Statistical Analysis With Latent Variables


User’s Guide



















Linda K. Muthén

Bengt O. Muthén













Following is the correct citation for this document:


Muthén, L.K. and Muthén, B.O. (1998-2017).  Mplus User’s Guide.  Eighth Edition.

Los Angeles, CA: Muthén & Muthén












Copyright © 1998-2017 Muthén & Muthén

Program Copyright © 1998-2017 Muthén & Muthén

Version 8

April 2017



The development of this software has been funded in whole or in part with Federal funds from the National Institute on Alcohol Abuse and Alcoholism, National Institutes of Health, under Contract No. N44AA52008 and Contract No. N44AA92009.  



Muthén & Muthén

3463 Stoner Avenue

Los Angeles, CA  90066

Tel: (310) 391-9971

Fax: (310) 391-8971




Chapter 1:  Introduction                                                                                                 1


Chapter 2:  Getting started with Mplus                                                                        13


Chapter 3:  Regression and path analysis                                                                     19


Chapter 4:  Exploratory factor analysis                                                                        43


Chapter 5:  Confirmatory factor analysis and structural equation modeling                55


Chapter 6:  Growth modeling, survival analysis, and N=1 time series analysis         113


Chapter 7:  Mixture modeling with cross-sectional data                                            165


Chapter 8:  Mixture modeling with longitudinal data                                                            221


Chapter 9:  Multilevel modeling with complex survey data                                       261


Chapter 10: Multilevel mixture modeling                                                                   395


Chapter 11: Missing data modeling and Bayesian analysis                                        443


Chapter 12: Monte Carlo simulation studies                                                              465     


Chapter 13: Special features                                                                                       499


Chapter 14: Special modeling issues                                                                           515


Chapter 15: TITLE, DATA, VARIABLE, and DEFINE commands                                   563


Chapter 16: ANALYSIS command                                                                           651


Chapter 17: MODEL command                                                                                 711


Chapter 18: OUTPUT, SAVEDATA, and PLOT commands                                   791


Chapter 19: MONTECARLO command                                                                   859


Chapter 20: A summary of the Mplus language                                                         893



We started to develop Mplus in 1995 with the goal of providing researchers with powerful new statistical modeling techniques.  We saw a wide gap between new statistical methods presented in the statistical literature and the statistical methods used by researchers in substantively-oriented papers.  Our goal was to help bridge this gap with easy-to-use but powerful software.  Version 1 of Mplus was released in November 1998; Version 2 was released in February 2001; Version 3 was released in March 2004; Version 4 was released in February 2006; Version 5 was released in November 2007, Version 6 was released in April 2010; and Version 7 was released in September 2012.  After four expansions of Version 7 during the last five years, we are now proud to present the new and unique features of Version 8.  With Version 8, we have gone a considerable way toward accomplishing our goal, and we plan to continue to pursue it in the future.


The new features that have been added between Version 7 and Version 8 would never have been accomplished without two very important team members, Tihomir Asparouhov and Thuy Nguyen.  It may be hard to believe that the Mplus team has only two programmers, but these two programmers are extraordinary.  Tihomir has developed and programmed sophisticated statistical algorithms to make the new modeling possible.  Without his ingenuity, they would not exist.  His deep insights into complex modeling issues and statistical theory are invaluable.  Thuy has developed the post-processing graphics module, the Mplus editor and language generator, and the Mplus Diagrammer based on a framework designed by Delian Asparouhov.  In addition, Thuy has programmed the Mplus language and is responsible for producing new release versions, testing, and keeping control of the entire code which has grown enormously.  Her unwavering consistency, logic, and steady and calm approach to problems keep everyone on target.  We feel fortunate to work with such a talented team.  Not only are they extremely bright, but they are also hard-working, loyal, and always striving for excellence.  Mplus Version 8 would not have been possible without them. 


Another important team member is Michelle Conn.  Michelle was with us at the beginning when she was instrumental in setting up the Mplus office and returned fifteen years ago.  Michelle wears many hats:  Chief Financial Officer, Office Manager, and Sales Manager, among others.  She was the driving force behind the design of the new shopping cart.  With the vastly increased customer base, her efficiency in multi-tasking and calm under pressure are much appreciated.  Noah Hastings joined the Mplus team in 2009.  He is responsible for testing the Graphics Module and the Mplus Diagrammer,  creating the pictures of the models in the example chapters of the Mplus User’s Guide, keeping the website updated, and providing assistance to Bengt with presentations, papers, and our book.  He has proven to be a most trustworthy and valuable team member.


We would also like to thank all of the people who have contributed to the development of Mplus in past years.  These include Stephen Du Toit, Shyan Lam, Damir Spisic, Kerby Shedden, and John Molitor.


Initial work on Mplus was supported by SBIR contracts and grants from NIAAA that we acknowledge gratefully. We thank Bridget Grant for her encouragement in this work.


Linda K. Muthén

Bengt O. Muthén

Los Angeles, California

April 2017