Introduction

Hi there ☺️ My name is Tim, and this repository contains my work on Bayesian growth mixture models (or GMMs for short) including hidden Markov chains and softmax regressions for representing latent class memberships. The work has been developed in cooperation with Dr. Nalan Basturk as part of my research assistantance in econometrics at Maastricht University.

Please note that this repository is work in progress 🔨

To-do checklist

• In the introduction, indicate what is the goal of this repository
• Include all R packages used
• Create a test to check for newer versions of packages and bonus to have it in a CI
• Normal vs Poisson simulation cases 16, 17, and 17 v2
• Quadratic trend components for Poisson model with three latent classes
• Four latent classes

Work developed

Placeholder

Software used

• Except for the implementations of the GMMs, all operations have been performed using R (R Core Team, 2022)
• The GMMs have been implemented using Stan and estimated using the No-U-Turn Sampler (or NUTS for short) via RStan: the R interface to Stan (Hoffman & Gelman, 2014; Stan Development Team, n.d.; Stan Development Team, 2024)
• In the context of parameter initializations for the NUTS, the R Stats Package has been used to apply Hartigan and Wong's (1979) K-means clustering algorithm with maximum ten iterations and two random sets (R Core Team and contributors worldwide, 2022)
• Moreover, the following R packages have been used: package by author (year), ..., and ...

Structure of repository

• 📄 ModelSpecifications
• 📁 ModelImplementations
• 📁 SimulationStudyData
• 📁 SimulationStudyResults

Future work

Define and implement a strategy for setting the hyperparameters listed below so that label switching is prevented. However, the hyperparameters are not allowed to be informative regarding classes.

• SD hyperparameters for Normal prior of constants
• SD hyperparameters for Normal prior of linear trend components
• SD hyperparameters for Normal prior of SDs for Normal distributions of dependent variable

Software references

• R Core Team. (2022). R: A Language and Environment for Statistical Computing (Version 4.2.2) [Programming language]. The R Project for Statistical Computing.
• R Core Team and contributors worldwide. (2022). The R Stats Package (Version 4.2.2) [R package]. The R Project for Statistical Computing.
• Stan Development Team. (2024). RStan: the R interface to Stan (Version 2.32.6) [R package]. The R Project for Statistical Computing.

References

• Hartigan, J. A. and Wong, M. A. (1979). Algorithm AS 136: A K-means clustering algorithm. Applied Statistics, 28(1), 100-108.
• Hoffman, M. D. and Gelman, A. (2014). The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15, 1593-1623.
• Stan Development Team. (n.d.). Stan Documentation Version 2.34. Stan. https://mc-stan.org/docs/