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

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

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)

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

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

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

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

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

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?

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

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

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

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 | t1@0 t2@1 t3@2; OUTPUT: sampstat standardized;

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

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 | t1@0 t2@1 t3@2; i-s@0; OUTPUT: sampstat standardized tech11 tech14;

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

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 | t1@0 t2@1 t3@2; OUTPUT: sampstat standardized tech11 tech14;

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)

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 | t1@0 t2@1 t3@2; OUTPUT: sampstat standardized tech11 tech14;

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.)

An Example Using Mplus Symptoms of PTSD: 2-Class Model 3-Class Model BIC = 178.04 Entropy = 1.00 Class 1 (n = 16); Class 2 (n = 6) 3-Class Model BIC = 131.99 Class 1 (n = 20); Class 2 (n = 1); Class 3 (n = 1)

PTSD – 2 Class Model

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

An Example Using Mplus Symptoms of SUD: 2-Class Model 3-Class Model BIC = 167.78 Entropy = 1.00 Class 1 (n = 1); Class 2 (n = 21) 3-Class Model BIC = 166.05 Class 1 (n = 18); Class 2 (n = 3); Class 3 (n = 1)

SUD – 3 Class Model

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?

Thank-You …for listening Everyone at the Baltimore VA Get slides from my ResearchGate page or e-mail mmoore@adelphi.edu