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Mplus Website Updates

Mplus Version History

Mplus Version 1 was first released in November 1998. Since that time, Mplus has undergone six major version updates with a few minor updates for each major version. The current Mplus version is Version 7. Following are the Mplus release dates:

Version 7 September 2012
Version 6 April 2010
Version 5 November 2007
Version 4 February 2006
Version 3 March 2004
Version 2 February 2001
Version 1 November 1998

Mplus Version 7.11, June 2013

Mplus Version 7.11 is now available. Mplus Version 7.11 includes corrections to minor problems that have been found since the release of Version 7.1 in May 2013.

Mplus Version 7.1, May 2013

Mplus Version 7.1 is now available. Mplus Version 7.1 includes corrections to minor problems that have been found since the release of Version 7 in September 2012 as well as the following new features:

  • Multiple group factor analysis: A new method
  • Multiple group factor analysis: Convenience features
  • Exploratory factor analysis: Convenience features
  • Mixture modeling: A 3-step modification
  • Mixture modeling: A new distal outcome stepwise method
  • New TECH4 output
  • GROUPING and KNOWNCLASS convenience features
  • DO option for MODEL TEST

The Version 7.1 Language Addendum can be found on the website along with the Mplus Version 7 User’s Guide. New version 7.1 examples can be found here.

Multiple Group Factor Analysis: A New Method

The ALIGNMENT option of the ANALYSIS command is used with multiple group models to assess measurement invariance and compare factor means and variances across groups (Asparouhov & Muthén, 2013). It is most useful when there are many groups as seen in country comparisons of achievement like the Programme for International Student Assessment (PISA), the Trends in International Mathematics and Science Study (TIMSS), and the Progress in International Reading Literacy Study (PIRLS) as well as in cross-cultural studies like the International Social Survey Program (ISSP) and the European Social Survey (ESS).

Multiple Group Factor Analysis: Convenience Features

The MODEL option of the ANALYSIS command is used to automatically set up multiple group models for the purpose of testing for measurement invariance using the GROUPING option or the KNOWNCLASS option.

The MODEL option has three settings: CONFIGURAL, METRIC, and SCALAR. These settings can be used alone to set up a particular model or together to test the models for measurement invariance. Chi-square difference testing is carried out automatically using scaling correction factors for MLM, MLR, and WLSM and using the DIFFTEST option for WLSMV and MLMV.

Exploratory Factor Analysis: Convenience Features

For exploratory factor analysis, chi-square difference testing of the number of factors is carried out automatically comparing m-1 factors to m factors. Chi-square difference testing is carried out automatically using scaling correction factors for MLM, MLR, and WLSM and using the DIFFTEST option for WLSMV and MLMV.

Mixture Modeling: A 3-Step Modification

An error has been corrected in the R3STEP, DU3STEP, and DE3STEP options. This error results in only minor differences in the results.

With DU3STEP, and DE3STEP distal outcome analysis, a check has been added to make sure that Step 3 classification of subjects agrees with Step 1 classification of subjects.

There is a new version of Web Note 15 posted on the website, also discussing the Lanza et al. method below.

Mixture Modeling: A New Distal Outcome Stepwise Method

A new stepwise distal outcome method proposed by Lanza et al. (2013) has been added. The AUXILIARY option is used in conjunction with TYPE=MIXTURE with one categorical latent variable to identify continuous and categorical variables for which the equality of means or probabilities across latent classes will be tested using a stepwise approach. The new AUXILIARY settings are referred to as DCON and DCAT.

New TECH4 Output

Standard errors and p-values are now available for the TECH4 estimates of latent variable means, variances, and covariances.

GROUPING And KNOWNCLASS Convenience Features

The GROUPING option can be specified by mentioning only the number of groups, for example,

GROUPING = country (34);

where country is the grouping variable and the number 34 specifies that there are 34 groups.

The KNOWNCLASS option can be specified in conjunction with the CLASSES option by mentioning only the number of groups, for example,

CLASSES = c (34);

KNOWNCLASS = c (country);

where country is the grouping variable and the number 34 specifies that there are 34 groups.

The NGROUPS option of the MONTECARLO command has been extended for use with TYPE=MIXTURE.

DO Option For Model Test

The DO option is now available for MODEL TEST. The DO option provides a do loop to facilitate specifying a set of tests involving model parameters that will be jointly tested using the Wald test.

Mplus Version 7, September 2012

Mplus Version 7 is now available. A new feature is the Mplus Diagrammer that can be used to draw an input diagram, to view a diagram created from an analysis, and to view a diagram created using an input without an analysis. Mplus Version 7 contains several new statistical features. Major new features include Bayesian measurement invariance analysis using BSEM, Bayesian two-level SEM analysis with random loadings, three-level and cross-classified SEM including random slopes, and three-step mixture modeling. Other additions include bi-factor EFA rotations, Bayesian EFA, Bayes plausible value plots, two-tier modeling, latent transition probabilities expressed as functions of covariates, probability parameterization for mixture models such as Mover-Stayer LTA, plots of moderated mediation and cross-level interactions, parallel analysis for determining the number of factors based on eigenvalues, and many new convenience and output features.

The Version 7 Mplus User's Guide contains 22 new examples and several changes to existing examples. Apart from adding new features, Mplus Version 7 contains corrections to minor problems that have been found since the release of Version 6.12 in November 2011.

Mplus Diagrammer

The Mplus Diagrammer has three different uses. First, it can be used to draw an input diagram while producing the MODEL command of an Mplus input on the right-hand side of the screen. The DATA and VARIABLE commands can be added to the Mplus input. Second, it can be used to view a diagram created from an analysis. The output diagram can be edited and by choosing the Input mode option of the Diagram menu, the output diagram can be modified for a new analysis. Third, it can be used to view a diagram created using an input without an analysis. Labels can be added to parameters of the diagram. The diagram along with the corresponding input file can be saved for future use. The diagram can be saved as a pdf for publication.

Bayesian Measurement Invariance Analysis Using BSEM

Bayesian SEM (BSEM) with zero-mean, small-variance priors for parameters that are hypothesized to be small, but not exactly zero, was introduced in the article:

Muthén, B. and Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, 313-335. Paper can be downloaded from here.

Mplus Version 7 generalizes this BSEM approach to the study of differences between parameters across groups and time as described in the following paper:

Muthén, B. and Asparouhov, T. (2012). Bayesian SEM (BSEM) applied to measurement invariance. In preparation.

The model specifications are made easy by the new convenience features for the MODEL and MODEL PRIORS commands: DO, DIFFERENCE, MODEL=ALLFREE, and automatic labeling. Output has been added to summarize the non-invariance findings.

Bayesian Two-Level SEM Analysis With Random Loadings (TYPE=TWOLEVEL RANDOM with | f BY)

Bayesian analysis in Mplus Version 7 makes it possible to analyze models with many random effects, where maximum-likelihood is impossible due to too many dimensions of integration. This feature is useful with models that have random factor loadings, which is an important part of studies of measurement invariance across groups and across time, particularly for a large number of groups or time points. Mplus Version 7 specifies random factor loadings using the new language:

lam1-lam10 | f BY y1-y10;

An example of a new type of analysis made possible by this feature is Individual Difference Factor Analysis of subject-specific measurement parameters as described in the new technical report:

Asparouhov, T. and Muthén, B. (2012). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. Technical Report.

