Mplus  
Monday May 23, 2022 



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:
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:
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:
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:
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:
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:
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:
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:
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:
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 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 twolevel and crossclassified time series models can be estimated. These include univariate autoregressive, regression, crosslagged, 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:
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 Threeparameter Logistic Regression Model with a guessing parameter (3PL), the Fourparameter 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:
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 3Step Mixture Modeling With Continuous Distal Outcomes (BCH) Recent research (Bakk & Vermunt, 2014) proposes a method called BCH for 3step 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 3step analysis using the MLR estimator. For manual 3step 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). Variablespecific 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 variablespecific 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:
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 NonNormal Distributions: TDistribution, SkewNormal, SkewT Mixture modeling with nonnormal 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 nonnormal 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 nonnormal distributions. Mediation Analysis With Effects Based On Counterfactuals (Causal Inference) Causallydefined 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 causallydefined 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 ContinuousTime Survival Analysis With Latent Variables The restructuring of routines for continuoustime 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 NonNormal Distributions: TDistribution, SkewNormal, SkewT Nonnormal 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 chisquare 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:
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 crosscultural 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. Chisquare 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, chisquare difference testing of the number of factors is carried out automatically comparing m1 factors to m factors. Chisquare 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 3Step 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 pvalues 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 twolevel SEM analysis with random loadings, threelevel and crossclassified SEM including random slopes, and threestep mixture modeling. Other additions include bifactor EFA rotations, Bayesian EFA, Bayes plausible value plots, twotier modeling, latent transition probabilities expressed as functions of covariates, probability parameterization for mixture models such as MoverStayer LTA, plots of moderated mediation and crosslevel 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 righthand 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 zeromean, smallvariance 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, 313335. 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 noninvariance findings. Bayesian TwoLevel 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 maximumlikelihood 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: lam1lam10  f BY y1y10; An example of a new type of analysis made possible by this feature is Individual Difference Factor Analysis of subjectspecific 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. ThreeLevel SEM (TYPE=THREELEVEL) Threelevel analysis considers data that have three levels of nesting, such as students, classroom, and school. In Mplus version 7, threelevel analysis is available using a full SEM on each of the three levels. There are two estimator options. The first estimator option is fullinformation maximum likelihood which allows continuous variables; random intercepts and slopes; and missing data. Nonnormality robust standard errors and a chisquare 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 threelevel models can be estimated using the following special features:
Mplus Version 7 also features threelevel 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 fourlevel 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. CrossClassified SEM (TYPE=CROSSCLASSIFIED) Crossclassified 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, crossclassified 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 crossclassified models can be estimated using the following special features:
Crossclassified analysis offers a variety of new analysis opportunities, such as
ThreeStep Latent Class Modeling Mplus Version 7 features a proper threestep analyzeclassifyanalyze 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 3Step approach using Mplus. Paper can be downloaded from here. Mplus Web Notes: No. 15, Version 5, October 4, 2012. The threestep approach is specified using the AUXILIARY option of the VARIABLE command with the settings R3STEP, DU3STEP, and DE3STEP. The threestep 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 MoverStayer latent transition analysis. BiFactor EFA Rotations (ROTATION=BIGEOMIN, BICFQUARTIMAX) 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, BIGEOMIN and BICFQUARTIMAX 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. TwoTier Modeling Simplified maximumlikelihood computations are used when models have a twotier model structure. For twotier model structures, orthogonality among factors reduces the number of dimensions necessary for numerical integration. Mplus Version 7 automatically detects the possibility of twotier computations. Plots Of Moderated Mediation And CrossLevel 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), crosslevel 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
General Features:
New Mplus User's Guide Examples Following are 22 new Version 7 User's Guide Examples
New Technical Reports, Web Notes, and FAQs Technical Reports:
Web Notes:
FAQs:
Mplus Version 6.12, November 2011 Mplus Version 6.12 is available for Windows, Mac OS X, and Linux for both 32 and 64bit 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 64bit 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
General
Analysis Conditional on Covariates Mplus Version 6.1 has modified TYPE=GENERAL for models with all continuous outcomes and maximumlikelihood 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 continuousnormal 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 righthand 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 maximumlikelihood 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:
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 chisquare 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. Singlelevel 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:
Complex Survey Data
Survival Analysis
Missing Data (DATA MISSING)
General Features
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
New Technical Appendices and Technical Reports
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
Fit Statistics
Starting Values
Modification Indices
Monte Carlo Studies and Multiple Imputation
Important Corrections
Technical Appendices
Changed Example
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
Exploratory Factor Analysis
Missing Data Modeling
New Models For Count Variables
Mixture Modeling
Multilevel Modeling
General Features
Monte Carlo Simulation
