Probabilistic GSCA: A Likelihood-Based Approach to Component-Based Structural Equation Modeling

This paper introduces probabilistic generalized structured component analysis (pGSCA), a likelihood-based framework for component-based structural equation modeling. pGSCA embeds GSCA within a generative model by incorporating multivariate normal disturbances into its submodels and is estimated by direct maximum likelihood, using expectation–maximization estimates as initial values. This formulation enables formal statistical inference, including asymptotic standard errors, information criteria, and likelihood-ratio tests (LRTs)—capabilities unavailable in conventional GSCA. Simulation results show that pGSCA performs comparably to GSCA in recovering component weights, loadings, and path coefficients, while additionally providing accurate estimates of disturbance covariance matrices. The asymptotic standard errors exhibit well-calibrated Type I error rates and confidence interval coverage, and LRTs yield well-controlled Type I error rates and high empirical power for model comparison. An empirical example illustrates formal likelihood-based model comparison. Overall, pGSCA substantially expands the inferential scope of GSCA while retaining its component-based nature.