Growth Mixture Modeling of Longitudinal Data

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Growth Mixture Modeling of Longitudinal Data

• David Huang, Dr.P.H., M.P.H.
• UCLA, Integrated Substance Abuse Program

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Longitudinal Data

• Subjects have repeated measures on some
  characteristics over time, which could be
• Medical history (ex blood pressure)
• Childrens learning curve (ex. math score)
• Babys growth curve (ex. weight)
• Drug use history (ex. heroin use)

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Growth Curve Modeling

• Level 1 represents intra-individual difference in
  repeated measures over time. (individual growth
  curve).
• Level 2 represents variation in individual growth
  curves.

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Growth Curve Model with One Class (N 436)
Days use per month
Years Since The First Use
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Limitation of Growth Curve Model

• Assume that growth curves are a sample from a
  single finite population. The growth model only
  represents a single average growth rate.

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Growth Mixture Modeling

• Including latent classes into growth curve
  modeling.
• Modeling individual variation in growth rates.
• Classifying trajectories by latent class
  analysis.

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Growth Mixture Model in Mplus
Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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Source Terry Duncan (2002). Growth Mixture
Modeling of Adolescent Alcohol Use Data.
www.ori.org/methodology
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• This study is based on 436 male heroin addicts
  who were admitted to the California Civil Addict
  Program at 1964-1965 and were followed in the
  three follow-up studies conducted every ten years
  over 33 years.

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Growth Curve Model with Two Classes (N 436)
Days use per month
Years Since The First Use
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Growth Curve Model with Three Classes (N 436)
Days of use per month
Years Since The First Use
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Growth Curve Model with Four Classes (N 436)
Days of use per month
Years Since The First Use
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Growth Curve Model with Five Classes (N 436)
Days of use per month
Years Since The First Use
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Goodness of fit

• Loglikelihood
• Akaike Information Criterion (AIC)
• Bayesian Information Criterion (BIC)
• Sample-size Adjusted BIC
• Entropy

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Adjusted BIC Index by Latent Classes
Adjusted BIC
Latent Classes
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Difficulties in Model fitting

• EM algorithm reaches a local maxima, rather than
  a global maxima.
• Repeat EM algorithm with different sets of
  initial values.
• Use BIC to compare the goodness-of-fit of models

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Example of Wrong Starting Values
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Difficulties in Model fitting

• EM algorithm would NOT converge.
• Start with a simple model. Set variance of
  intercept and slope at zero. Assume residuals
  are constant across the classes.

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Difficulties in Model fitting

• Individual classification is model dependent and
  initial value dependent. Individual
  classification could vary in different models.

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References

• Terry Duncan (2002). Growth Mixture Modeling of
  Adolescent Alcohol Use Data. www.ori.org/methodolo
  gy
• Muthén, B. (2004). Latent variable analysis
  Growth mixture modeling and related techniques
  for longitudinal data. In D. Kaplan (ed.),
  Handbook of quantitative methodology for the
  social sciences (pp. 345-368). Newbury Park, CA
  Sage Publications.