discrete_choice_models

Extended discrete choice modeling notebook with Fair's affair data & STAR98 education analysis. Covers Logit, Probit, GLM, diagnostics, model comparison, marginal effects, and advanced topics like censored regression and count models. Complete with visualizations and validation techniques.

Overview

Features

• Multiple Model Types: Logit, Probit, Ordered Logit, Negative Binomial, and Binomial GLM
• Real Datasets: Fair's Affair Data (1974) and STAR98 Education Data
• Complete Analysis Pipeline: EDA → Model Estimation → Diagnostics → Validation
• Advanced Topics: Censored regression, count models, link function comparison
• Visualizations: ROC curves, residual diagnostics, influence analysis
• Model Validation: Cross-validation, multicollinearity checks, information criteria

Datasets

1. Fair's Affair Data (1974)

• Observations: 6,366 women
• Variables: 9 predictors including marriage rating, age, years married, religiosity
• Outcome: Binary indicator of extramarital affairs
• Source: Fair, Ray. 1978. "A Theory of Extramarital Affairs," Journal of Political Economy

2. STAR98 Education Data

• Observations: 303 California school districts
• Variables: 13 main + 8 interaction terms
• Outcome: Number of 9th graders scoring above national median in math
• Source: California Department of Education standardized testing

Technical Implementation

Core Models

• Binary Choice: Logit vs Probit comparison with marginal effects
• Ordered Response: Ordered logit for rating scale data
• Count Data: Negative binomial for frequency analysis
• Proportions: Binomial GLM with multiple link functions

Advanced Features

• Model Diagnostics: Residual analysis, influence measures, multicollinearity checks
• Validation: 5-fold cross-validation, ROC analysis, prediction tables
• Comparison Metrics: AIC, BIC, pseudo-R², classification reports
• Visualization: CDF/PDF comparisons, residual plots, Cook's distance

Findings

Fair's Affair Data

• Most significant predictors: Marriage satisfaction (strong negative), religiosity (negative), years married (positive)
• Model performance: 72% accuracy with good calibration but poor minority class detection
• Logit vs Probit: Functionally equivalent results with near-identical marginal effects

STAR98 Education Data

• Best predictors: Low-income percentage (strong negative), Asian student percentage (positive)
• Exceptional fit: Pseudo-R² approaching 1.000 (potential separation issues)
• Optimal link: Complementary log-log outperforms standard logit/probit

Theoretical Foundations

The notebook covers essential discrete choice theory:

• Random utility maximization framework
• Logistic vs normal error distributions
• Marginal effects interpretation
• Odds ratios and probability calculations
• IIA assumption and model limitations

Practical Applications

1. Policy Analysis: Understanding determinants of social behaviors
2. Educational Research: Identifying factors affecting student achievement
3. Model Selection: Comparative evaluation of different specifications
4. Diagnostic Testing: Comprehensive validation of model assumptions

Dependencies

statsmodels>=0.14.0
pandas>=1.5.0
numpy>=1.24.0
matplotlib>=3.7.0
scipy>=1.10.0
scikit-learn>=1.2.0  # For cross-validation only

Quick Start

1. Clone the repository
2. Install requirements: pip install -r requirements.txt
3. Open the Jupyter notebook: jupyter notebook discrete_choice_models.ipynb
4. Run cells sequentially or explore specific sections

Notebook Structure

1. Introduction & Theory - Discrete choice model foundations
2. Fair's Affair Data - Binary choice modeling with diagnostics
3. Alternative Specifications - Ordered, count, and censored models
4. STAR98 GLM Analysis - Binomial regression with interactions
5. Model Diagnostics - Validation and influence analysis
6. Advanced Topics - Multicollinearity, model selection, best practices

Limitations & Considerations

• Class imbalance: Affair data has 68% negative cases
• Perfect separation: STAR98 data shows quasi-complete separation
• Model complexity: Some specifications with high-dimensional interactions
• Historical data: 1974 social norms may differ from contemporary patterns

Citation

If using this code for research, please cite:

• Fair, R. (1978). A Theory of Extramarital Affairs. Journal of Political Economy
• McFadden, D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior

Contributing

Contributions welcome! Please:

1. Fork the repository
2. Create a feature branch
3. Add tests for new functionality
4. Submit a pull request

License

This project is licensed under the MIT License - see the LICENSE file for details.

Note

This notebook is designed for educational and research purposes. Real-world applications may require additional considerations and validation.