GBM_LCCM

This repository contains the code for estimating Gaussian Bernoulli Mixture – Latent Class Choice Models (GBM-LCCM) using the Expectation Maximization (EM) algorithm. The model combines a Gaussian Mixture Model (GMM) for continuous variables and a Bernoulli (dummy) mixture for discrete variables to determine latent classes. Each latent class also has its own weighted multinomial logit model for modeling choice behavior.

Overview

The GBM_LCCM code:

• Processes Data: Constructs sparse matrices for choice sets, decision-makers, and observations from long-format choice data.
• Estimates Class Membership: Uses a Gaussian mixture approach (with support for multiple covariance structures such as full, tied, diag, and spherical) and a Bernoulli model for discrete/dummy variables.
• Estimates Class-Specific Models: Implements a weighted multinomial logit model for each latent class.
• Optimizes via EM: Alternates between calculating latent class responsibilities (E-step) and updating model parameters (M-step) until convergence.
• Outputs Results: Displays model fit statistics (log-likelihood, AIC, BIC), parameter estimates (with standard errors, t-statistics, and p-values), and optionally exports prediction enumerations.

Requirements

• Python 3.7+ (tested with Python 3.12)

Usage

For an example of how to use this code, refer to the Jupyter Notebook: GBM_LCCM_Example.ipynb.

Configuration

• Covariance Types: Choose from 'full', 'tied', 'diag', or 'spherical'.
• EM Algorithm Settings: Adjust tol (tolerance) and max_iter (maximum iterations) to control convergence.
• Initialization: Choose between 'random' or 'kmeans' initialization for the GMM parameters (GMM_Initialization).

Contributing

Contributions, bug fixes, and feature suggestions are welcome. Please open an issue, submit a pull request, or feel free to contact me directly.

Acknowledgements

• Author: Georges Sfeir.
• Advising: Filipe Rodrigues.
• Based On: The latent class choice model (lccm) package, methodologies from Bishop's Pattern Recognition and Machine Learning, and some function from the GaussianMixture class of sklearn.mixture.

More Information

For more information about the GBM_LCCM model see the following paper:

Sfeir, G., Abou-Zeid, M., Rodrigues, F., Pereira, F.C., Kaysi, I. (2021). “Latent class choice model with a flexible class membership component: A mixture model approach.” Journal of Chocie Modelling, 41, 100320. https://doi.org/10.1016/j.jocm.2021.100320

Citation

If you find this model useful in your research or work, please cite it by citing the paper above.