1. Growth mixture modeling
Michael Moore, Ph.D.
Growth mixture modeling
An Introduction and Illustrative Example

2. Overview What is growth mixture modeling (GMM)?
How do you determine how many classes are present in your data?
Issues in GMM
How do you do it?
An example of GMM using Mplus

3. What is GMM?
Growth mixture modeling (GMM): Goal is characterized inter-individual differences in intra- individual change over time (Nesselroade, 1991)
Can we reliably classify people on the basis on how they change over time?
Applications include: how people develop, naturally, over time, how people change during therapy, etc.
Person-centered: classify individuals, not describe relationships between variables (unlike regression, factor analysis)

4. What is GMM? Extension of latent variable growth curve modeling (LGM)
Goal is to characterize individuals on basis of estimate of growth parameters (intercept & slope)
Intercept – where you begin (before change)
Slope – describes rate & shape of change process
GMM identifies subgroups on basis of intercept & slope

5. What is GMM? GMM similar to latent class analysis (LCGA)
LCGA, unlike GMM, assumes homogeneity in growth trajectories within a class

6. LGM vs. LCGA vs. GMM
(Shiyko, Ram, & Grimm, 2012)

7. How many classes? Many different indices of fit:
Posterior probabilities – what is the probability of being in a given class for a given individual
Entropy – aggregate of posterior probabilities (closer to 1, the better)
Akaike/Bayesian Information Criteria (A/BIC) – smaller is better
Lo, Mendell, Rubin (2001) Likelihood Ratio Test (LMR- LRT) – compares the estimated model with model with one fewer class, p < .05 indicates estimated model is superior
Bootstrap Likelihood Ratio Test (BLRT) – LRT with bootstrapped samples, very computation intense

8. How many classes?
Limited research (Nylund, Asparouhov, Muthén, 2007) suggests that BLRT and A/BIC perform best
BUT, Nylund et al. suggest use of BIC & LMR to narrow down to a few models, then use BLRT

9. How many classes?
Remember: GMM is exploratory technique, so a priori theory is best judge (Bauer & Curran, 2003; Muthén, 2003; Rindskopf, 2003)
Like EFA
Replication is important, if not essential
Does this class make sense?
Is Class A really different from Class B?
Does each class contain a sufficient number of people to be considered reliable?

10. Issues in GMM Problems with convergence
GMMs notorious for convergence problems
May need to give the computer a lot more time to do its thing
Have to worry about computer settling on solution that is not optimal (“local solution”)
OK to change defaults
Mplus default = 10 random starts & 2 optimizations at the final stage
Correct solution only obtained in 23% of 200 data sets with default starts – OK to increase number of starts to 50 – 100 (Hipp & Bauer, 2006)
Increasing starts will increase computation time
Not much research as guide

11. Issues in GMM Sample size?
Fit indices correctly identified number of classes with n = 500+ (Nylund, et al., 2007)
Again, not much research to guide decision-making

12. How do you do it? Recommendations by Jung & Wickrama (2008)
Specify a single-class LGM
Look for significant (unmodeled) variability in this trajectory

13. LGM Mplus Syntax
DATA: file is ‘C:\filename.dat’; VARIABLE: names are id sex t1 t2 t3; usevar = t1-t3; missing = all (999); ANALYSIS: type = missing H1; MODEL: i s | OUTPUT: sampstat standardized;

14. How do you do it? Specify LCGA without covariates
LCGA results will be cleaner than GMM – in case of non-convergence/ill fit, makes isolating cause(s) easier

15. LCGA Mplus Syntax
DATA: file is ‘C:\filename.dat’; VARIABLE: names are id sex t1 t2 t3; usevar = t1-t3; missing = all (999); classes = c(3); ANALYSIS: type = mixture; starts = 10 2; stiterations = 10; MODEL: % overall % i s | OUTPUT: sampstat standardized tech11 tech14;

16. How do you do it? Specify GMM without covariates
Specify GMM with covariates
Can examine predictor(s) of intercept/slope & class membership (not included)

17. GMM Mplus Syntax
DATA: file is ‘C:\filename.dat’; VARIABLE: names are id sex t1 t2 t3; usevar = t1-t3; missing = all (999); classes = c(3); ANALYSIS: type = mixture; starts = 10 2; stiterations = 10; MODEL: % overall % i s | OUTPUT: sampstat standardized tech11 tech14;

18. How do you do it? Validate classes
Done via identification of correlates of class membership
Can have Mplus save a data file containing which class each participant is predicted to be in
Then merge with existing dataset(s)

19. GMM Mplus Syntax
DATA: file is ‘C:\filename.dat’; VARIABLE: names are id sex t1 t2 t3; usevar = t1-t3; idvariable = id; missing = all (999); classes = c(3); SAVEDATA: file is C:\; save = filename; ANALYSIS: type = mixture; starts = 10 2; stiterations = 10; MODEL: % overall % i s | OUTPUT: sampstat standardized tech11 tech14;

20. An Example Using Mplus
Investigation of 6-week, residential ACT treatment for comorbid PTSD/SUD
Very small sample size (n = 23)
Participants assessed at pre-, post-treatment, & 4-6 week follow-up
Treatment consisted of:
ACT education group (2x weekly, 60 mins.)
ACT process group (3x weekly, 90 mins.)
Coping skills group (2x weekly, 90 mins.)
Trauma education group (1x weekly, 60 mins.)
Insomnia group (1x weekly, 60 mins.)
Anger mgmt. group (1x weekly, 60 mins.)
Daily living skills group (2x weekly, 75 mins.)
Individual case mgmt. sessions (1x weekly, 50 mins.)

21. An Example Using Mplus Symptoms of PTSD: 2-Class Model 3-Class Model
BIC =
Entropy = 1.00
Class 1 (n = 16); Class 2 (n = 6)
3-Class Model
BIC =
Class 1 (n = 20); Class 2 (n = 1); Class 3 (n = 1)

22. PTSD – 2 Class Model

23. An Example Using Mplus Symptoms of PTSD:
Class 1 – PTSD sxs decrease over acute tx, but increase over fup
Class 2 – PTSD sxs increase over acute tx, but decrease over fup
Predicted outcome from an ACT/exposure model
Exp avoidance lower in Class 2 (vs. Class 1) – p < .001

24. An Example Using Mplus Symptoms of SUD: 2-Class Model 3-Class Model
BIC =
Entropy = 1.00
Class 1 (n = 1); Class 2 (n = 21)
3-Class Model
BIC =
Class 1 (n = 18); Class 2 (n = 3); Class 3 (n = 1)

25. SUD – 3 Class Model

26. An Example Using Mplus Symptoms of SUD:
Class 1 – Relative stability of SUD sx over time
Class 2 – SUD sxs increase over acute tx, but decrease over time
Exp avoidance lower in Class 2 (vs. Class 1) – p < .001
Sx increase during acute tx & desistence afterwards predicted by ACT/exposure model?

27. Thank-You …for listening Everyone at the Baltimore VA
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