Difficulties
1. Sample size requirement (N, J, or mixing proportions).
2. Trade-off between convergence and model flexibility.
2. Trade-off between convergence and model flexibility.
Q: Why NOT constrained GMMs?
A:
1) retains per-specific trajectories within each class.
2) Reduce the frequency of singularities in the likelihood (?)
Q: Disadvantages of CPGMMs.
A:
1) lose the ability to obtain person-specific trajectories and the ability to differentiate between-person and within-person sources of variance.
2) researchers have the additional responsibility to select the structure of marginal covariance.
A:
1) retains per-specific trajectories within each class.
2) Reduce the frequency of singularities in the likelihood (?)
Q: Disadvantages of CPGMMs.
A:
1) lose the ability to obtain person-specific trajectories and the ability to differentiate between-person and within-person sources of variance.
2) researchers have the additional responsibility to select the structure of marginal covariance.
Further research directions:
- Different fit indices have different purposes. They should be applied by considering their appropriate situations.
- High Pareto's K values happen for the 4-class solution.
- The MLE local maxima and the HMC multimodalities.
- Prior distributions.
a) forgot to assign a prior distribution for the slope of the quadratic term.
b) assigned informative prior distributions to mean parameters.
c) the more appropriate the prior distribution chosen, the faster the model.
d) the concentration parameter values of the Dirichlet prior distribution. Maybe that is due to that we allow the covariance matrix to be freely estimated across latent classes, and this is too ambitious. Maybe we mis-capture too many between-subject, within-class variances that actually are between-class heterogeneous? If we go back to the middle version and set the same concentration values for the Dirichlet prior distribution, the problem vanished.
e) Data does not constraint parameters through the likelihood, then including a weakly informative prior can help to constrain posterior to reasonable values.
f) when prior distribution conflicts with the data, the label-switching problem will happen?