Three-Level SEM (TYPE=THREELEVEL)

Three-level analysis considers data that have three levels of nesting, such as students, classroom, and school. In Mplus version 7, three-level analysis is available using a full SEM on each of the three levels. There are two estimator options. The first estimator option is full-information maximum likelihood which allows continuous variables; random intercepts and slopes; and missing data. Non-normality robust standard errors and a chi-square test of model fit are available. The second estimator option is Bayes which allows continuous, categorical, and combinations of these variable types; random intercepts and random slopes; and missing data.

All three-level models can be estimated using the following special features:

  • Multiple group analysis
  • Missing data
  • Complex survey data
  • Random slopes
  • Linear and non-linear parameter constraints
  • Maximum likelihood estimation for all outcome types
  • Wald chi-square test of parameter equalities

Mplus Version 7 also features three-level multiple imputation of missing data for both continuous and categorical variables. Furthermore, complex survey data for continuous variables can be analyzed with TYPE=COMPLEX THREELEVEL, allowing for stratification, finite population sampling, and weights on all three levels. With four-level data, using TYPE=COMPLEX THREELEVEL the SEs are adjusted for the highest level clustering, while the variation for each of the three lower levels is modeled.

Cross-Classified SEM (TYPE=CROSSCLASSIFIED)

Cross-classified analysis considers data where a unit is nested in two different types of clusters which are not nested in each other, such as students nested in neighborhoods crossed with schools. In Mplus Version 7, cross-classified analysis is available using a full SEM on each of the three levels. There is one estimator option, Bayes, which allows continuous, categorical, and combinations of these variable types; random intercepts and slopes; and missing data.

All cross-classified models can be estimated using the following special features:

  • Missing data
  • Random slopes

Cross-classified analysis offers a variety of new analysis opportunities, such as

  • New longitudinal modeling where time and subject are the two cluster variables
  • Analysis with more than one random mode, including random subjects-random contexts and random subjects-random items as in random item IRT analysis and Generalizability analysis
  • Estimation of the multiple membership model of Jeon and Rabe-Hesketh (2012) in Journal of Educational and Behavioral Statistics

Three-Step Latent Class Modeling

Mplus Version 7 features a proper three-step analyze-classify-analyze approach to investigate covariates and distal outcomes related to categorical latent variables. The procedures are described in the new web note:

Asparouhov, T. and Muthén, B. (2012). Auxiliary variables in mixture modeling: A 3-Step approach using Mplus. Paper can be downloaded from here. Mplus Web Notes: No. 15, Version 5, October 4, 2012.

The three-step approach is specified using the AUXILIARY option of the VARIABLE command with the settings R3STEP, DU3STEP, and DE3STEP. The three-step approach is also available for Monte Carlo studies.

Latent Transition Probabilities Expressed As Functions Of Covariates (TECH15, LTA Calculator)

Mplus Version 7 has new features for latent transition analysis (LTA) with covariates. When covariates correspond to groups using KNOWNCLASS, the new option TECH15 provides latent transition probabilities for each group. When covariates are continuous, the LTA calculator can be used to compute latent transition probabilities for any values of the covariates.

Probability Parameterization For Mixture Models (PARAMETERIZATION=PROBABILITY)

A probability parameterization is provided as an alternative to the logit and loglinear parameterizations for models with categorical latent variables. This simplifies the specification of latent class and latent transition models that involve hypotheses expressed in terms of restrictions on conditional probabilities. An example is latent transition probabilities of zero and one for Stayers in Mover-Stayer latent transition analysis.

Bi-Factor EFA Rotations (ROTATION=BI-GEOMIN, BI-CF-QUARTIMAX)

Mplus Version 7 allows EFA rotation for models with a general factor that influences all items in addition to a set of specific factors. The EFA rotation is performed to give a simple factor loading pattern for the specific factors. This draws on the Jennrich and Bentler (2011, 2012) Psychometrika articles. Two rotations are available, BI-GEOMIN and BI-CF-QUARTIMAX using either orthogonal or oblique rotations among the specific factors.

Bayesian EFA

Mplus Version 7 has the new feature of ESTIMATOR=BAYES for EFA. In each MCMC iteration, an EFA rotation is made and the posterior distribution recorded. The approach protects against loading sign switching over the MCMC iterations.

Bayes Plausible Value Plots

Bayesian estimation provides a plausible value distribution for each individual's factor scores and latent response variables values. Mplus Version 7 provides a plot of these plausible value distributions going beyond the conventional reporting of only the mean and standard error. Specific factors and latent response variables are selected for plotting using the FACTORS and LRESPONSE options of the SAVEDATA and PLOT commands. The plausible values can be used in subsequent analyses using TYPE=IMPUTATION in the DATA command.

Two-Tier Modeling

Simplified maximum-likelihood computations are used when models have a two-tier model structure. For two-tier model structures, orthogonality among factors reduces the number of dimensions necessary for numerical integration. Mplus Version 7 automatically detects the possibility of two-tier computations.

Plots Of Moderated Mediation And Cross-Level Interactions (LOOP, PLOT)

The LOOP option is used in conjunction with the PLOT option in the MODEL CONSTRAINT command to create plots of variables. For example, it is useful for plotting indirect effects with moderation and mediation (Preacher, Rucker, & Hayes, 2007), cross-level interactions in multilevel regression (Bauer & Curran, 2005), and sensitivity graphs for causal effect mediation modeling (Imai, Keele, & Tingley, 2010; Muthén, 2011).

Parallel Analysis For Determining The Number Of Factors Based On Eigenvalues

The PARALLEL option is used with TYPE=EFA in the ANALYSIS command to determine the optimum number of factors in an exploratory factor analysis by comparing eigenvalues for sample data and randomly drawn data. It is available for continuous outcomes using maximum likelihood estimation.

New Convenience And Output Features

Several new convenience and output features are included in Mplus Version 7. In addition to the random loading feature | f BY and the plot feature LOOP mentioned above, Mplus Version 7 adds the following new convenience features

  • DO - used in DEFINE, MODEL CONSTRAINT, MODEL PRIORS to provide a do loop to facilitate specifying the same expression for a set of parameters
  • COVARIANCE - used in MODEL PRIORS to assign a prior to the covariance between two parameters
  • DIFFERENCE - used in MODEL PRIORS to assign priors to the difference between two parameters. The DO and DIFFERENCE options can be used together to simplify the assignment of priors to a large set of difference parameters for models with multiple groups and multiple time points.
  • Automatic labeling function - used in the ANALYSIS command to automatically give parameter labels for many groups
  • MODEL=ALLFREE - used in the ANALYSIS command with TYPE=MIXTURE, the KNOWNCLASS option, ESTIMATOR=BAYES, and the automatic labeling function to relax across-class equality constraints
  • BITERATIONS - used in the ANALYSIS command to specify the maximum and minimum numbers of iterations for each Markov chain Monte Carlo (MCMC) chain when the potential scale reduction (PSR) convergence criterion is used
  • PRIOR - used in the ANALYSIS command to request a plot of the prior distribution for each parameter that has a proper prior
  • KOLMOGOROV- used in the ANALYSIS command to request a Kolmogorov-Smirnov test of equality of the posterior parameter distributions across the different chains using draws from the chains
  • TECH15 - used in the OUTPUT command to give marginal and conditional probabilities for models with more than one categorical latent variable, for example, latent transition probabilities
  • TECH16 - used in the OUTPUT command to present results from testing that variances are greater than zero using the Bayes factor approach

General Features:

  • CENTERING has been moved from the VARIABLE command to the DEFINE command
  • The default number of random starts for TYPE=MIXTURE has been increased from STARTS=10 2 to STARTS=20 4
  • The default number of TECH14 random starts has been increased from LRTSTARTS=0 0 20 5 to LRTSTARTS=0 0 40 8
  • Asterisks have been added to mark significance for EFA factor loadings and for Bayes estimates

