Mixture Modeling

Auxiliary Variables

• Asparouhov, T. & Muthén, B. (2014). Auxiliary variables in mixture modeling: Using the BCH method in Mplus to estimate a distal outcome model and an arbitrary second model. Mplus Web Notes: No. 21. May 14, 2014. Revised December 23, 2020. Download scripts.
  
  
• Asparouhov, T. & Muthén, B. (2014) Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 21:3, 329-341. The posted version corrects several typos in the published version. An earlier version of this paper was posted as web note 15. Download scripts.
  
  

Factor Mixture Analysis

• Kim, Y.K. & Muthén, B. (2009). Two-part factor mixture modeling:  Application to an aggressive behavior measurement instrument. Structural Equation Modeling, 6(4): 602–624. DOI: 10.1080/10705510903203516
  
  
• Lubke, G. & Muthén, B. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling, 14(1), 26–47. DOI: 10.1207/s15328007sem1401_2
  
  
• Muthén, B. & Asparouhov, T. (2006). Item response mixture modeling: Application to tobacco dependence criteria. Addictive Behaviors, 31, 1050-1066. DOI: 10.1016/j.addbeh.2006.03.026
  
  
• Lubke, G.H. & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10(1),21-39. DOI: 10.1037/1082-989X.10.1.21.
  
  

General Mixture Modeling

• Morin, A.J.S., & Wang, J.C.K. (2015, In Press). A gentle introduction to mixture modeling using physical fitness data. In N. Ntoumanis, & N. Myers (Eds.), An introduction to intermediate and advanced statistical analyses for sport & exercise scientists. London, UK: Wiley
  
  
• Morin, A. J. S. (2015, In Press). Person-centered research strategies in commitment research. In J.P. Meyer (Ed.), The handbook of employee commitment. Cheltenham, UK: Edward Elgar. Download supplements.
  
  
• Muthén, B. (2008). Latent variable hybrids:  Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 1-24. Charlotte, NC: Information Age Publishing, Inc.
  
  
• Muthén, B. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29(1), 81-117. DOI: 10.2333/bhmk.29.81
  
  
• Muthén, B. (2001). Latent variable mixture modeling. In G. A. Marcoulides & R. E. Schumacker (eds.), New Developments and Techniques in Structural Equation Modeling (pp. 1-33). Lawrence Erlbaum Associates. Mplus inputs and outputs.
  
  

Growth Mixture Modeling

• Muthén, B. & Asparouhov T. (2015). Growth mixture modeling with non-normal distributions. Statistics in Medicine, 34:6, 1041–1058. DOI: 10.1002/sim6388. Download paper.
  
  
• Muthén, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.
  
  
• Muthén, B. & Brown, H. (2009). Estimating drug effects in the presence of placebo response: Causal inference using growth mixture modeling. Statistics in Medicine, 28(27), 3363-85. DOI: 10.1002/sim.3721
  
  
• Muthén, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S., Carlin, J., & Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3(4), 459-475. DOI: 10.1093/biostatistics/3.4.459 Mplus inputs and outputs.
  
  
• Muthén, B. & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55(2),463-9. DOI: 10.1111/j.0006-341x.1999.00463.x
  
  

Latent Class Analysis

• Asparouhov, T. & Muthén, B. (2015). Residual associations in latent class and latent transition analysis. Structural Equation Modeling: A Multidisciplinary Journal, 22:2, 169-177, DOI: 10.1080/10705511.2014.935844 Download Mplus files.
  
  
• Asparouhov, T. & Muthén, B. (2014) Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 21:3, 329-341. DOI:10.1080/10705511.2014.915181 The posted version corrects several typos in the published version. An earlier version of this paper was posted as web note 15. Download scripts.
  
  
• Nylund, K.L., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling. A Monte Carlo simulation study. Structural Equation Modeling, 14, 535-569. DOI: 10.1080/10705510701575396
  
  

Latent Transition Analysis

• Muthén, B. & Asparouhov, T. (2011). LTA in Mplus: Transition probabilities influenced by covariates. Mplus Web Notes: No. 13. July 27, 2011.

Multilevel Mixture Modeling

• Collie, R.J., Malmberg, L.-E., Martin, A.J., Sammons, P., & Morin, A.J.S. (2020). A multilevel person-centered examination of teachers’ workplace demands and resources: Links with work-related well-being. Frontiers in Psychology, 11, 626. DOI: 10.3389/fpsyg.2020.00626
  
  
• Henry, K. & Muthén, B. (2010). Multilevel latent class analysis: An application of adolescent smoking typologies with individual and contextual predictors. Structural Equation Modeling, 17(2), 193–215. DOI: 10.1080/10705511003659342 View figures and syntax for all models.
  
  
• Muthén, B. & Asparouhov, T. (2009). Multilevel regression mixture analysis. Journal of the Royal Statistical Society, Series A, 172, 639-657. DOI: 10.1111/j.1467-985X.2009.00589.x
  
  
• Asparouhov, T. & Muthén, B. (2008). Multilevel mixture models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 27-51. Charlotte, NC: Information Age Publishing, Inc.
  
  

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