ESTIMATORS AND ALGORITHMS
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 GelmanRubin potential scaling reduction using parallel computing in multiple MCMC chains. Posterior predictive checks are provided.
Frequentist analysis uses maximum likelihood and weighted least squares estimators. Mplus provides maximum likelihood estimation for all models. With censored and categorical outcomes, an alternative weighted least squares estimator is also available. For all types of outcomes, robust estimation of standard errors and robust chisquare tests of model fit are provided. These procedures take into account nonnormality of outcomes and nonindependence of observations due to cluster sampling. Robust standard errors are computed using the sandwich estimator. Robust chisquare tests of model fit are computed using mean and mean and variance adjustments as well as a likelihoodbased approach. Bootstrap standard errors are available for most models. The optimization algorithms use one or a combination of the following: QuasiNewton, Fisher scoring, NewtonRaphson, and the Expectation Maximization (EM) algorithm (Dempster et al., 1977). Linear and nonlinear parameter constraints are allowed. With maximum likelihood estimation and categorical outcomes, models with continuous latent variables and missing data for dependent variables require numerical integration in the computations. The numerical integration is carried out with or without adaptive quadrature in combination with rectangular integration, GaussHermite integration, or Monte Carlo integration.