New Mplus User's Guide Examples

Following are 22 new Version 7 User's Guide Examples

  • 3.18: Moderated mediation with a plot of the indirect effect
  • 4.7: Bi-factor exploratory factor analysis with continuous factor indicators
  • 5.28: EFA with residual variances constrained to be greater than zero
  • 5.29: Bi-factor EFA using ESEM
  • 5.30: Bi-factor EFA with two items loading on only the general factor
  • 5.31: Bayesian bi-factor CFA with two items loading on only the general factor and cross-loadings with zero-mean and small-variance priors
  • 5.32: Bayesian MIMIC model with cross-loadings and direct effects with zero-mean and small-variance priors
  • 5.33: Bayesian multiple group model with approximate measurement invariance using zero-mean and small-variance priors
  • 8.13: LTA for two time points with a binary covariate influencing the latent transition probabilities
  • 8.14: LTA for two time points with a continuous covariate influencing the latent transition probabilities
  • 8.15: Mover-stayer LTA for three time points using a probability parameterization
  • 9.2: Two-level regression analysis for a continuous dependent variable with a random slope
  • 9.19: Two-level mimic model with continuous factor indicators, random factor loadings, two covariates on within, and one covariate on between with equal loadings across levels
  • 9.20: Three-level regression for a continuous dependent variable
  • 9.21: Three-level path analysis with a continuous and a categorical dependent variable
  • 9.22: Three-level MIMIC model with continuous factor indicators, two covariates on within, one covariate on between level 2, one covariate on between level 3 with random slopes on both within and between level 2
  • 9.23: Three-level growth model with a continuous outcome and one covariate on each of the three levels
  • 9.24: Regression for a continuous dependent variable using cross-classified data
  • 9.25: Path analysis with continuous dependent variables using cross-classified data
  • 9.26: IRT with random binary items using cross-classified data
  • 9.27: Multiple indicator growth model with random intercepts and factor loadings using cross-classified data
  • 11.5: Multiple imputation for a set of variables with missing values

New Technical Reports, Web Notes, and FAQs

Technical Reports:

  • Asparouhov, T. and Muthén, B. (2012). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. Technical Report.
  • Asparouhov, T. and Muthén, B. (2012). Comparison of computational methods for high-dimensional item factor analysis. Technical Report.
  • Muthén, B. and Asparouhov, T. (2012). Saddle Points. Technical Report.

Web Notes:

  • Asparouhov, T. and Muthén, B. (2012). Using Mplus TECH11 and TECH14 to test the number of latent classes. Paper can be downloaded from here. Mplus Web Notes: No. 14. May 22, 2012.
  • Asparouhov, T. and Muthén, B. (2012). Auxiliary variables in mixture modeling: A 3-Step approach using Mplus. Paper can be downloaded from here. Mplus Web Notes: No. 15, Version 5, October 4, 2012.

FAQs:

  • LTA with transition probs varying as a function of covariates

Mplus Version 6.12, November 2011

Mplus Version 6.12 is available for Windows, Mac OS X, and Linux for both 32- and 64-bit computers.

In Version 6.12, the Mac OS X version is available using a new editor in addition to the command line. Mplus Version 6.12 contains corrections to minor problems that have been found since the release of Version 6.11. Two minor additions have also been made to accommodate the analyses in the Muthen (2011) paper Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. A normal distribution function (PHI) has been added to the DEFINE and MODEL CONSTRAINT commands and the FREQWEIGHT option is now available with ESTIMATOR=BAYES.

Mplus Version 6.11, April 2011

Mplus Version 6.11 is available for Windows, Mac OS X, and Linux for both 32- and 64-bit computers.

The Linux distributions that have been tested are Ubuntu, RedHat, Fedora, Debian, and Gentoo. Mplus for Linux does not run on the Sun Solaris operating system. The multiprocessing feature in Mplus for Linux is the standard multiprocessing feature available in Mplus for Windows. The Linux version does not currently have special cluster computing capabilities.

The Mac OS X and Linux versions are available from the command line. The Mac and Linux versions do not have the plot capabilities of the Windows version. Instead, the GH5 file produced by the PLOT command can be read and plots made by the R program using the HDF5 package. Click here for R functions for plots.

Mplus Version 6.11 contains corrections to minor problems that have been found since the release of Version 6.1.

Mplus Version 6.1, October 2010

Mplus Version 6.1 contains corrections to minor problems that have been found since the release of Version 6 and the following new features. See the Version 6.1 Language Addendum with the Mplus Version 6 User's Guide for further information.

Bayesian Analysis

  • Improved algorithms for Bayesian analysis with covariance and correlation parameters, including allowing non-block-diagonal matrices and accessing priors for individual elements (ALGORITHM= GIBBS(PX1), GIBBS(PX2), GIBBS(PX3), GIBBS(RW))
  • Change of default for Bayesian estimation for multiple imputation to MODEL=COVARIANCE using GIBBS(PX1)
  • Improved multiple imputation estimation
  • Printing of Bayes priors in TECH1, including means and variances
  • Faster transmission of PLOT information using binary format

General

  • Number of variables allowed in NAMES list no longer limited to 500
  • More than 500 replicate weights allowed
  • Standardization of observed variables added to DEFINE (STANDARDIZE)
  • New layout of Tests of Model Fit
  • RMSEA confidence intervals added for MLM, MLMV, and WLS estimators
  • Simplified language for list functions for equalities and labels
  • Saving of estimated covariance matrix for continuous outcomes

Analysis Conditional on Covariates

Mplus Version 6.1 has modified TYPE=GENERAL for models with all continuous outcomes and maximum-likelihood estimation so that the likelihood is considered for the outcomes conditional on the covariates (x variables, exogenous observed variables). This is in line with regression analysis where the distribution of the covariates is not part of the model, but the model is expressed for the outcomes given the covariates. As in regression, the covariates are assumed to be freely correlated, but the parameters of the covariate part of the model are not estimated. In a model with all continuous-normal outcomes, the unconditional approach of not conditioning on the covariates and letting the parameters of the covariate part of the model be estimated was used initially in SEM. This leads to the same estimates, standard errors, and test of model fit as in the conditional approach. The unconditional approach, however, does not generalize to other model settings, such as with categorical outcomes and mixture modeling, without adding unnecessary assumptions. Using the conditional approach therefore makes Mplus take a consistent approach across model types. Following are some implications of this change.

The default parameterization does not covary covariates with other variables such as exogenous factors. If a user wants such variables to be related, this has to be specified using either ON or WITH. Because covariates are characterized as exogenous variables, using ON with the covariates on the right-hand side is a natural approach.

Because the loglikelihood is reported for the outcomes given the covariates, its metric is not changed by changing the covariates, so that models can be compared with respect to BIC as long as they have the same outcomes.

Starting with Version 6, Mplus deletes individuals who have missing data on one or more covariates as the default. If a user does not want this to happen, a distributional assumption such as normality has to be added for the covariates. Using maximum-likelihood estimation in Mplus this is accomplished by including the covariates in the model. This is done by mentioning means, thresholds, or variances of the covariates in the MODEL command. An alternative is to use multiple imputation in Mplus, where data sets are created from a Bayesian analysis imputing values for the covariates. In either case, the modeling has been extended to make assumptions about the covariates.

Mplus Version 6, April 2010

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
  • Random slopes for latent variables
  • 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)

New Mplus Users' Guide Chapter 11

The new Mplus Users' Guide Chapter 11 is entitled Missing Data and Bayesian analysis. It contains 7 new examples shown below.

