Hi Stan folks,
I want to share a recent Psychometrika paper that might be useful for those working on growth mixture models (GMMs) or interested in diagnosing and addressing estimation issues in Stan:
“Bayesian Identification and Estimation of Growth Mixture Models”
by Xingyao Xiao, Sophia Rabe-Hesketh, and Anders Skrondal
Published April 2025 | [Link to paper]
GitHub with code and diagnostics: GitHub - DoriaXiao/BayesianIdentification
We apply GMMs to data from the National Longitudinal Survey of Youth (NLSY) to investigate whether children follow different reading development trajectories between ages 6 and 14. These models allow for latent subgroups with different growth patterns, but as many of you know, fitting them in Stan can be tricky.
This paper addresses problematic MCMC behavior in finite mixture models, especially issues stemming from what we call degenerate nonidentifiability—where small or indistinguishable classes create local nonidentifiability and poor convergence. We describe phenomena like “stuck” or “miniscule-class” chains and show how these arise even in correctly specified models.
What might be useful to the Stan community:
- A proposed definition of Bayesian identification via the marginal likelihood, integrating over latent variables
- Detailed diagnostics for detecting estimation pathologies in mixture models
- Strategies like using weakly informative priors to mitigate convergence issues
- A fully worked applied example (GMMs on reading data from NLSY)
- A didactic overview of HMC in Stan for latent variable models
- Appendix A includes complete Stan code used for the modeling
We hope this combination of theory and practical tools can help others building or troubleshooting GMMs, latent class models, or other nontrivial hierarchical models in Stan.
Would love to hear your feedback or experiences—especially if you’ve run into similar issues in mixture models.
Best,
Doria (Xingyao)