Mplus

Mplus Version 6 is now available. The major new feature in Mplus Version 6 is Bayesian analysis using MCMC. This includes multiple imputation for missing data as well as plausible values for latent variables. Other additions include replicate weights for complex survey data, survival analysis models and plots, convenience features for modeling with missing data, and several new general features.

The Version 6 Mplus User's Guide contains 16 new examples and one new chapter. Apart from adding new features, Mplus Version 6 contains corrections to minor problems that have been found since the release of Version 5.21, May 2009.

Bayesian Analysis (ESTIMATOR=BAYES)

Bayesian analysis can offer more information on model estimation than obtained by maximum likelihood and weighted least squares estimation. Bayesian estimation is also useful in some cases when a model is computationally intractable using maximum likelihood estimation or when the sample size is small and asymptotic theory is unreliable. Bayesian estimation uses Markov chain Monte Carlo (MCMC) algorithms to create approximations to the posterior distributions of the parameters by iteratively making random draws in the MCMC chain. Bayesian analysis in Mplus has the following features:

• Single-level, multilevel, and mixture models
• Continuous and categorical outcomes (probit link)
• Default non-informative priors or user-specified informative priors (MODEL PRIORS)
• Multiple chains using parallel processing (CHAIN)
• Convergence assessment using Gelman-Rubin potential scale reduction factors
• Posterior parameter distributions with means, medians, modes, and credibility intervals (POINT)
• Posterior parameter trace plots
• Autocorrelation plots
• Posterior predictive checking plots

Multiple Imputation (DATA IMPUTATION)

Multiple imputation is carried out using Bayesian estimation to create several data sets where missing values have been imputed. The multiple imputations are random draws from the posterior distribution of the missing values. The multiple imputation data sets can be used for subsequent model estimation using maximum likelihood or weighted least squares estimation of each data set where the parameter estimates are averaged over the data sets and the standard errors are computed using the Rubin formula. A chi-square test of overall model fit is provided. The imputed data sets can be saved for subsequent analysis or analysis can be carried out at the time the imputed data sets are created. Imputation can be done based on an unrestricted H1 model using three different algorithms including sequential regressions. Imputation can also be done based on an H0 model specified in the MODEL command. The set of variables used in the imputation of the data do not need to be the same as the set of variables used in the analysis. Single-level and multilevel data imputation are available.

Plausible Values (PLAUSIBLE)

Plausible values are multiple imputations for missing values corresponding to a latent variable. They are available for both continuous and categorical latent variables. In addition to plausible values for each observation, a summary is provided over the imputed data sets for each observation and latent variable. For continuous latent variables, these include the mean, median, standard deviation, and 2.5 and 97.5 percentiles. For categorical latent variables, these include the proportions for each class.

Bayesian Analysis Features for Future Mplus Versions

Bayesian analysis using Mplus is an ongoing project. Features that are not yet implemented include:

• EFA and ESEM
• Logit link
• Censored, count, and nominal variables
• XWITH
• Weights
• Random slopes in single-level models
• Latent variable decomposition of covariates in two-level models
• c ON x in mixtures
• Mixture models with more than one categorical latent variable
• Two-level mixtures
• MODEL INDIRECT
• MODEL CONSTRAINT except for NEW parameters
• MODEL TEST

Complex Survey Data

• Using and generating replicate weights to obtain correct standard errors (REPWEIGHTS)
• Finite population correction factor for TYPE=COMPLEX (FINITE)
• Pearson and loglikelihood frequency table chi-square adjusted for TYPE=COMPLEX for models with weights
• Standardized values in TECH10 adjusted for TYPE=COMPLEX for models with weights

Survival Analysis

• New continuous-time survival analysis parameterization using a survival intercept to represent class (group) differences
• Survival plots (for discrete-time survival specify the event history variables using the DSURVIVAL option of the VARIABLE command)
  • Kaplan-Meier curve
  • Sample log cumulative hazard curve
  • Estimated baseline hazard curve
  • Estimated baseline survival curve
  • Estimated log cumulative baseline curve
  • Kaplan-Meier curve with estimated baseline survival curve
  • Sample log cumulative hazard curve with estimated log cumulative baseline curve

Missing Data (DATA MISSING)

• Creation of missing data dropout indicators for non-ignorable missing data (NMAR) modeling of longitudinal data
• Descriptive statistics for dropout (DESCRIPTIVE)
• Plots of sample means before dropout

General Features

• New method for second-order chi-square adjustment for WLSMV, ULSMV, and MLMV resulting in the usual degrees of freedom
• Merging of data sets (SAVEDATA)
• Bivariate frequency tables for pairs of binary, ordered categorical (ordinal), and/or unordered categorical (nominal) variables (CROSSTABS)
• Input statements that contain parameter estimates from the analysis as starting values (SVALUES)
• Standard errors for factor scores
• 90% confidence intervals (CINTERVALS)
• Saving of graph settings (Axis Properties)

 
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