New Examples

  • 5.24: EFA with covariates (MIMIC) with continuous factor indicators and direct effects
  • 5.25: SEM with EFA and CFA factors with continuous factor indicators
  • 5.26: EFA at two time points with factor loading invariance and correlated residuals across time
  • 5.27: Multiple-group EFA with continuous factor indicators
  • 7.30: Continuous-time survival analysis using a Cox regression model to estimate a treatment effect
  • 11.1: Growth model with missing data using a missing data correlate
  • 11.2: Descriptive statistics and graphics related to dropout in a longitudinal study
  • 11.3: Modeling with data not missing at random (NMAR) using the Diggle-Kenward selection model
  • 11.4: Modeling with data not missing at random (NMAR) using a pattern-mixture model
  • 11.5: Multiple imputation for a set of variables with missing values followed by the estimation of a growth model
  • 11.6: Multiple imputation of plausible values using Bayesian estimation of a growth model
  • 11.7: Multiple imputation using a two-level factor model with categorical outcomes followed by the estimation of a growth model
  • 12:12 Monte Carlo simulation study for a multiple group EFA with continuous factor indicators with measurement invariance of intercepts and factor loadings
  • 13.17: Merging data sets
  • 13.18: Using replicate weights
  • 13.19: Generating, using, and saving replicate weights

New Technical Appendices and Technical Reports

  • Asparouhov, T. & Muthén, B. (2010). Plausible values for latent variables using Mplus. Technical Report. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2010). Multiple imputation with Mplus. Technical report. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2010). Bayesian analysis of latent variable models using Mplus. Technical Report. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2010). Bayesian analysis using Mplus: Technical implementation. Technical appendix. Los Angeles: Muthén & Muthén.
  • Muthén, B. (2010). Bayesian analysis in Mplus: A brief introduction. Technical report. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2010). Simple second order chi-square correction. Technical appendix. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2009). Resampling methods in Mplus for complex survey data. Technical appendix. Los Angeles: Muthén & Muthén.
  • Asparouhov, T. & Muthén, B. (2008). Pearson and log-likelihood chi-square test of fit for latent class analysis estimated with complex samples. Technical appendix. Los Angeles: Muthén & Muthén.
  • Muthén, B., Asparouhov, T., Boye, M.E., Hackshaw, M.D., & Naegeli, A.N. (2009). Applications of continuous-time survival in latent variable models for the analysis of oncology randomized clinical trial data using Mplus. Technical Report.
  • Muthén, B., Asparouhov, T., Hunter, A. & Leuchter, A. (2010). Growth modeling with non-ignorable dropout: Alternative analyses of the STAR*D antidepressant trial. Submitted for publication.

Mplus Version 5.21, May 2009

Mplus Version 5.21 contains corrections to minor problems that have been found since the release of Version 5.2.

Mplus Version 5.2, November 2008

Mplus Version 5.2 contains corrections to minor problems that have been found since the release of Version 5.1, general speed improvements, and the following new features:

Speed Improvements

  • For large models with continuous outcomes and maximum likelihood estimation for TYPE=GENERAL
  • Faster optimization algorithm for TYPE=TWOLEVEL with categorical outcomes
  • Convergence improvements for TYPE=TWOLEVEL with categorical outcomes

Fit Statistics

  • Overall tests of model fit for multiple imputation with continuous outcomes and maximum likelihood estimation
  • Chi-square and bivariate fit statistics for counts with a large number of variables and for categorical variables with missing data (TECH10)

Starting Values

  • New starting value routines for TYPE=GENERAL, TYPE=EFA, TYPE=TWOLEVEL EFA, and TYPE=GENERAL with exploratory structural equation modeling (ESEM)

Modification Indices

  • New setting for modification indices which gives modification indices for residual covariances and direct effects from covariates to indicators MODINDICES (ALL);

Monte Carlo Studies and Multiple Imputation

  • New approach for ordering factors in exploratory structural equation modeling (ESEM) the same way across replications in Monte Carlo and Multiple Imputation analyses

Important Corrections

  • Factor scores for ESEM with categorical outcomes
  • TECH14 correction when OPTSEED is used
  • Correction for target rotation option

Technical Appendices

  • Chi-square statistics with multiple imputation

Changed Example

  • The Monte Carlo EFA Example 11.5 has been replaced by an example taking an exploratory structural equation modeling (ESEM) approach to EFA. Monte Carlo EFA has been disallowed. The new example is available from the User's Guide examples on the web site.

Mplus Version 5.1, May 2008

Version 5.1 contains corrections to minor problems that have been found since the release of Version 5, general speed improvements, and the following new features. See the Version 5.1 Language Addendum and the Version 5.1 Examples Addendum for further information.

Exploratory Structural Equation Modeling

  • EFA factors specified in the MODEL command
  • Target rotation allowing user-specified rotation targets
  • Factor scores for EFA factors
  • Monte Carlo simulation for EFA factors

Exploratory Factor Analysis

  • Change of the default rotation from oblique QUARTIMIN to oblique GEOMIN
  • Row standardization

Missing Data Modeling

  • Auxiliary m setting to specify variables that are missing data correlates in addition to the analysis variables for TYPE=GENERAL with continuous outcomes and maximum likelihood estimation

New Models For Count Variables

  • Negative binomial model with a dispersion parameter
  • Zero-inflated negative binomial model
  • Zero-truncated negative binomial model
  • Negative binomial hurdle model

Mixture Modeling

  • Auxiliary r option for investigating covariates not in the model that predict latent class membership using pseudo-class draws

Multilevel Modeling

  • Speed improvements for two-level weighted least squares estimation with many categorical outcomes and many latent variables
  • Convergence improvements with near-singular estimated between-level covariance matrices
  • Option to fix unrestricted model to sample statistics or estimate the unrestricted model in TYPE=TWOLEVEL EFA
  • Automatic creation of cluster-mean variables
  • Eigenvalue plots for within- and between-level correlation matrices

General Features

  • Three new functions in the DEFINE command: SUM, MEAN, and CLUSTER_MEAN
  • Expanded MODEL CONSTRAINT features

Monte Carlo Simulation

  • New data generation options for count variables
  • Monte Carlo simulation for EFA factors specified in the MODEL command

New Technical Appendices

  • Exploratory structural equation modeling
  • Auxiliary variables predicting missing data

New Examples

  • 1: EFA with covariates (MIMIC) with continuous factor indicators and direct effects
  • 2: SEM with EFA and CFA factors with continuous factor indicators
  • 3: EFA at two timepoints with factor loading invariance and correlated residuals across time
  • 4: Multiple-group EFA with continuous factor indicators
  • 5: Monte Carlo simulation study for a multiple-group EFA with continuous factor indicators with measurement invariance of intercepts and factor loadings
  • 6: GMM for a count outcome using a negative binomial model

Mplus Version 5, November 2007

Mplus Version 5 contains several new general features as well as features specific to exploratory factor analysis, mixture modeling, and multilevel modeling. Mplus Version 5 also has new features that improve computational speed and memory capacity.

The Version 5 Mplus User's Guide contains 13 new examples and 50 examples revised from their earlier versions either to make the input simpler or because of default changes. The new examples are listed at the end of this description. The Version 5 Mplus User's Guide will be available online.

Following is a list of the new features in Mplus Version 5.

