Mixture class recovery in GMM under varying degrees of class separation: Frequentist versus bayesian estimation

Psychological Methods

Volumn 18, Issue 2, 2013, Pages 186-219

  Depaoli, Sarah ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian estimation; Growth mixture modeling; Latent class separation; Markov chain Monte Carlo; Priors

Indexed keywords

ARTICLE; BAYES THEOREM; BEHAVIORAL SCIENCE; COMPARATIVE STUDY; HUMAN; MONTE CARLO METHOD; PROBABILITY; SAMPLE SIZE; STATISTICAL ANALYSIS; STATISTICAL BIAS; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; STATISTICS; TIME;

BAYES THEOREM; BEHAVIORAL SCIENCES; BIAS (EPIDEMIOLOGY); DATA INTERPRETATION, STATISTICAL; HUMANS; MARKOV CHAINS; MODELS, STATISTICAL; MONTE CARLO METHOD; SAMPLE SIZE; STATISTICAL DISTRIBUTIONS; TIME FACTORS;

EID: 84879532581     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0031609     Document Type: Article

References (61)

1. Asparouhov, T., & Muthén, B. (2010). Bayesian analysis using Mplus. Los Angeles, CA: Muthén & Muthén.
2. Bauer, D. J. (2007). Observations on the use of growth mixture models in psychological research. Multivariate Behavioral Research, 42, 757-786.
3. Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338-363.
4. Berger, J. (2006). The case for objective Bayesian analysis. Bayesian Analysis, 3, 385-402.
5. Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. New York, NY: Wiley.
6. Brown, L. D. (2008). In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies. The Annals of Applied Statistics, 2, 113-152.
7. Candel, J. J. M., & Winkens, B. (2003). Performance of empirical Bayes estimators of level-2 random parameters in multilevel analysis: A Monte Carlo study for longitudinal designs. Journal of Educational and Behavioral Statistics, 28, 169-194.
8. Celeux, G., Hurn, M., & Robert, C. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association, 95, 957-970.
9. Chung, T., Maisto, S. A., Cornelius, J. S., & Martin, C. S. (2004). Adolescents' alcohol and drug use trajectories in the year following treatment. Journal of Studies on Alcohol, 69, 105-114.
10. Darniede, W. F. (2011). Bayesian methods for data-dependent priors (Doctoral dissertion). Ohio State University, Columbus.
11. Depaoli, S. (in press). The impact of "inaccurate" informative priors for growth parameters in Bayesian growth mixture modeling. Structural Equation Modeling.
12. Diebolt, J., & Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society, 56, 363-375.
13. Enders, C. K., & Tofighi, D. (2008). The impact of misspecifying classspecific residual variances in growth mixture models. Structural Equation Modeling, 15, 75-95.
14. Farrar, D. (2006). Approaches to the label-switching problem of classification, based on partition-space relabeling and label-invariant visualization. Blacksburg, VA: Virginia Polytechnic Institute and State University.
15. Frühwirth-Schnatter, S. (2001). Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. Journal of the American Statistical Association, 96, 194-209.
16. Gelman, A. (1996). Inference and monitoring convergence. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 131-143). New York, NY: Chapman & Hall.
17. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis. New York, NY: Chapman & Hall/CRC.
18. Gelman, A., & Rubin, D. B. (1992a). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-511.
19. Gelman, A., & Rubin, D. B. (1992b). A single series from the Gibbs sampler provides a false sense of security. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics 4 (pp. 625-631). Oxford, England: Oxford University Press.
20. Ghosh, J. K., & Mukerjee, R. (1992). Non-informative priors (with discussion). In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics 4 (p. 195-210). Oxford, England: Oxford University Press.
21. Gueorguieva, R., Mallinckrodt, C., & Krystal, J. (2011). Trajectories of depression severity in clinical trials of Duloxetine. Archives of General Psychiatry, 68, 1227-1237.
22. Henson, J. M., Reise, S. P., & Kim, K. H. (2007). Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling, 14, 202-226.
23. Hipp, J. R., & Bauer, D. J. (2006). Local solutions in the estimation of growth mixture models. Psychological Methods, 11, 36-53.
24. Jasra, A., Holmes, C. C., & Stephens, D. A. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science, 20, 50-67.
25. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16, 39-59.
26. Kaplan, D. (2002). Methodological advances in the analysis of individual growth with relevance to education policy. Peabody Journal of Education, 77, 189-215.
27. Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343-1370.
28. Kenny, D. A. (1979). Correlation and causality. New York, NY: Wiley.
