these methods, we discuss a Monte Carlo simulation on a nonrecursive model with factors and composites.