Operating System and Number of Processors

  • Mplus Version 5 is available not only on 32-bit but also on 64-bit operating systems allowing the following memory capacity
    • 32-bit Mplus on 32-bit machine: 2GB, or 3GB if system booted with /3GB
    • 32-bit Mplus on 64-bit machine: 4GB
    • 64-bit Mplus on 64-bit machine: 8 terabytes (8 x 1024GB)
  • Mplus Version 5 has no limit on the number of processors used for parallel computing. The number of processors is limited only by what is available on the system.

General Features

  • Standard errors for standardized solutions and R-square
  • P-values
  • Standardized and normalized residuals
  • New option: MODEL = NOCOVARIANCES which fixes all covariance parameters at zero
  • Default changes: MISSING, MEANSTRUCTURE, H1 as the default
  • New options: LISTWISE = ON, NOMEANSTRUCTURE, NOCHISQUARE
  • Saving standardized results

Exploratory Factor Analysis

  • Additional factor loading matrix rotations: Quartimin, Geomin, and many others
  • Standard errors for rotated loadings and factor correlations
  • Non-normality robust standard errors and chi-square tests of model fit
  • Modification indices for residual correlations
  • Maximum likelihood estimation with censored, categorical, and count variables
  • Exploratory factor analysis for complex survey data (stratification, clustering, and weights)
    TYPE = COMPLEX EFA # #;
  • Exploratory factor mixture analysis with class-specific rotations
    TYPE = MIXTURE EFA # #;
  • Two-level exploratory factor analysis for continuous and categorical variables with new rotations and standard errors, including unrestricted model for either level
    TYPE = TWOLEVEL EFA # # UW # # UB;

Mixture Modeling

  • Faster computations using random starts distributed over several processors
    PROCESSORS = 4 (STARTS);
  • Equality tests of means across classes for variables not in the model using posterior probability-based multiple imputations
    AUXILIARY = x1-x10(e);
  • Modified TECH14 LRTSTARTS and new K-1STARTS option
  • New language for c ON c and u ON x
  • TECH10 and chi-square for counts
  • P-values saved for TECH11 and TECH14 with Monte Carlo simulation

Multilevel Modeling

  • Simple two-level limited-information weighted least squares estimator for categorical variables
    • computational demand virtually independent of number of factors/random effects
    • high-dimensional integration replaced by multiple instances of one- and two-dimensional integration
    • generalization of the Muthen (1984) single-level WLS
    • possible to explore many different models in a time-efficient manner
    • variables can be categorical, continuous, combinations
    • residuals can be correlated (no conditional independence assumption)
    • model fit chi-square testing
    • can produce unrestricted level 1 and level 2 correlation matrices for EFA
    • saving sample statistics and weight matrix for subsequent analyses
      TYPE = TWOLEVEL;
      ESTIMATOR = WLSM;
  • Improved integration algorithms for two-level mediation models

New Technical Appendices

  • Standardized Coefficients and Their Standard Errors
  • Standardized and Normalized Residuals
  • Mixture Exploratory Factor Analysis
  • Equality Test of Means Across Latent Classes Using Wald Chi-Square Based on Draws From Posterior Probabilities
  • Two-Level Weighted Least Squares Estimation. Proceedings of the Joint Statistical Meeting, August 2007, Biometrics Section

New Examples in the Version 5 Mplus User's Guide

  • 4.1: Exploratory factor analysis with continuous factor indicators
  • 4.2: Exploratory factor analysis with categorical factor indicators
  • 4.3: Exploratory factor analysis with continuous, censored, categorical, and count factor indicators
  • 4.4: Exploratory factor mixture analysis with continuous latent class indicators
  • 4.5: Two-level exploratory factor analysis with continuous factor indicators
  • 4.6: Two-level exploratory factor analysis with both individual- and cluster-level factor indicators
  • 6.18: Multiple group multiple cohort growth model
  • 9.1: Two-level regression analysis for a continuous dependent variable with a random intercept
  • 9.2: Two-level regression analysis for a continuous dependent variable with a random slope
  • 9.4: Two-level path analysis with a continuous, a categorical, and a cluster-level observed dependent variable
  • 9.9: Two-level SEM with categorical factor indicators on the within level and cluster-level continuous observed and random intercept factor indicators on the between level
  • 9.15: Two-level multiple indicator growth model with categorical outcomes (three-level analysis)
  • 11.11: Monte Carlo simulation study for a two-level mediation model with random slopes

Mplus Version 4.21

Version 4.21 contains general improvements to statistical algorithms and corrections of minor problems that have been found since Version 4.2.

Mplus Version 4.2

Version 4.2 contains corrections to minor problems that have been found since the release of Version 4.1 along with the following changes.

Speed Improvements

  • Multi-processing speed gains due to parallel computations with dual/multi-core processor computers and computers that support Hyper-Threading Technology
  • Overall speed improvements
  • Speed improvements for examples with multiple latent class variables

Timing trials were carried out for several examples using different computer configurations. Click here to see the results of the timing trials.

Two-level Modeling With Multiple Latent Class Variables

  • Two-level latent transition analysis and Markov modeling (see User's Guide Addendum Example 7)

Modeling With Between-Level Latent Class Variables

  • Two-level regression with between-level mixtures for regression coefficients (see User's Guide Addendum Examples 1 and 2)
  • Two-level IRT mixture analysis with between-level classes (see User's Guide Addendum Example 3)
  • Two-level latent class analysis with between-level classes (see User's Guide Addendum Example 4)
  • Two-level growth analysis with between-level classes (see User's Guide Addendum Example 5)
  • Two-level growth mixture analysis with between-level classes (see User's Guide Addendum Example 6)
  • Two-level latent transition analysis with between-level classes (see User's Guide Addendum Example 8)

New Options For Complex Survey Data Weights With TYPE=TWOLEVEL

  • Level-1 and level-2 weights
  • Options for different scaling of weights such as scaling to cluster size or effective cluster size

Click here for technical details about the scaling of sampling weights for two-level models.

Indirect Effects In Monte Carlo Simulation Studies

  • Indirect effect Monte Carlo summaries with MODEL INDIRECT

Added Output For Exploratory Factor Analysis

  • Factor structure
  • Factor determinacy

Added Output for TYPE = Imputation

  • Standardized solution and R-square

Response Pattern Classification

  • Response pattern summaries for categorical outcomes arranged by frequency, latent class, factor scores, and posterior probabilities

Added Mixture Output

  • Odds ratios for regression of latent class variable on covariates

Added Output For Estimates In IRT Metric

  • WLSMV estimator
  • ML estimator with probit link

New Graphics Features

  • IRT curves also for the WLSMV estimator and ML estimator with probit link
  • Added options for highlighting individual curves
  • Posterior probabilities added to the graphing information
  • Offsetting feature for overlapping mean curves
  • Window-management options for adjusted mean curves

Mplus Version 4.1

Version 4.1 contains corrections of minor problems that have been found since the release of Version 4 along with the following changes.

Algorithmic Changes

  • Speed has been improved for mixture models that use bootstrap standard errors
  • Speed has been improved and new options added for the parametric bootstrapped likelihood ratio test for the number of classes in mixture models (TECH14)
  • The algorithm for count variables has been improved

Item Response Theory (IRT) Additions

  • Item Characteristic Curves and Information Curves are now available in the PLOT command
  • Output in 2PL IRT metric is provided with maximum likelihood estimation of one- factor models with binary items

Other New Features

  • The CONSTRAINT option of the VARIABLE command is available with numerical integration
  • The BOOTSTRAP option is available with sampling weights
  • The LRTSTARTS option and the LRTBOOTSTRAP options have been added to be used in conjunction with TECH14

The LRTSTARTS option is used in conjunction with the TECH14 option of the OUTPUT command to specify for the k-1 and k class models the number of random sets of starting values to generate in the initial stage and the number of optimizations to use in the final stage.

