1. Latent Growth Curve Modeling In Mplus: An Introduction and Practice Examples Part II Edward D. Barker, Ph.D. Social, Genetic, and Developmental Psychiatry Centre Institute of Psychiatry, King’s College London

2. Outline  Basic unconditional GMM  Introduction  Mplus code  Output and graphs  Conditional GMM (predictor)  Introduction  Mplus code  Output  Class-specific variance?  Introduction  Mplus code  Output and graphs  Exporting probabilities  Save from Mplus  Import to SPSS  Transpose file  Merge with data file  Run “weighted” frequency  Practice: 1 to 6 traj solutions

3. General Mixture Models  Latent growth curve models examine individual variation around a single mean growth curve  What we have been examining up to now  Growth Mixture models relaxes this assumption  Population may consist of a mixture of distinct subgroups defined by their developmental trajectories  Heterogeneity in developmental trajectories  Each of wich may represent distinct etiologies and/or outcomes

4. When are GMMs appropriate?  Populations contain individuals with normative growth trajectories as well as individuals with non-normative growth  Delinquent behaviors and early onset vs. late onset distinction (Moffitt, 1993)  Different factors may predict individual variation within the groups as well as distal outcomes of the growth processes  May want different interventions for individuals in different subgroups on growth trajectories. We could focus interventions on individuals in non- normative growth directories that have undesirable consequences.

5. Deciding on number of classes  Muthén, 2004  Estimate 1 to 6 trajectory solutions (Familiar with EFAs?)  Compared fit indices (to be covered)  Add trajectory specific variation to models  Model fit and classification accuracy improves  Important: usefulness of the latent classes (Nagin, 2005)  Check to make sure the trajectories make sense from your data  Do they validate?  NO? Is this related to age-range, predictors, outcomes, covariates?  Look at early publications with 6-7 trajectories....

6. Deciding on number of classes  Bayesian Information Criterion  BIC = -2logL + p ln n  where p is number of free parameters (15)  n is sample size (1102)  -2(-18553.315) + 15(log(1102)) = 37211.703  smaller is better, pick solution that minimizes BIC

7. Deciding on number of classes  Entropy  This is a measure of how clearly distinguishable the classes are based on how distinctly each individual’s estimated class probability is.  If each individual has a high probability of being in just one class, this will be high.  It ranges from zero to one with values close to one indicating clear classification.

8. Deciding on number of classes  Lo, Mendell, and Rubin likelihood ratio test (LMR-LRT)  Tests class K is better fit to data compared to K-1 class  2 vs. 1; 3 vs 2; 4 vs 3, etc.

9. GMM: Muthén & Muth é n, 2000 Intercept Slope D12D13D14D15D16D17 1.0 2.0 3.0 4.0 5.0 0.0 C

10. GMM: Nagin variety Intercept Slope D12D13D14D15D16D17 1.0 2.0 3.0 4.0 5.0 0.0 C

11. GMM: Nagin variety

12. GMM: Selected output

14. GMM: Starting values

15. Practice 1  Run basic GMM  Write Mplus code  Annotate output  View graph of estimate and observed trajectories  Get starting values (write them down)  Change basic GMM code  Include starting values  Re-run and examine trajectories

16. Outline  Basic unconditional GMM  Introduction  Mplus code  Output and graphs  Conditional GMM (predictor)  Introduction  Mplus code  Output  Class-specific variance?  Introduction  Output and graphs  Exporting probabilities  Save from Mplus  Import to SPSS  Transpose file  Merge with data file  Run “weighted” frequency  Practice: 1 to 6 traj solutions

17. GMM: Conditional

18. Conditional: Selected output

19. Starting values for conditional

20. Practice 2  Run Conditional GMM without starting values  Annotate output  View graph of estimated and observed trajectories  Run Conditional GMM with starting values  Get starting values from basic GMM model  Annotate output  View graph of observed and estimated trajectories  Question: do starting values always work?

21. Outline  Basic unconditional GMM  Introduction  Mplus code  Output and graphs  Conditional GMM (predictor)  Introduction  Mplus code  Output  Class-specific variance?  Introduction  Output and graphs  Exporting probabilities  Save from Mplus  Import to SPSS  Transpose file  Merge with data file  Run “weighted” frequency

22. Class specific variance

24. Class specific variance: Selected output

26. Starting values: Selected output

27. Practice 3  Run basic GMM  Rename and add class specific variance  Annotate output to note changes  Run again  Use starting values from original model

28. Outline  Basic unconditional GMM  Introduction  Mplus code  Output and graphs  Conditional GMM (predictor)  Introduction  Mplus code  Output  Class-specific variance?  Introduction  Output and graphs  Exporting probabilities  Transpose file  Merge with data file  Run “weighted” ANOVA  Mplus code  SPSS code  Output  Practice: 1 to 6 traj solutions

29. Exporting probabilites

33. Transposing

34. Practice 4  Run basic GMM with starting values  Save data  Import to SPSS  Transpose  Merge with original SPSS data file  Weight by PROB  Run frequency on TRAJ

35. Outline  Basic unconditional GMM  Introduction  Mplus code  Output and graphs  Conditional GMM (predictor)  Introduction  Mplus code  Output  Class-specific variance?  Introduction  Output and graphs  Exporting probabilities  Transpose file  Merge with data file  Run “weighted” ANOVA  Mplus code  SPSS code  Output  Practice: 1 to 6 traj solutions

36. End