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Mplus provides both Bayesian and frequentist inference. Bayesian analysis uses Markov chain Monte Carlo (MCMC) algorithms. Posterior distributions can be monitored by trace and autocorrelation plots. Convergence can be monitored by the Gelman-Rubin potential scaling reduction using parallel computing in multiple MCMC chains. Posterior predictive checks are provided.
TECH10 is now available for Bayes and WLSMV with standardized residuals for response patterns and univariate and bivariate tables for fuller model fit assessment with categorical variables.
TECH 10 for Bayes includes Pearson posterior predictive checking for univariate and bivariate tables with categorical variables (Asparouhov & Muthen, 2021a).
Random correlations are available for continuous, binary, ordered categorical (ordinal), or combinations of these variable types for TYPE=TWOLEVEL and TYPE=CROSSCLASSIFIED for ESTIMATOR=BAYES (Asparouhov & Muthén, 2023b, Section 9.1).
This is available for single-level models with no 3-way interactions
Categorical dependent variables with and without latent centering for intensive longitudinal data analysis using residual dynamic structural equation modeling
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