The LRTBOOTSTRAP option is used in conjunction with the TECH14 option of the OUTPUT command to specify the number of bootstrap draws to be used in estimating the p-value of the parametric bootstrapped likelihood ratio test (McLachlan & Peel, 2000). The default number of bootstrap draws is determined by the program using a sequential method in which the number of draws varies from 2 to 100.

Mplus Version 4, February 2006

Mplus Version 4.0 contains several new general features as well as features specific to multilevel modeling and complex survey data analysis, mixture modeling, and analysis with categorical outcomes. Mplus Version 4.0 also introduces continuous-time survival analysis that is fully integrated into the general latent variable modeling framework of Mplus. Some of the new features such as those related to parameter constraints make twin, sibling, and family genetics modeling convenient and flexible.

The Version 4 Mplus User's Guide contains 19 new examples and 19 examples revised from their earlier versions to make the input simpler. The new examples are listed at the end of this description. Chapter 13 of the Mplus User's Guide has three new sections that describe the testing of measurement invariance for both continuous and categorical outcomes, how to avoid local maxima in mixture modeling, and the calculation of probabilities from probit regression coefficients. The Version 4 Mplus User's Guide is available online.

Following is a list of the new features in Mplus Version 4.0. The page numbers in parentheses refer to the pages in the Version 4 Mplus User's Guide where these features are described. An asterisk following the page numbers indicates that these pages describe a new example.

General Features

Data transformation

  • Rearrange data from wide to long format (246-248*, 371-373)
  • Rearrange data from long to wide format (373-375)
  • Create a binary and a continuous variable from a continuous variable with a floor effect for use in two-part (semicontinuous) modeling (105-107*, 301-303*, 375-378)
  • Create binary missing data indicators for missing data modeling (378-379)
  • Create binary event-history variables for discrete-time survival modeling (379-381)
  • Rearrange longitudinal data from a format where time points represent measurement occasions to a format where time points represent age or another time-related variable (381-384)

Extension of the MODEL CONSTRAINT command (484-487)

  • Including parameters not used in the MODEL command (72-73*, 74-75*, 75-76*, 76-77*, 164-166*, 167-169*, 485)
  • Implicit constraints (72-73*, 487)
  • Parameter can appear on both LHS and RHS (72-73*, 487)
  • Parameter can appear more than once on the LHS
  • Inequality constraints (72-73*)
  • Constraints involving observed variables (76-77*, 399-400, 486)

Wald test of parameter constraints (487-488)

Simplified language for equality constraints involving a list of parameters (465-466)

Bollen-Stine (residual) bootstrapped standard errors and chi-square p-value (434-435)

Display of outliers and influential observations (530-531)

  • Mahalanobis distance
  • Individual log likelihood contribution
  • Influence of each observation on the fitting function, likelihood displacement
  • Influence of each observation of the parameter estimates, Cook's D

Allowing a singular sample covariance matrix for covariates

Log-likelihood correction factors for chi-square testing with ESTIMATOR = MLR

Printing of chi-square contribution from each group in multiple-group analysis

Monte Carlo simulations of missing data expanded to let the missing data probability be a function of dependent variables that are continuous, censored, binary, ordered categorical, and counts, enabling, for example, generation of discrete-time survival data (299-300*), two-part data (301-303*), and data with non-ignorable missingness

Overall speed improvements

Interactive controls during iterative optimization (442-444)

Multilevel Modeling and Complex Survey Data Analysis

Two-level modeling with censored, nominal, and count outcomes (249-251*)

Complex survey data options (400-403)

  • Analysis of three-level data using TYPE = COMPLEX TWOLEVEL;
  • Subpopulation analysis
  • Improved treatment of a single PSU in a stratum

Reduction of dimensions of numerical integration for certain multilevel models using maximum likelihood estimation

Improved multiple-group analysis of complex survey categorical data using WLS, WLSM, and WLSMV estimation

Two-level MODEL INDIRECT

Between-level factor scores for random intercepts

Random slopes for dependent variables without numerical integration

Mixture Modeling

Bootstrapped parametric likelihood ratio test to determine the number of classes in mixture modeling (519)

Training data in the form of prior probabilities for latent classes (406)

Extended output for modeling with categorical latent variables

  • Alternative reference classes for displaying regression coefficients for a categorical latent variable regressed on covariates
  • TECH7 and RESIDUAL output for covariates in models with categorical outcomes

Analysis of Categorical Outcomes

Choice of probit or logit link for maximum likelihood estimation (428)

Improvements of bootstrapped standard errors for categorical data analysis with WLSM and WLSMV

Improvements in handling zero cells with categorical data analysis using WLS, WLSM, and WLSMV including a new option to add a value to the frequency of each cell (438)

Modified check of information matrix singularity for categorical data analysis using WLS, WLSM, and WLSMV estimation

Continuous-Time Survival Analysis

Cox regression - non parametric estimation (111-112*)

Parametric proportional hazards model - baseline hazard as a step function (112-113*)

Cox regression with random effects

Parametric proportional hazards model with random effects (114-115*)

Cox regression mixture model (203-204*)

Parametric proportional hazards mixture model

Multilevel Cox regression (251-252*)

Multilevel parametric proportional hazards model

Twin, Sibling, and Family Genetics Modeling

Two-group twin model for continuous outcomes where factors represent the ACE components (68-70*)

Two-group twin model for categorical outcomes where factors represent the ACE components (70-72*)

Two-group twin model for continuous outcomes using parameter constraints (74-75*)

Two-group twin model for categorical outcomes using parameter constraints (75-76*)

QTL sibling model for a continuous outcome using parameter constraints (76-77*)

Two-group twin model for categorical outcomes using maximum likelihood and parameter constraints (164-166*)

Two-group IRT twin model for factors with categorical factor indicators using parameter constraints (167-169*)

New Examples in the Version 4 Mplus User's Guide

5.18: Two-group twin model for continuous outcomes where factors represent the ACE components

5.19: Two-group twin model for categorical outcomes where factors represent the ACE components

5.20: CFA with parameter constraints

5.21: Two-group twin model for continuous outcomes using parameter constraints

5.22: Two-group twin model for categorical outcomes using parameter constraints

5.23: QTL sibling model for a continuous outcome using parameter constraints

6.20: Continuous-time survival analysis using the Cox regression model

6.21: Continuous-time survival analysis using a parametric proportional hazards model

6.22: Continuous-time survival analysis using a parametric proportional hazards model with a factor influencing survival

7.27: Factor mixture (IRT) analysis with binary latent class and factor indicators

7.28: Two-group twin model for categorical outcomes using maximum likelihood and parameter constraints

7.29: Two-group IRT twin model for factors with categorical factor indicators using parameter constraints

8.16: Continuous-time survival mixture analysis using a Cox regression model

9.16: Linear growth model for a continuous outcome with time-invariant and time-varying covariates carried out as a two-level growth model using the DATA WIDETOLONG command

9.17: Two-level growth model for a count outcome using a zero-inflated Poisson model (three-level analysis)

9.18: Two-level continuous-time survival analysis using Cox regression with a random intercept

11.8: Monte Carlo simulation study for discrete-time survival analysis

11.9: Monte Carlo simulation study for a two-part (semicontinuous) growth model for a continuous outcome

11.10: Monte Carlo simulation study for a two-level continuous-time survival analysis using Cox regression with a random intercept

Mplus Version 3.13

Version 3.13 contains corrections of minor problems that have been found since Version 3.12. In addition, it contains some general improvements to statistical algorithms, a few new features, and enhanced error messages.

