Mplus Version History

Mplus Version 1 was released in November 1998. Since that time, Mplus has undergone seven major version updates with a few minor updates for each major version. The current Mplus version is Version 8. Following are the Mplus release dates:

Version 8 April 2017

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 8.11, May 3, 2024

Mplus Version 8.11 is now available. Mplus Version 8.11 includes corrections to minor problems that have been found since the release of Version 8.10 in June 2023 as well as the following new features:

DSEM (Dynamic Structural Equation Modeling) of intensive longitudinal data for categorical outcomes is now available for TYPE=CROSSCLASSIFIED. For an application, see Muthén, Asparouhov and Shiffman (2024).
RDSEM (Residual Dynamic Structural Equation Modeling) is now available for TYPE=CROSSCLASSIFIED. For applications, see Muthén, Asparouhov and Keijsers (2024) and Muthén, Asparouhov and Shiffman (2024).
Continuous-Time Residual Dynamic Structural Equation Modeling (CT-RDSEM) is available for TYPE=TWOLEVEL and TYPE=TWOLEVEL RANDOM using the CTIME option of the VARIABLE command to specify the time variable and the DRIFT option of the PLOT command to plot autoregressive curves (Asparouhov & Muthén, 2024).
New H5RESULTS option of the SAVEDATA command for saving the results of an analysis to an H5 file that can be used in R to create an R data frame with possible connections to the MplusAutomation package
The CLUSTER_MEAN option of the DEFINE command is now available for TYPE=THREELEVEL and TYPE=CROSSCLASSIFIED.

The Versions 8.9, 8.10, and 8.11 Mplus Language Addendum can be found on the website along with the Mplus Version 8 User’s Guide.

Mplus Version 8.10, June 15, 2023

Mplus Version 8.10 is now available. Mplus Version 8.10 includes corrections to minor problems that have been found since the release of Version 8.9 in February 2023 as well as the following new features:

Addition of residual covariances, residual auto-regressions, and random intercepts to automatic testing of longitudinal measurement invariance.
PSEM for categorical variables using weighted least-squares estimation (Asparouhov & Muthén, (2023a).
New PSEM penalty functions: LASSO and GEOMIN.
Additional output for DIFF priors when ALIGNMENT is used.
Hat (^) language allowed with ESEM.
Between-level histogram for cluster-specific random effects with colors denoting significance.
SAVEDATA for cluster-specific random effects.

Mplus Version 8.9, February 28, 2023

Mplus Version 8.9 is now available. Mplus Version 8.9 includes corrections to minor problems that have been found since the release of Version 8.8 in April 2022 as well as the following new features:

Automatic testing of measurement invariance for single-group longitudinal models is now available using the MODEL option of the ANALYSIS command.
Alignment is now available for single-group longitudinal models (Asparouhov & Muthén, 2023a, Section 5.3).
Multiple group alignment has been extended by allowing SEM and giving standardized results (Asparouhov & Muthén, 2022).
New setting for ALIGNMENT=FIXED to choose the optimal reference group or time point. The setting is the asterisk (*) symbol.
A new method called Penalized Structural Equation Modeling (PSEM) is available. PSEM uses an Alignment Loss Function (ALF) prior for maximum likelihood estimation that can improve estimation of models like EFA, SEM, multiple group alignment, longitudinal alignment, and growth modeling (Asparouhov & Muthén, 2023a).
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).
New DSEM features are available. They include random correlations and changes to TINTERVAL, SAVEDATA, MONTECARLO and plots. See Mplus Web Talk No. 6.

The Version 8.9 Mplus Language Addendum can be found on the website along with the Mplus Version 8 User’s Guide.

Mplus Version 8.8, April 26, 2022

Mplus Version 8.8 is now available. Mplus Version 8.8 includes corrections to minor problems that have been found since the release of Version 8.7 in November 2021 as well as the following new features:

Alignment for ESEM and SEM (Asparouhov & Muthen, 2022a), including models with cross-loadings; ML and WLSMV estimators with Delta and Theta parameterizations; and continuous, binary, and ordinal variables.
Bayes estimation for residual SEM (RSEM; Asparouhov & Muthen 2022b) with count, nominal, and logit-binary distal outcomes.
Bayes estimation with censored variables for single-level SEM, mixture models, models with latent variable interactions, RSEM, and DSEM.
TECH10 standardized residuals for response patterns and univariate and bivariate frequency tables (Asparouhov & Muthen, 2022c) for Bayes with two-part ordinal models and Bayes with PREDICTOR=OBSERVED as used in Mplus Web Talk 4, Part 2.