29. Lambert, P. C., Sutton, A. J., Burton, P. R., Abrams, K. R., & Jones, D. R. (2005). How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS. Statistics in Medicine, 24, 2401-2428.
30. Lee, S.-Y. (2007). Structural equation modeling: A Bayesian approach. Chichester, England: Wiley.
31. Lubke, G. H., & Muthén, B. O. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21-39.
32. Lubke, G. H., & Muthén, B. O. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling, 14, 26-47.
33. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York, NY: Wiley.
34. Morin, A., Mainano, C., Nagengast, B., Marsh, H., Morizot, J., & Janosc, M. (2011). General growth mixture analysis of adolescents' developmental trajectories of anxiety: The impact of untested invariance assumptions on substantive interpretations. Structural Equation Modeling, 18, 613-648.
35. Muthén, B. O. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological Methods, 8, 369-377.
36. Muthén, B. O. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (Ed.), Handbook of quantitative methodology for the social sciences (pp. 345-368). Newbury Park, CA: Sage.
37. Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17, 313-335.
38. Muthén, B. O., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882- 891.
39. Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.
40. Muthén, L. K., & Muthén, B. (2012). Mplus user's guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
41. Nagin, D. S. (1999). Analyzing developmental trajectories: A semiparametric, group-based approach. Psychological Methods, 4, 139-157.
42. Natarajan, R., & McCulloch, C. E. (1998). Gibbs sampling with diffuse proper priors: A valid approach to data-driven inference? Journal of Computational and Graphical Statistics, 7, 267-277.
43. Nylund, K., 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.
44. O'Hagan, A. (1998). Eliciting expert beliefs in substantial practical applications. The Statistician, 47, 21-35.
45. O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. R., Garthwaite, P. H., Jenkinson, D. J., . . . Rakow, T. (2006). Uncertain judgments: Eliciting experts' probabilities. New York, NY: Wiley.
46. Raftery, A. E., & Lewis, S. M. (1996). Implementing MCMC. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 115-130). New York, NY: Chapman & Hall.
47. Richardson, S., & Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society, 59, 731-792.
48. Rindskopf, D. (2003). Mixture or homogeneous? Comment on Bauer and Curran (2003). Psychological Methods, 8, 364-368.
49. Roeder, K., & Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894-902.
50. Schaeffer, C., Petras, H., Ialongo, N., Masyn, K., Hubbard, S., Poduska, J., & Kellan, S. (2006). A comparison of girl's and boy's aggressive-disruptive behavior trajectories across elementary school: Prediction to young adult antisocial outcomes. Journal of Consulting and Clinical Psychology, 74, 500-510.
51. Sinharay, S. (2004). Experiences with Markov chain Monte Carlo convergence assessment in two psychometric examples. Journal of Educational and Behavioral Statistics, 29, 461-488.
52. Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman & Hall/CRC.
53. Stephens, M. (2000). Dealing with label switching in mixture models. Journal of the Royal Statistical Society, 62, 795-809.
54. Szapocznik, J., Feaster, D. J., Mitrani, V. B., Prado, G., Smith, L., Robinson-Batista, C., . . . Robbins, M. S. (2004). Structural ecosystems therapy for HIV-Seropositive African American women: Effects on psychological distress, family hassles, and family support. Journal of Consulting and Clinical Psychology, 72, 288-303.
55. Tofighi, D., & Enders, C. K. (2008). Identifying the correct number of classes in growth mixture models. In G. R. Hancock & K. M. Samuelson (Eds.), Advances in latent variable mixture models (pp. 317-341). Charlotte, NC: Information Age.
56. Tolvanen, A. (2008). Latent growth mixture modeling: A simulation study (Doctoral dissertation). University of Jyväskylä, Jyväskylä, Finland.
57. Tueller, S., & Lubke, G. (2010). Evaluation of structural equation mixture models: Parameter estimates and correct class assignment. Structural Equation Modeling, 17, 165-192.
58. van der Linden, W. J. (2008). Using response times for item selection in adaptive testing. Journal of Educational and Behavioral Statistics, 33, 5-20.
59. Wasserman, L. (2000). Asymptotic inference for mixture models using data-dependent priors. Journal of the Royal Statistical Society, 62, 159-180.
60. Yang, M., & Dunson, D. B. (2010). Bayesian semiparametric structural equation models with latent variables. Psychometrika, 75, 675-693.
61. Zhang, Z., Hamagami, F., Wang, L., Nesselroade, J. R., & Grimm, K. (2002). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Development, 31, 374 - 383.