New Technical Appendices
New Examples
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
General Features
Exploratory Factor Analysis
Mixture Modeling
Multilevel Modeling
New Technical Appendices
New Examples in the Version 5 Mplus User's Guide
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
Timing trials were carried out for several examples using different computer configurations. Click here to see the results of the timing trials. Twolevel Modeling With Multiple Latent Class Variables
Modeling With BetweenLevel Latent Class Variables
New Options For Complex Survey Data Weights With TYPE=TWOLEVEL
Click here for technical details about the scaling of sampling weights for twolevel models. Indirect Effects In Monte Carlo Simulation Studies
Added Output For Exploratory Factor Analysis
Added Output for TYPE = Imputation
Response Pattern Classification
Added Mixture Output
Added Output For Estimates In IRT Metric
New Graphics Features
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
Item Response Theory (IRT) Additions
Other New Features
The LRTSTARTS option is used in conjunction with the TECH14 option of the OUTPUT command to specify for the k1 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 pvalue 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 continuoustime 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
Extension of the MODEL CONSTRAINT command (484487)
Wald test of parameter constraints (487488) Simplified language for equality constraints involving a list of parameters (465466) BollenStine (residual) bootstrapped standard errors and chisquare pvalue (434435) Display of outliers and influential observations (530531)
Allowing a singular sample covariance matrix for covariates Loglikelihood correction factors for chisquare testing with ESTIMATOR = MLR Printing of chisquare contribution from each group in multiplegroup 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 discretetime survival data (299300*), twopart data (301303*), and data with nonignorable missingness Overall speed improvements Interactive controls during iterative optimization (442444) Multilevel Modeling and Complex Survey Data Analysis Twolevel modeling with censored, nominal, and count outcomes (249251*) Complex survey data options (400403)
Reduction of dimensions of numerical integration for certain multilevel models using maximum likelihood estimation Improved multiplegroup analysis of complex survey categorical data using WLS, WLSM, and WLSMV estimation Twolevel MODEL INDIRECT Betweenlevel 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
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 ContinuousTime Survival Analysis Cox regression  non parametric estimation (111112*) Parametric proportional hazards model  baseline hazard as a step function (112113*) Cox regression with random effects Parametric proportional hazards model with random effects (114115*) Cox regression mixture model (203204*) Parametric proportional hazards mixture model Multilevel Cox regression (251252*) Multilevel parametric proportional hazards model Twin, Sibling, and Family Genetics Modeling Twogroup twin model for continuous outcomes where factors represent the ACE components (6870*) Twogroup twin model for categorical outcomes where factors represent the ACE components (7072*) Twogroup twin model for continuous outcomes using parameter constraints (7475*) Twogroup twin model for categorical outcomes using parameter constraints (7576*) QTL sibling model for a continuous outcome using parameter constraints (7677*) New Examples in the Version 4 Mplus User's Guide 5.18: Twogroup twin model for continuous outcomes where factors represent the ACE components 5.19: Twogroup twin model for categorical outcomes where factors represent the ACE components 5.20: CFA with parameter constraints 5.21: Twogroup twin model for continuous outcomes using parameter constraints 5.22: Twogroup twin model for categorical outcomes using parameter constraints 5.23: QTL sibling model for a continuous outcome using parameter constraints 6.20: Continuoustime survival analysis using the Cox regression model 6.21: Continuoustime survival analysis using a parametric proportional hazards model 7.27: Factor mixture (IRT) analysis with binary latent class and factor indicators 8.16: Continuoustime survival mixture analysis using a Cox regression model 9.18: Twolevel continuoustime survival analysis using Cox regression with a random intercept 11.8: Monte Carlo simulation study for discretetime survival analysis 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:
Following are new features in Version 3.13:
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 chisquare 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
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 discretetime survival analysis models. The three modules are: a Mixture AddOn, a Multilevel AddOn, and a Combination AddOn. This arrangement allows users flexibility in selecting the addon modules that best meet their analysis needs. AddOn 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 AddOn 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 maximumlikelihood 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 AddOn The Mixture AddOn 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 AddOn The Multilevel AddOn estimates models for clustered data. It provides conventional multilevel analysis as well as new extensions that integrate multilevel modeling and SEM. The Multilevel AddOn contains statistical developments beyond Mplus Version 2. An example of one new feature is twolevel logistic regression. Another example is twolevel factor analysis with categorical indicators. Click here for more information. Combination AddOn The Combination AddOn includes both the Mixture AddOn and the Multilevel AddOn. 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 twolevel 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 Mplus Version 2.1 contains new options for the analysis of multilevel data in both crosssectional 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. Fullinformation 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. Nonnormality robust standard errors and a chisquare 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 YuanBentler 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 timevarying 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 timevarying covariates describe slope variation across individuals. TYPE=COMPLEX MIXTURE can now be used to obtain standard errors corrected for nonindependence of observations in mixture models. A sandwich estimator is used. Note that a nonmixture 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 NonNormal 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 chisquare test statistic for missing data with nonnormal outcomes by using a sandwich estimator and the YuanBentler 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 observeddata loglikelihood directly. EM optimizes the completedata loglikelihood using the expectationmaximization (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 chisquare 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 chisquare 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 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 discretetime survival analysis and nonignorable 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 chisquare 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. 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 sigmabetween covariance or correlation matrix and the sample pooledwithin 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. 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 prespecified number of iterations to automatically terminating iterations after convergence. Mplus Version 1, November 19, 1998 