Mplus Version 8.7, November 1, 2021

Mplus Version 8.7 is now available. Mplus Version 8.7 includes corrections to minor problems that have been found since the release of Version 8.6 in March 2021 as well as the following new features:

Regressions among residuals in SEM for observed and latent variables. The new language introduced in Version 8.1 for regressions among residuals for lagged variables with RDSEM using the LAGGED option and the Bayes estimator has been extended to regular single-level models for the maximum likelihood, weighted least squares, and Bayes estimators. This includes growth models with auto-regressions among the residuals and random intercept cross-lagged models (RI-CLPM and RI-ARMA) for panel data. The new modeling features are described in Asparouhov & Muthen (2021a) and illustrated further in Mplus Web Talk No. 4.
RI-CLPM for both binary and ordinal categorical variables is available using a new Bayes algorithm, including access to the residual parameters of the Theta matrix (Asparouhov & Muthen, 2021a).
RDSEM residual modeling has been extended to include both lagged variables and variables that occur at the same time (Asparouhov & Muthen, 2021a).
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).
Bayes LCA modeling with local dependence for ordinal variables has been added (Asparouhov & Muthen, 2021a).
For maximum likelihood estimators, an improved chi-square test for two-level modeling with zero between-level residuals has been added (Asparouhov & Muthen, 2021b).
For TYPE = TWOLEVEL with the Bayes estimator, saving of multiple draws of between-level factors scores (random effects) using the * setting of the FILE option of the SAVEDATA command, for example, FILE = between*.dat;
New setting for the USEOBSERVATIONS option of the VARIABLE command to exclude clusters with no within-cluster variation. This is useful with longitudinal data where a portion of the sample does not change over time. USEOBSERVATIONS = variable EQ _CLUSVAR;
New plot options are available for time-series analysis including a step function to allow day of the week effects, more than one Loop insert, and histograms for each time point.

Mplus Version 8.6, March 22, 2021

Mplus Version 8.6 is now available. Mplus Version 8.6 includes corrections to minor problems that have been found since the release of Version 8.5 in November 2020 as well as the following new features:

Added output features and a new Calculator for Latent Transition Analysis that make it more convenient to interpret analysis results especially when assessing effects of covariates on transition probabilities. The Calculator is found in the Mplus menu of the Mplus Editor. The new features are described in Mplus Web Talk No. 2: Using Mplus to do Latent Transition Analysis and Random Intercept Latent Transition Analysis and the technical appendix LTA Interpretation of Probabilities, Odds, and Odds Ratios Results
Simplified 3-step estimation for Latent Transition Analysis described in Section 9 of revised Mplus Web Note 21
Entropy for each latent class variable when there are multiple latent class variables such as in Latent Transition Analysis
Bayes estimation for the TYPE=IMPUTATION option of the DATA command. This gives non-symmetric CIs with imputed data. The new feature is described in the technical appendix Analyzing Imputed Data with the Bayesian Estimator in Mplus
Speed improvement for Bayes estimation with count variables
Multiple processor computation for Bayes estimation with logit link for binary variables
Saving of data sets and parameter estimates generated using the BOOTSTRAP option of the ANALYSIS command. This helps diagnose problematic analyses of bootstrap draws. The new feature is described in the technical appendix Bootstrap Computational Problems
Scaling of sampling weights when the KNOWNCLASS option of the VARIABLE command is used. This scales the weights to the total number in each known class which is also what is done using multiple-group analysis

Mplus Version 8.5, November 16, 2020

Mplus Version 8.5 is now available. Mplus Version 8.5 includes corrections to minor problems that have been found since the release of Version 8.4 in November 2019 as well as the following new features:

Automatic reordering of latent classes for mixture models
Bayes estimation for count, nominal, and binary variables using a logit link for both real data analysis and Monte Carlo simulation studies for single-level, two-level, and mixture models with a single categorical latent variable. The Bayesian estimation is particularly valuable in cases with many latent variables where maximum-likelihood would be intractable due to too heavy numerical integration. The logit link for binary variables makes odds ratio interpretations available also with Bayes (Asparouhov & Muthén, 2020).
Bayes estimation of mixture models with categorical latent variable regression on observed variables
Data imputation for count, nominal, and binary variables with a logit link
Multilevel data saving

The Version 8.5 Mplus Language Addendum can be found on the website along with the Mplus Version 8 User’s Guide.

