1. Latent Variable Mixture Growth Modeling in Mplus
Dagmar Amtmann, Ph.D.
University of Washington
Department of Rehabilitation Medicine

2. Research Questions
Can individuals be sorted into reliably different subgroups based on their theta values on 3MS?
How many classes can be identified?
Can clinically useful predictors of membership in classes be identified?

3. Growth Mixture Models Build on conventional growth modeling
Identify underlying patterns when groups are unknown
Random coefficients that capture individual variation are continuous latent variables or growth factors.
The goal: Estimate the variation of the growth factors and to study the influence of background variables on this variation.

4. Categorical latent variable modeling captures heterogeneity that corresponds to qualitatively different development.
Each individual obtains a posterior probability estimate for being a member of each underlying latent class. The probability estimate is a function of the model estimates and the values of each individual on the observed variables.
Useful in early diagnosis or providing preventive interventions where early identification of problematic development is essential.

5. Selecting the model
The same number of classes (nested/hierarchical models
the likelihood-ratio chi-square difference
Models with different numbers of classes standard information criteria, such as Akakike’s and BIC may be used.

6. The Bayesian information criterion (BIC) BIC = Log (L) – 0.5 * (k)
L is the value of the model’s maximized likelihood,
n is the sample size, and k is the number of parameters in the model
Always negative
The value of BIC closest to 0 indicates a better fitting model
A difference of
0 to 2 BIC points = weak evidence
2 to 6 BIC points = positive evidence
6 to 10 BIC points = strong evidence
10+ BIC points = very strong

7. People w/Alzheimer Years 1 to 9 339 Individuals
3-class vs 4 class model

10. Normal Population Years 1 to 9 2,318
3 & 4 class models with education as predictor

13. Latent Variable Mixture Growth Modeling in Mplus
Dagmar Amtmann, Ph.D.
University of Washington
Department of Rehabilitation Medicine