Growth mixture modeling with non-normal distributions

Statistics in Medicine

Volumn 34, Issue 6, 2015, Pages 1041-1058

  Muthén, Bengt ^a   Asparouhov, Tihomir ^a  

^a Mplus   (United States)

Author keywords

Body mass index; Skew t distribution; Survival; Trajectory classes

Indexed keywords

AGE DISTRIBUTION; ARTICLE; BODY MASS; DATA ANALYSIS; GROWTH MIXTURE MODELING; GROWTH RATE; HUMAN; HYPERTENSION; INTERMETHOD COMPARISON; LONGITUDINAL STUDY; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONNORMAL DISTRIBUTION; OUTCOME ASSESSMENT; PROCESS DEVELOPMENT; PROCESS MODEL; RISK ASSESSMENT; RISK FACTOR; RISK REDUCTION; SCORING SYSTEM; STATISTICAL DISTRIBUTION; SURVIVAL RATE; ADOLESCENT; ADULT; AFRICAN AMERICAN; AGED; CHILD; FEMALE; MALE; MIDDLE AGED; MONTE CARLO METHOD; PROPORTIONAL HAZARDS MODEL; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; SURVIVAL; YOUNG ADULT;

ADOLESCENT; ADULT; AFRICAN AMERICANS; AGED; BODY MASS INDEX; CHILD; FEMALE; HUMANS; HYPERTENSION; LIKELIHOOD FUNCTIONS; LOGISTIC MODELS; LONGITUDINAL STUDIES; MALE; MIDDLE AGED; MODELS, STATISTICAL; MONTE CARLO METHOD; PROPORTIONAL HAZARDS MODELS; STATISTICAL DISTRIBUTIONS; SURVIVAL ANALYSIS; YOUNG ADULT;

EID: 84922236834     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6388     Document Type: Article

References (27)

1. Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics 1982; 38:963-974.
2. McLachlan GJ, Peel D. Finite Mixture Models, Wiley: New York.
3. Verbeke G, Lesaffre E. A linear mixed-effects model with heterogeneity in the random effects population. Journal of the American Statistical Association 1996; 91:217-221.
4. Muthén B, Shedden K. Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 1999; 55:463-469.
5. Nagin DS, Land KC. Age, criminal careers, and population heterogeneity: specification and estimation of a nonparametric, mixed Poisson model. Criminology 1993; 31:327-362.
6. Roeder K, Lynch KG, Nagin DS. Modeling uncertainty in latent class membership: a case study in criminology. Journal of the American Statistical Association 1999; 94:766-776.
7. Lin H, McCulloch CE, Turnbull BW, Slate E, Clark LC. A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations. Statistics in Medicine 2000; 19(10): 1303-1318.
8. Lin H, Turnbull BW, McCulloch CE, Slate E. Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association 2002; 97:53-65.
9. Muthén B, Brown H. Estimating drug effects in the presence of placebo response: causal inference using growth mixture modeling. Statistics in Medicine 2009; 28:3363-3385.
10. Muthén B, Asparouhov T, Growth mixture modeling: analysis with non-Gaussian random effects. In Longitudinal Data Analysis, Fitzmaurice G, Davidian M, Verbeke G, Molenberghs G (eds.) Chapman & Hall/CRC Press: Boca Raton, 2009; 143-165.
11. Muthén B, Asparouhov T, Hunter A, Leuchter A. Growth modeling with non-ignorable dropout: alternative analyses of the STAR*D antidepressant trial. Psychological Methods 2011; 16:17-33.
12. Erosheva EA, Matsueda RL, Telesca D. Breaking bad: two decades of life-course data analysis in criminology, developmental psychology, and beyond. Annual Review of Statistics and its Applications 2014; 1:301-332.
13. Pearson K. Contributions to the theory of mathematical evolution. Philosophical Transactions of the Royal Society of London A 1895; 186:343-414.
14. Schork NJ, Schork MA. Skewness and mixtures of normal distributions. Communications Statistics Theory Methods 1988; 17:3951-3969.
15. Bauer DJ, Curran PJ. Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes. Psychological Methods 2003; 8:338-363.
16. Lin T, Wu PH, McLachlan GJ, Lee SX. The skew-t factor analysis model. Submitted. Available from: http://arxiv.org/abs/1310.5336 [accessed on 4 December 2014].
17. Lee S, McLachlan GJ. Finite mixtures of multivariate skew t-distributions: some recent and new results. Journal of Statistics and Computing 2014; 24:181-202.
18. Asparouhov T, Muthén B. Structural equation models and mixture models with continuous non-normal skewed distributions. Accepted for publication in Structural Equation Modeling 2014).
19. Lu X, Huang Y. Bayesian analysis of nonlinear mixed-effects mixture models for longitudinal data with heterogeneity and skewness. Statistics in Medicine 2014; 33:2701-2880.
20. Boik RJ, Robison-Cox JF. Derivatives of the incomplete beta function. Journal of Statistical Software3: 1998; 1-19.
21. Murphy SA, van der Vaart AW. On profile likelihood. Journal of the American Statistical Association 2000; 95:449-465.
22. Larsen K. Joint analysis of time-to-event and multiple binary indicators of latent classes. Biometrics 2004; 60(1): 85-92.
23. Asparouhov T, Masyn K, Muthén B. Continuous time survival in latent variable models. Proceedings of the Joint Statistical Meeting in Seattle, August 2006. ASA section on Biometrics, Seattle, Washington, 2006; 180-187.
24. Muthén L, Muthén B. Mplus User's Guide Seventh Edition. Muthén & Muthén: Los Angeles, CA, 2012.
25. Nonnemaker JM, Morgan-Lopez AA, Pais JM, Finkelstein EA. Youth BMI trajectories: evidence from the NLSY97. Obesity 2009; 17:1274-1280.
26. Dawber TR, Kannel WB, Lyell LP. An approach to longitudinal studies in a community: the Framingham study. Annals of the New York Academy of Sciences 1963; 107:539-556.
27. Muthén B, Asparouhov T, Boye M, Hackshaw M, Naegeli A. Applications of continuous-time survival in latent variable models for the analysis of oncology randomized clinical trial data using Mplus, Technical Report 2009. Available from: wwww.statmodel.com [accessed on 4 December 2014].