Mplus Version 8.4, November 19, 2019

Mplus Version 8.4 is now available. Mplus Version 8.4 includes corrections to minor problems that have been found since the release of Version 8.3 in April 2019 as well as the following new features:

Significant speed improvements for computationally demanding mixture models, particularly with multiple latent class variables such as with Latent Transition Analysis and Random Intercept Latent Transition Analysis. These speed improvements are achieved using a new approach to the random starts perturbation options STARTS and STSCALE as well as new algorithms. These developments are described in Random Starting Values and Multistage Optimization. A Section 3 timing table for 5 mixture examples shows the large speed improvements in version 8.4 relative to 8.3.
Substantially simplified output for mixture models with multiple latent class variables
Expanded Bayesian fit statistics in 3 areas: improved posterior predictive p-values (PPP) when there are missing data, Bayesian CFI/TLI/RMSEA including confidence intervals, and a Bayesian version of the Wald test of parameter restrictions using the MODEL TEST command.
Improved algorithms for ML estimation of large multivariate three-level models with missing data
Monte Carlo output for CFI/TLI; new summary for RMSEA

Mplus Version 8.3, April 30, 2019

Mplus Version 8.3 is now available. Mplus Version 8.3 includes corrections to minor problems that have been found since the release of Version 8.2 in November 2018 as well as the following new features:

Significant speed improvements for Bayesian computations using a new parallelized computing approach (Asparouhov & Muthén, 2019a). In addition, Bayesian algorithms have been reorganized to produce faster computations. The resulting speed-up is particularly noteworthy for multilevel and time series (DSEM/RDSEM) analyses where in some cases the computing time is cut in half and even cut down to 20% of the version 8.2 timings. Timing tables for a variety of examples are presented in the technical documentation. (Download timing examples - i9-9900k, Proc=4).
Bayesian estimation of twolevel models with latent variable interactions using the XWITH option (Asparouhov & Muthén, 2019b). This is especially helpful for models with moderation where maximum-likelihood estimation is problematic due to the need for numerical integration. (Download the Section 4 Bayes examples)
The BOOTSTRAP option is available for TYPE=COMPLEX (Bootstrap technical appendix). In addition to being available for TYPE=GENERAL, the BOOTSTRAP option is available for TYPE=GENERAL when the WEIGHT option is used.

Mplus Version 8.2, November 1, 2018

Mplus Version 8.2 is now available. Mplus Version 8.2 includes corrections to minor problems that have been found since the release of Version 8.1 in June 2018 as well as the following new features:

XWITH for Bayes. This avoids slow computations using ML when many XWITH terms are included. ML bootstrapping to get non-symmetric confidence intervals is not needed with Bayes because such intervals are part of its estimation. 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 (RDSEM)
STANDARDIZED, RESIDUAL, AND TECH4 for RDSEM
Speed improvements for Bayes two-level analysis especially with random variances
SUM and MEAN options for the MODEL CONSTRAINT command. See the DEFINE command for examples

Mplus Version 8.1, June 5, 2018

Mplus Version 8.1 is now available. Mplus Version 8.1 includes corrections to minor problems that have been found since the release of Version 8 in April 2017 as well as the following new features:

