1. Growth Mixture Modeling of Longitudinal Data David Huang, Dr.P.H., M.P.H. UCLA, Integrated Substance Abuse Program

2. Longitudinal Data Subjects have repeated measures on some characteristics over time, which could be Medical history (ex blood pressure) Children’s learning curve (ex. math score) Baby’s growth curve (ex. weight) Drug use history (ex. heroin use)

4. Growth Curve Modeling Level 1 represents intra-individual difference in repeated measures over time. (individual growth curve). Level 2 represents variation in individual growth curves.

5. Growth Curve Model with One Class (N = 436) Years Since The First Use Days use per month

6. Limitation of Growth Curve Model Assume that growth curves are a sample from a single finite population. The growth model only represents a single average growth rate.

7. Growth Mixture Modeling Including latent classes into growth curve modeling. Modeling individual variation in growth rates. Classifying trajectories by latent class analysis.

8. Growth Mixture Model in Mplus Source: Terry Duncan (2002). Growth Mixture Modeling of Adolescent Alcohol Use Data. www.ori.org/methodology

14. This study is based on 436 male heroin addicts who were admitted to the California Civil Addict Program at 1964-1965 and were followed in the three follow-up studies conducted every ten years over 33 years.

15. Growth Curve Model with Two Classes (N = 436) Years Since The First Use Days use per month

16. Growth Curve Model with Three Classes (N = 436) Years Since The First Use Days of use per month

17. Growth Curve Model with Four Classes (N = 436) Years Since The First Use Days of use per month

18. Growth Curve Model with Five Classes (N = 436) Years Since The First Use Days of use per month

19. Goodness of fit Loglikelihood Akaike Information Criterion (AIC) Bayesian Information Criterion (BIC) Sample-size Adjusted BIC Entropy

20. Adjusted BIC Index by Latent Classes Latent Classes Adjusted BIC

21. Difficulties in Model fitting EM algorithm reaches a local maxima, rather than a global maxima. Repeat EM algorithm with different sets of initial values. Use BIC to compare the goodness-of-fit of models

22. Example of Wrong Starting Values Three Classes (WRONG STRATING VALUES) Three Classes Member 1Member 2Member 3Member 1Member 2Member 3 Intercept21.443.4314.11*6.4010.08**26.06** Slope-1.16-1.250.67-0.021.26**-0.58 Treatment on I-0.13-0.010.16 -0.08-0.04 Treatment on S0.0050.06-0.01-0.020.0020.01 Class mean-2.43**-1.15---0.71--0.41 Treatment on class0.05**-0.05--0.03*--0.004 % of individual in each class (estimated) 161.8 (0.32) 73.7 (0.14)275.5 (0.54)178.9 (0.35) 121.8 (0.24) 210.3 (0.41) % of individual in each class (observed) 162 (0.32) 70 (0.14)279 (0.54)176 (0.34) 123 (0.24)212 (0.41) Log Ho-31234.5-31132.3 Akaike (AIC)62533.062328.7 Bayesian (BIC)62668.662464.3 Adjusted BIC62567.062362.7 Entropy0.8970.890

24. Difficulties in Model fitting EM algorithm would NOT converge. Start with a simple model. Set variance of intercept and slope at zero. Assume residuals are constant across the classes.

25. Difficulties in Model fitting Individual classification is model dependent and initial value dependent. Individual classification could vary in different models.

27. References Terry Duncan (2002). Growth Mixture Modeling of Adolescent Alcohol Use Data. www.ori.org/methodology Muthén, B. (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 Publications.