Latent Growth Curve Modeling In Mplus: An Introduction and Practice Examples Part II

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. 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 Outline

3. 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 General Mixture Models

4. 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. When are GMMs appropriate?

5. 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 . . . . Deciding on number of classes

6. 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 Deciding on number of classes

7. 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. Deciding on number of classes

8. 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. Deciding on number of classes

9. GMM: Muthén & Muthén, 2000 C Slope Intercept 1.0 1.0 1.0 1.0 1.0 1.0 5.0 2.0 4.0 3.0 1.0 0.0 D12 D13 D14 D15 D16 D17

10. GMM: Nagin variety C Slope Intercept 1.0 1.0 1.0 1.0 1.0 1.0 5.0 2.0 4.0 3.0 1.0 0.0 D12 D13 D14 D15 D16 D17

11. GMM: Nagin variety

12. GMM: Selected output

13. GMM: Selected output

14. GMM: Starting values

15. 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 Practice 1

16. 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 Outline

17. GMM: Conditional

18. Conditional: Selected output

19. Starting values for conditional

20. 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? Practice 2

21. 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 Outline

22. Class specific variance

23. Class specific variance

24. Class specific variance: Selected output

25. Class specific variance: Selected output

26. Starting values: Selected output

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

28. 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 Outline

29. Exporting probabilites

30. Exporting probabilites

31. Exporting probabilites

32. Exporting probabilites

33. Transposing

34. 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 Practice 4

35. 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 Outline

36. End