Time series analysis of intensive longitudinal data using residual dynamic structural equation modeling (Asparouhov, Hamaker, & Muthén, 2018; Asparouhov & Muthén, 2018a, (Download scripts); Asparouhov & Muthén, 2018b, (Download scripts))
Latent variable decomposition (latent variable centering) of predictors with random slopes for DSEM, RDSEM, and other TYPE=TWOLEVEL models using the Bayes estimator (Asparouhov & Muthén, 2018b, (Download scripts)) as shown in Example 9.1 for a random intercept model in the Mplus Version 8 User’s Guide
Lagged categorical outcomes and random slopes for categorical predictors using latent variable decomposition (latent variable centering) for DSEM and other TYPE=TWOLEVEL models using the Bayes estimator (Asparouhov & Muthén, 2018b, (Download scripts))
Automatic checking of whether two structural equation models are nested or equivalent (Bentler & Satorra. 2010) implemented and expanded to multiple group models and the weighted least squares estimators (Asparouhov & Muthén, 2018c, (Download scripts))
Expanded and modified SRMR (Asparouhov & Muthén, 2018d)
Bivariate residual tests and factor score standard errors for the weighted least squares estimators
Cluster-specific plots for TWOLEVEL
Expanded odds ratio output
Standard errors for correlations with TYPE=BASIC using the H1SE option of the OUTPUT command

Input examples showing the new features are given in the

Version 8.1 Mplus Language Addendum.

Time Series Analysis Of Intensive Longitudinal Data Using Residual Dynamic Structural Equation Modeling (RDSEM)

Time series analysis of intensive longitudinal data using dynamic structural equation modeling (Asparouhov, Hamaker, & Muthén, 2018) focuses on the regression of an outcome at a certain timepoint on the same outcome at one or more previous time points. Residual dynamic structural equation modeling (RDSEM; Asparouhov, Hamaker, & Muthén, 2018; Asparouhov & Muthén, 2018a) focuses on a regression of an outcome at a certain time point on one or more predictors at the same time point. In RDSEM, the autoregression across time is specified for the residual of the outcome. RDSEM is available for both N=1 and multilevel models with two levels.

Mplus Version 8, April 20, 2017

Mplus Version 8 is now available. Mplus Version 8 includes corrections to minor problems that have been found since the release of Version 7.4 in November 2015 as well as the following new features:

Time series analysis features
- N=1 time series analysis (User’s Guide ex 6.23 – 6.28)
- Two-level time series analysis (User’s Guide ex 9.30 – 9.37)
- Cross-classified time series analysis (User’s Guide ex 9.38 – 9.40)
- Time series plots (sample values, ACF, PACF, estimated factor scores)
Other new features
- Two-level modeling with random variances (User’s Guide ex 9.28, 9.29)
- Two-level random autocorrelation modeling
- Standardization for two-level models with random slopes and random variances
- Random slopes for covariates with missing data
- New within/between scatter plots and histograms for two-level models, including sample and model-estimated cluster-specific means and variances
- New Posterior Predictive P-values for BSEM (PPPP; Hoijtink & van deSchoot, 2017; Asparouhov & Muthén, 2017)
- Output in HTML format

Time Series Analysis

Time series analysis is used to analyze intensive longitudinal data such as those obtained with ecological momentary assessments, experience sampling methods, daily diary methods, and ambulatory assessments. Such data typically have a large number of time points, for example, twenty to two hundred. The measurements are typically closely spaced in time. In Mplus, both N=1 models and a variety of two-level and cross-classified time series models can be estimated. These include univariate autoregressive, regression, cross-lagged, confirmatory factor analysis, Item Response Theory, and structural equation models for continuous, binary, ordered categorical (ordinal), or combinations of these variable types. The estimation is carried out using Bayesian analysis (Asparouhov, Hamaker & Muthén, 2017). Papers on these topics can be found on our time series page.

Mplus Version 7.4, November 2015

Mplus Version 7.4 is now available. Mplus Version 7.4 includes corrections to minor problems that have been found since the release of Version 7.31 in May 2015 as well as the following new features:

New IRT models: 3PL, 4PL, and Partial Credit Models
Bootstrap extensions: Bootstrap standard errors for standardized coefficients, bootstrap confidence intervals for standardized coefficients, and bootstrap for internal and external Monte Carlo simulation studies
R-square and standardized coefficients for models with latent variable interactions using XWITH (Muthén & Asparouhov, 2015)
MODEL INDIRECT for Bayes using the IND option
Standardized for MODEL INDIRECT for models that require numerical integration
DIC for models with random loadings, three-level random slopes, and cross-classified random slopes
Counterfactually-defined causal effects for ordinal mediators and ordinal outcomes
New plots: Bootstrap distributions, moderation plots, and sensitivity plots (TYPE=SENSITIVITY PLOT2;)
Saving of propensity scores
Test of proportional odds for logistic regression with ordinal outcomes (Brant Wald Test)
Random starts for weighted least squares estimators
Option to generate an ID variable that corresponds to the record number (DEFINE: idvariable = _RECNUM;)
Mplus R functions were updated to handle new plots in Version 7.4

The Version 7.4 Mplus Language Addendum can be found on the website along with the revised Mplus Version 7 User’s Guide.