Following are the changes to statistical algorithms that are included in Version 3.13:

  • Improved precision in numerical integration with maximum likelihood estimation
  • Improved weighted least squares estimation with categorical outcomes when there are empty cells

Following are new features in Version 3.13:

  • Weighted least squares estimation with censored outcomes allowing missing data
  • Saving of standard errors and all fit statistics for internal Monte Carlo simulations
  • An increase in length from 510 to 2048 for constraints in the MODEL CONSTRAINT command

Mplus Version 3.12

Version 3.12 contains general improvements to statistical algorithms and corrections of minor problems that have been found since Version 3.11.

Mplus Version 3.11

Version 3.11 fixes a data sorting error related to the new STRATIFICATION option. A few other small problems that came up were also corrected.

Mplus Version 3.1

The Mplus Version 3.1 update includes the following new features:

Stratification

Standard error estimation and chi-square model testing is now possible with complex survey data obtained by stratified sampling. This new feature avoids standard errors that are too large due to ignoring stratification. A description of how stratification is implemented in Mplus can be found in Mplus Web Note #9. Click here to download Mplus Web Note #9.

The STRATIFICATION option of the VARIABLE command is used in conjunction with TYPE=COMPLEX to identify the variable that contains stratification information. The STRATIFICATION option can be used in conjunction with the CLUSTER and WEIGHT options of the VARIABLE command.

Improved Optimization Algorithms With Numerical Integration

For analyses requiring numerical integration, the computational algorithm has been improved. This results in faster computations and also allows the use of fewer integration points which further increases computational speed.

Keyboard Shortcuts

Two keyboard shortcuts have been created, one to run Mplus and a second to view graphs.

Run Mplus - Alt+R
View graphs - Alt+V

Mplus Version 3, March 2004

Mplus Version 3 significantly enhances the two major strengths of Mplus, simplicity of use and modeling generality. Mplus Version 3 introduces a multitude of unique features in areas of structural equation modeling, growth modeling, mixture modeling, multilevel modeling, and combinations of such modeling features.

Mplus Version 3 is divided into a base program and three modules that can be added to the base program. The Mplus Base Program estimates models with continuous latent variables representing factors and random effects. It provides factor analysis models, path analysis models, structural equation models (SEM), growth, and discrete-time survival analysis models. The three modules are: a Mixture Add-On, a Multilevel Add-On, and a Combination Add-On. This arrangement allows users flexibility in selecting the add-on modules that best meet their analysis needs. Add-On modules can be purchased at any time after the base program is purchased.

Click here for information on Mplus Version 3 Pricing.

Click here for answers to frequently asked questions.

Program Content

Following is a brief description of what is included in the Mplus Version 3 Base program and each Add-On module. Each module includes graphical displays of descriptive statistics and analysis results, and Monte Carlo simulation capabilities. Examples of some new statistical features are given below.

Click here for more information on new Monte Carlo and graphics features that are available in the base program and the three modules.

Mplus Base Program

The Mplus Base Program estimates models with continuous latent variables representing factors and random effects. It provides factor analysis models, path analysis models, structural equation models, and growth models. The Mplus Base Program includes statistical developments beyond Mplus Version 2. An example of a new feature is maximum-likelihood estimation with interactions between continuous latent variables using both continuous and categorical latent variable indicators. Another new feature that has been frequently asked for by users is indirect, specific indirect, and total effects with Delta method and bootstrap standard errors and asymmetric confidence intervals.

Click here for more information.

Mixture Add-On

The Mixture Add-On estimates models with categorical latent variables using latent classes. It provides latent class analysis, finite mixture modeling, and growth mixture modeling. It contains statistical developments beyond Mplus Version 2. An example of a new feature is fully automated starting values and automatic search for multiple maxima. Another new feature is the regression of one categorical latent variable on another categorical latent variable as in latent transition analysis and hidden Markov modeling.

Click here for more information.

Multilevel Add-On

The Multilevel Add-On estimates models for clustered data. It provides conventional multilevel analysis as well as new extensions that integrate multilevel modeling and SEM. The Multilevel Add-On contains statistical developments beyond Mplus Version 2. An example of one new feature is two-level logistic regression. Another example is two-level factor analysis with categorical indicators.

Click here for more information.

Combination Add-On

The Combination Add-On includes both the Mixture Add-On and the Multilevel Add-On. In addition, it includes models that handle both clustered data and latent classes at the same time. It contains statistical developments beyond Mplus Version 2. An example of one new feature is two-level latent class analysis. Another example is multilevel growth mixture modeling.

Mplus Version 2.14

Mplus Version 2.14 contains improved error messages and corrections of minor bugs that have been found since Version 2.13. No new developments are included in Version 2.14.

Mplus Version 2.13

Mplus Version 2.13 contains speed and output improvements for multilevel models with random slopes, convergence improvements for multilevel and mixture models, and new standard error options for missing data analysis.

Mplus Version 2.12

Mplus Version 2.12 contains three new output options to guide in choosing the number of latent classes in mixture modeling.

Mplus Version 2.1

Mplus Version 2.1 contains several additions and changes relative to Version 2.02. They are listed below:

  • Multilevel modeling
  • Missing data with non-normal outcomes
  • Mixture modeling
  • Modeling with categorical outcomes
  • Convergence
  • Monte Carlo

Multilevel Modeling

Mplus Version 2.1 contains new options for the analysis of multilevel data in both cross-sectional and longitudinal settings. Below is a description of these new features. Mplus Version 2.1 also includes multilevel Monte Carlo simulations. This is described in the section Monte Carlo.

Full-information maximum likelihood estimation for continuous outcomes is now available for TYPE=TWOLEVEL. Mean structures and multiple group analysis are allowed. TYPE=TWOLEVEL MISSING provides maximum likelihood estimation under the assumption of MAR. Non-normality robust standard errors and a chi-square test of model fit are available using ESTIMATOR=MLR which is the default. These standard errors are obtained using a sandwich estimator and the test of model fit is obtained using an extension of the Yuan-Bentler T2* test statistic (Sociological Methodology, 2000) to multilevel models. Random slopes for independent observed ariables are available for the regression of observed and latent dependent variables using TYPE=TWOLEVEL RANDOM.

New features are available for the analysis of longitudinal data with continuous outcomes using TYPE=RANDOM and TYPE=RANDOM MISSING. These include individually varying times of observation and random slopes for time-varying covariates. Unlike conventional structural equation modeling and in line with conventional multilevel modeling, individually varying times of observation are included as variables in the data set. Random slopes for time-varying covariates describe slope variation across individuals.

TYPE=COMPLEX MIXTURE can now be used to obtain standard errors corrected for non-independence of observations in mixture models. A sandwich estimator is used. Note that a non-mixture analysis can be obtained by using TYPE=COMPLEX MIXTURE and specifying one class. This provides an alternative to the standard errors in TYPE=COMPLEX.

Missing Data On Non-Normal Outcomes

Mplus Version 2.02 allowed missing data for continuous outcomes under the assumption of multivariate normality using maximum likelihood estimation under MAR. Version 2.1 has added standard errors and a chi-square test statistic for missing data with non-normal outcomes by using a sandwich estimator and the Yuan-Bentler T2* (Sociological Methodology, 2000) test statistic. This estimator can be selected for TYPE = MISSING by asking for ESTIMATOR = MLR.

