| Aspect | What the paper offers | |--------|-----------------------| | | Demonstrates how to embed Bayesian Markov‑Chain Monte Carlo (MCMC) estimation inside the traditional maximum‑likelihood (ML) framework of LISREL 9.1, expanding the toolbox for researchers dealing with small samples, non‑normal data, or complex hierarchical models. | | Practical LISREL code | Includes complete LISREL syntax blocks (both ML and Bayesian sections) that you can copy‑paste into your own .lis files. The authors also provide a short “cheat‑sheet” of the most frequently used command‑line options for the LISREL and MCMC modules. | | Empirical illustration | Uses a multilevel educational dataset (N = 1,236 students nested in 84 schools) to compare ML‑based SEM, Bayesian SEM, and a hybrid approach. The results showcase differences in parameter estimates, credible intervals, and model‑fit indices (CFI, RMSEA, SRMR). | | Model‑fit diagnostics | Introduces a new set of Bayesian fit statistics (posterior predictive p‑value, DIC, WAIC) that are computed directly by LISREL’s MCMC routine, and explains how to interpret them alongside the classic chi‑square, CFI, and RMSEA. | | Tips for LISREL 9.1 users | - How to set the random‑seed for reproducible MCMC runs. - Memory‑management tricks for large covariance matrices. - Common pitfalls (e.g., “non‑identifiable priors”) and how to diagnose them with LISREL’s MATRIX output. | | Future directions | Discusses the potential of variational Bayes and Hamiltonian Monte Carlo extensions that may appear in upcoming LISREL releases (e.g., LISREL 10). |
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