latent growth curve modeling in mplus: an introduction and practice examples part ii

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