New IRT Models: 3PL, 4PL, and the Partial Credit Model

Three new models have been added for categorical dependent variables: the Three-parameter Logistic Regression Model with a guessing parameter (3PL), the Four-parameter Logistic Regression Model with lower (guessing) and upper asymptote parameters (4PL), and the Partial Credit Model (PCM). The 3PL and 4PL models are available for only binary variables. The PCM model is available for only ordered categorical (ordinal) variables. The PCM model with a binary variable is the same as the logistic regression model. Both observed and latent predictors are allowed. This means that the modeling includes IRT modeling with covariates. Translations to common IRT parameterizations are provided in the output. These models are available for TYPE=GENERAL, TYPE=COMPLEX, TYPE=MIXTURE, and TYPE=TWOLEVEL for the ML, MLF, and MLR estimators (Asparouhov & Muthén, 2015).

Mplus Version 7.31, May 2015

Mplus Version 7.31 is now available. Mplus Version 7.31 includes corrections to minor problems that have been found since the release of Version 7.3 in October 2014.

Mplus Version 7.3, October 2014

Mplus Version 7.3 is now available. Mplus Version 7.3 includes corrections to minor problems that have been found since the release of Version 7.2 in May 2014 as well as the following new features:

A new method for 3-step mixture modeling with continuous distal outcomes (BCH)
Deviance Information Criterion (DIC) for Bayesian analysis of two-level models with continuous outcomes
Posterior predictive p-values (PPP) for Bayesian analysis of two-level, three-level, and cross-classified models
Multiple-group alignment for polytomous items using maximum-likelihood estimation
Variable-specific entropy
PARAMETERIZATION=RESCOV with 3-step mixture modeling
Higher-order moment output of skewness and kurtosis with the SAMPSTAT option and TYPE=BASIC
Plot of conditional expectation functions for skew-SEM

The Version 7.3 Mplus Language Addendum can be found on the website along with the Mplus Version 7 User’s Guide.

A New Method for 3-Step Mixture Modeling With Continuous Distal Outcomes (BCH)

Recent research (Bakk & Vermunt, 2014) proposes a method called BCH for 3-step mixture modeling with continuous distal outcomes. This method performs better in some cases than the method proposed by Lanza et al. (2013) referred to as DCON in Mplus. The BCH method can be used for either automatic or manual 3-step analysis using the MLR estimator. For manual 3-step analysis, the BCH method has an advantage over the Lanza et al.’s method because covariates can be included. The Mplus implementation of the BCH method is described in Asparouhov and Muthen (2014a).

Variable-specific Entropy

The ENTROPY option of the OUTPUT command is used in conjunction with TYPE=MIXTURE to request the entropy contribution for each latent class indicator in mixture modeling. This information is useful for understanding each indicator’s importance in distinguishing among the latent classes. This variable-specific entropy is described in Asparouhov and Muthen (2014b).

Mplus Version 7.2, May 2014

Mplus Version 7.2 is now available. Mplus Version 7.2 includes corrections to minor problems that have been found since the release of Version 7.11 in June 2013 as well as the following new features:

