Gaussian Process – Latent Class Choice Model (GP-LCCM)

This repository contains the code for estimating Gaussian Process – Latent Class Choice Models (GP-LCCM) using the Expectation Maximization (EM) algorithm. The model employs a Gaussian Process Classifier to flexibly model class membership probabilities and uses class-specific weighted multinomial logit models to explain choice behavior.

Overview

The GP_LCCM code:

• Processes Data: Constructs sparse matrices from long-format data that map alternatives, observations, and decision-makers. It also allows for imposing analyst-defined choice set constraints.
• Class Membership Modeling via Gaussian Process: Uses a Gaussian Process Classifier (from scikit-learn) to estimate the probability that each individual belongs to a latent class. The classifier returns both probability estimates and a log marginal likelihood.
• Class-Specific Choice Modeling: Implements a weighted multinomial logit model for each latent class to model the choice behavior of individuals. It uses numerical optimization (BFGS) to update the parameters and compute standard errors.
• Expectation Maximization (EM) Algorithm: 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: GP_LCCM_Example.ipynb.

Configuration

• Gaussian Process Kernel: The code uses a default kernel (a dot product) from scikit-learn. You can modify the kernel settings near the top of the code as needed.
• EM Algorithm Settings: Adjust tol (tolerance) and max_iter (maximum iterations) to control convergence.

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 and functions from the GaussianProcessClassifier class of sklearn.

More Information

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

Sfeir, G., Rodrigues, F., Abou-Zeid, M. (2022). “Gaussian Process Latent Class Choice Models.” Transportation Research Part C: Emerging Technologies, 136, 103552. https://doi.org/10.1016/j.trc.2022.103552

Citation

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