Latent Growth Curve Modeling In Mplus:Latent Growth Curve Modeling In Mplus:An Introduction and Practice ExamplesAn Introduction and Practice Examples
Part IIPart II
Edward D. Barker, Ph.D.
Social, Genetic, and Developmental Psychiatry Centre Institute of Psychiatry, King’s College London
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
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
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.
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 . . . .
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
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.
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.
GMM: Muthén & Muthén, 2000
Intercept Slope
D12 D13 D14 D15 D16 D17
1.0 1.01.0 1.0 1.0 1.0
1.0 2.0 3.0 4.0 5.00.0
C
GMM: Nagin variety
Intercept Slope
D12 D13 D14 D15 D16 D17
1.0 1.01.0 1.0 1.0 1.0
1.0 2.0 3.0 4.0 5.00.0
C
GMM: Nagin variety
GMM: Selected output
GMM: Selected output
GMM: Starting values
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
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
GMM: Conditional
Conditional: Selected output
Starting values for conditional
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?
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
Class specific variance
Class specific variance
Class specific variance: Selected output
Class specific variance: Selected output
Starting values: Selected output
Practice 3
Run basic GMM Rename and add class specific variance Annotate output to note changes
Run again Use starting values from original model
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
Exporting probabilites
Exporting probabilites
Exporting probabilites
Exporting probabilites
Transposing
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
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
End
