Growth Mixture Modeling of Longitudinal Data

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) Days use per month Years Since The First Use

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

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

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

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

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

13. 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) Days use per month Years Since The First Use

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

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

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

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 Adjusted BIC Latent Classes

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

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.