Latent Growth Curve Modeling In Mplus:

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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, Kings
College London
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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

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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

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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.

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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
  . . . .

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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

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Deciding on number of classes

• Entropy
• This is a measure of how clearly distinguishable
  the classes are based on how distinctly each
  individuals 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.

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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.

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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
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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
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GMM Nagin variety
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GMM Selected output
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GMM Selected output
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GMM Starting values
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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

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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

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GMM Conditional
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Conditional Selected output
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Starting values for conditional
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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?

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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

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Class specific variance
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Class specific variance
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Class specific variance Selected output
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Class specific variance Selected output
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Starting values Selected output
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Practice 3

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

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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

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Exporting probabilites
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Exporting probabilites
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Exporting probabilites
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Exporting probabilites
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Transposing
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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

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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

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• End