Mixture modeling with non-normal distributions: t-distribution, skew-normal, skew-T
Mediation analysis with direct and indirect effects based on counterfactuals (causal inference)
Latent class and latent transition analysis with residual covariances for categorical indicators
Restructured routines for continuous-time survival analysis with latent variables
Structural equation modeling (SEM) with non-normal distributions: t-distribution, skew-normal, skew-T
New order of operations for the DEFINE command
Double do loops for the DEFINE, MODEL CONSTRAINT, MODEL TEST, and MODEL PRIORS commands
ALIGNMENT option for binary outcomes using maximum-likelihood, including TYPE=COMPLEX using MLR
Bootstrap standard errors and confidence intervals for maximum likelihood estimation with ALGORITHM=INTEGRATION
Standard errors for TECH4 for the Delta parameterization of weighted least squares and z-tests and p-values for TECH4
Standardized coefficients with standard errors for models with covariates using weighted least squares estimation
New plots: Estimated distributions; Estimated medians, modes, and percentiles; and Scatterplots of individual residuals (Asparouhov & Muthen, 2014)
For Monte Carlo studies, TYPE=TWOLEVEL, and ESTIMATOR=BAYES, the output contains a table showing the correlation and mean square error comparing true and estimated factor scores
For the ALIGNMENT option and real data, RANKING=filename.csv; in the SAVEDATA command produces a comma-delimited file that shows the rankings of groups based on the group factor means and also shows the significance of the factor mean differences
For Monte Carlo studies using the ALIGNMENT option, the output contains a table showing the correlation and mean square error comparing true and estimated factor means
Parameter names given for parameter numbers listed as non-identified
Several lines can be commented out by starting the first line with !* and ending the last line with *!
New features for the Mac Editor: Correction to undo function and addition of All file types

The Version 7.2 Mplus Language Addendum can be found on the website along with the Mplus Version 7 User’s Guide.

Mixture Modeling With Non-Normal Distributions: T-Distribution, Skew-Normal, Skew-T

Mixture modeling with non-normal distributions is available using the DISTRIBUTION option of the ANALYSIS command in conjunction with TYPE=MIXTURE. This analysis is particularly useful for strongly skewed variables. The DISTRIBUTION option has three non-normal settings: SKEWNORMAL, TDISTRIBUTION, and SKEWT. The DISTRIBUTION option can be used with only continuous variables although the analysis model can contain other types of variables. Asparouhov and Muthén (2014a) describes the theory behind the implementation of mixture modeling with non-normal distributions.

Mediation Analysis With Effects Based On Counterfactuals (Causal Inference)

Causally-defined direct and indirect effects in mediation analysis as described in Muthén (2011) and Muthén and Asparouhov (2014) are available using MODEL INDIRECT with maximum likelihood estimation. The effects are available for a single mediator and a single outcome. The causally-defined direct and indirect effects are different than the usual direct and indirect effects of SEM in several cases, for example for models with a binary outcome, a count outcome, a binary mediator, and moderation that involves the mediator.

Latent Class And Latent Transition Analysis With Residual Covariances For Categorical Indicators

For latent class analysis and latent transition analysis, PARAMETERIZATION=RESCOVARIANCES allows the WITH option to be used to specify residual covariances for binary and ordered categorical (ordinal) outcomes using maximum likelihood estimation (Asparouhov & Muthén, 2014b). These residual covariances can be free across classes, constrained to be equal across classes, or appear in only certain classes.

Restructured Routines For Continuous-Time Survival Analysis With Latent Variables

The restructuring of routines for continuous-time survival analysis with latent variables has resulted in changes to the SURVIVAL and BASEHAZARD options (see Asparouhov, 2014, Section 9).

Structural Equation Modeling (SEM) With Non-Normal Distributions: T-Distribution, Skew-Normal, Skew-T

Non-normal distributions for factors and observed variables are available using he DISTRIBUTION option of the ANALYSIS command in conjunction with TYPE=GENERAL (Asparouhov & Muthén, 2014a). These new methods are experimental in that they have not been extensively used in practice. A chi-square test of model fit is available for testing the H0 model against an unrestricted model of means, variances, covariances, skew, and degrees of freedom using the H1MODEL option of the OUTPUT command.

New Order Of Operations For The DEFINE Command

The order of operations for the DEFINE command has changed. Previously transformations following the CLUSTER_MEAN, CENTER, and STANDARDIZE options did not use variables transformed using these options. For example, if an interaction variable was created after the CENTER option using the same variables, the interaction did not use centered variables. Now the interaction uses centered variables.

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.

New Statistical Analysis Features
- Expanded mixture modeling capabilities
- More fit indices
- Factor scores for more models
- Monte Carlo capabilities for mixture models
New Convenience Features
- Revised Mplus User's Guide
- Expanded language generator
- Additional data saving features
- More output options
Increased Computational Speed

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