Mixture Modeling

Several additions and changes have been made for mixture modeling in Mplus Version 2.1. A major improvement has been made with respect to computational speed. Computational time has been reduced by more efficient data handling and by improved optimization algorithms. The ALGORITHM option has been added to the ANALYSIS command. This option allows the choice of three optimizations algorithms: ODLL, EM, and EMA. ODLL optimizes the observed-data log-likelihood directly. EM optimizes the complete-data log-likelihood using the expectation-maximization (EM) algorithm. EMA is an accelerated EM procedure. EMA is used as the default.

Another improvement is the addition of sample weights to mixture modeling.

Additional model fit information is now available for the latent class indicator part of the model. This is obtained by using the TECH10 option of the OUTPUT command. TECH10 includes information about the cell frequency contributions to the chi-square and univariate and bivariate estimated probabilities and residuals.

In the estimation of the thresholds of the latent class indicator part of the model, thresholds approaching extreme values are fixed to the values specified in LOGHIGH and LOGLOW and are not included in the set of free parameters in the model. This results in fewer convergence problems due to a singular information matrix.

For all analyses, model identification status is now checked using the information matrix estimate of the MLF estimator because this has been found to be the most reliable check of identification of the model.

Mixture modeling with complex sample data has also been added using TYPE=COMPLEX MIXTURE. This is discussed in the multilevel modeling section above.

Modeling With Categorical Outcomes

Mplus Version 2.1 contains several additions and changes for the analysis of categorical dependent variables. Version 2.1 offers an alternative parameterization when one or more dependent variables are categorical. In addition, computational efficiency has been improved.

Alternative Parameterization

Mplus now allows users two options for the parameterization of the model when one or more dependent variables are categorical. The first parameterization is referred to as DELTA. This is the parameterization that has been available in earlier versions of Mplus and is the default in Version 2.1. In the DELTA parameterization, scale factors are allowed to be parameters in the model, but residual variances for latent response variables of observed categorical outcome variables are not. The second parameterization is referred to as THETA. In the THETA parameterization, residual variances for latent response variables of observed categorical outcome variables are allowed to be parameters in the model, but scale factors are not.

The DELTA parameterization was selected as the default because it has been found to perform better in many situations. The THETA parameterization is preferred when hypotheses involving residual variances are of interest such as with multiple group analysis and analysis of longitudinal data. In addition, there are certain models that can only be estimated using the THETA parameterization because they have been found to impose improper parameter constraints with the DELTA parameterization. These are models where a categorical dependent variable is both influenced by and influences either another observed dependent variable or a latent variable.

Computational Efficiency

Space allocation demands have been reduced in Mplus Version 2.1 for models where one or more dependent variables are categorical. This has resulted in the ability to analyze models with more variables. In addition, computational speed has been improved. A NOCHISQUARE option in the OUTPUT command has also been added to avoid the computation of chi-square for WLSM and WLSMV. This greatly reduces computation time for problems with many variables.

Convergence

Numerical robustification of optimization when variables are on very different scales has been implemented in the estimation of all models except TYPE=MIXTURE, TYPE=RANDOM, TYPE=TWOLEVEL when ESTIMATOR=ML, MLR, or MLF, and when one or more dependent variables are categorical. The SDITERATIONS option has been added to allow users to change the number of steepest descent iterations.

Monte Carlo

Two new Monte Carlo features have been added to Mplus Version 2.1. The MONTECARLO command has been expanded to include the generation of clustered data with and without missing data for single or multiple groups. Data can also be generated for analysis with random effects using the | symbol. The data generation model is allowed to be different from the analysis model.

An Addendum to the Mplus User's Guide, explaining the latest additions and changes found in Version 2.1, is available for download.

Mplus Version 2, February 2001

Version 2 of Mplus contains several new features that make the analyses more flexible, more convenient, and faster.

Following is a description of the new features contained in Version 2 followed by information about Version 2 pricing.

New Statistical Analysis Features

Expanded Mixture Modeling Capabilities

The latent variable mixture modeling capabilities of Mplus have been greatly expanded in Version 2. An important expansion is that missing data are now allowed for the categorical latent class indicators in the mixture part of the model and for the continuous observed outcomes in the structural equation part of the model. Maximum likelihood estimation is performed under MAR. The missing data capability also makes it possible to do new types of analyses such as mixture discrete-time survival analysis and non-ignorable missing data modeling.

Another expansion is that latent class indicator variables can now be binary and/or ordered categorical. In addition, these variables can be repeated measures of the same variable and have a growth model specified for them.

Fit indices have been added including a chi-square test against the unrestricted model for the latent class indicators, an entropy measure, and a classification table. Factor scores are also available for mixture models along with many additions to the output including modification indices, standardized parameter estimates, and missing data information. In addition, training data can now include fractional class probabilities. The mixture model algorithms have been robustified numerically to avoid computational failures and error messages have been added to aid in diagnosing estimation problems.

More Fit Indices

More fit indices are available for all models. The additional fit indices include SRMR, CFI, and TLI. RMSEA has been added for all models that did not have it previously. In addition, a new fit index has been developed called WRMR. This index uses residuals weighted by their standard deviations which is particularly useful for models that include sample statistics on different scales such as models with mean or threshold structures.

Factor Scores For More Models

Factor scores are now available for all models in Mplus except models with clustered data and for exploratory factor analysis. This includes models with ordered categorical outcomes and combinations of categorical and continuous outcomes and also models with missing data.

Monte Carlo Capabilities For Mixture Models

The Monte Carlo facilities in Mplus have been expanded in Version 2. Data can now be generated for mixture models within the Monte Carlo facility in Mplus.

New Convenience Features

Revised Mplus User's Guide

The Mplus User's Guide has been revised for Version 2. Important additions are new examples for mixture models and expanded output descriptions.

Expanded Language Generator

Version 2 of Mplus includes a language generator to assist in preparing input files. The language generator takes users through a series of screens to help them quickly set up an Mplus input file. The language generator contains all of the Mplus commands except DEFINE, MODEL, and MONTECARLO.

Additional Data Saving Features

Version 2 of Mplus allows users to save many analysis results that were previously only printed in the output. These include sample statistics in the form of correlation or covariance matrices, the estimated sigma-between covariance or correlation matrix and the sample pooled-within correlation and covariance matrices for multilevel models, the covariance matrix of parameter estimates, and the means and covariance matrix for the latent variables. All of these results are saved using an E15.8 format. In addition, an identification variable can be saved to aid in merging with other data sets outside of Mplus.

Parameter estimates, standard errors of the parameter estimates, and fit statistics can also be saved. This is useful for Monte Carlo studies when data have been generated outside of Mplus, and Mplus is used for subsequent analyses. A DOS batch file to aid in these types of analyses is available with Version 2 on the Mplus website.

More Output Options

The Mplus output has been expanded to include new information. Users can now request that analysis results be presented as confidence intervals in addition to the standard format. When modeling with missing data, a summary of the missing data patterns in the data being analyzed is now printed. It is also now possible to request the standard errors for the H1 model and the estimated covariance and correlation matrices for the parameter estimates of the H1 model. Factor score coefficients and a factor score posterior covariance matrix can be requested for confirmatory factor analysis models with continuous factor indicators. An option also exists for obtaining a factor score determinacy value for each factor in the model.

Increased Computational Speed

The program now executes faster for most problems. In particular, improvements have been made for mixture problems. For mixture models, speed is also improved due to a change from using a pre-specified number of iterations to automatically terminating iterations after convergence.

Mplus Version 1, November 19, 1998