BayesianHierarchialModelling

Exploring the Relationship Between Depression Rates and Voting Outcomes in the 2024 U.S. Election: A Bayesian Hierarchical Modelling Approach

Exploring the Relationship Between Depression Rates and Voting Outcomes in the 2024 U.S. Election: A Bayesian Hierarchical Modelling Approach

A comprehensive Bayesian statistical analysis investigating the association between county-level depression prevalence and Republican voting patterns in the 2024 U.S. Presidential Election

IMAGES

🎯 Project Overview

This project examines whether higher depression rates in U.S. counties are associated with increased support for Donald Trump in the 2024 presidential election, while controlling for demographic factors and accounting for state-level variations through sophisticated Bayesian hierarchical modeling.

Key Findings

Main Result: Each 1% increase in depression prevalence corresponds to an estimated 1.85 percentage point increase in GOP vote share (95% CI: [1.19, 2.53]), after adjusting for race, gender, and population size.

State Variation: The relationship between depression and voting behavior varies significantly across states, with some states showing stronger positive associations and others showing negligible or even negative relationships.

📊 Dataset

• Scope: 3,107 counties across 50 U.S. states
• Variables:
  • County-level depression prevalence rates
  • 2024 Presidential election voting outcomes
  • Demographic composition (race, gender)
  • Population statistics

🔬 Methodology

Statistical Approach

• Framework: Bayesian hierarchical modeling using the brms package
• Family: Gaussian regression with identity link
• Variance Modeling: Population-weighted residual variance
• Model Comparison: Leave-One-Out Cross-Validation (LOO)

Model Evolution

1. Exploratory OLS - Initial relationship assessment
2. Bayesian Linear Regression - Baseline model with demographic controls
3. Hierarchical Random Intercept - State-level variation in baseline support
4. Hierarchical Random Intercept + Slope - State-specific depression effects (Best Model)

🏗️ Repository Structure

├── ASM.R                     # Main analysis script
├── data/
│   └── data.csv             # County-level dataset
├── results/
│   ├── figures/             # Generated visualisations
│   └── models/              # Saved model objects
├── README.md
└── requirements.txt         # R package dependencies

🚀 Getting Started

Prerequisites

# Install required packages
install.packages(c(
  "brms",        # Bayesian regression models
  "ggplot2",     # Data visualisation
  "dplyr",       # Data manipulation
  "readr",       # Data import
  "bayesplot",   # MCMC diagnostics
  "patchwork",   # Multiple plots
  "loo",         # Model comparison
  "skimr",       # Data summary
  "rstan",       # Stan interface
  "GGally"       # Pairwise plots
))

Running the Analysis

1. Clone the repository

   git clone https://github.com/yourusername/depression-voting-analysis.git
   cd depression-voting-analysis

2. Execute the main script

   source("ASM.R")

3. Key outputs will include:

   • Model comparison statistics
   • State-specific effect visualisations
   • Posterior predictive checks
   • Diagnostic plots

📈 Key Visualisations

State-Specific Depression Effects

Our central finding visualises how the depression-voting relationship varies by state:

• Positive effects: States like Texas show stronger associations between depression and Republican support
• Negative effects: States like New York show opposite or negligible relationships
• Uncertainty: Confidence intervals reflect varying sample sizes across states

Model Diagnostics

• Posterior predictive checks confirm good model fit
• Convergence diagnostics (R̂ = 1.00) indicate reliable sampling
• LOO comparison validates hierarchical model superiority

🎯 Results Summary

Predictor	Effect Size	95% Credible Interval	Interpretation
Depression Prevalence	+1.85	[1.19, 2.53]	1% ↑ depression → 1.85pp ↑ GOP vote
Race (% White)	+0.60	[0.57, 0.63]	1% ↑ white → 0.60pp ↑ GOP vote
Gender (% Male)	+103.56	[88.77, 117.74]	1pp ↑ male → 1.04pp ↑ GOP vote

State-Level Variation

• Random Intercept SD: 39.20 (substantial baseline differences)
• Random Slope SD: 2.08 (moderate variation in depression effects)
• Correlation: -0.96 (states with higher baseline GOP support show weaker depression effects)

🔍 Model Comparison

Model	ELPD Difference	Standard Error
Hierarchical (Intercept + Slope)	0.0	0.0
Hierarchical (Intercept Only)	-79.4	17.9
Bayesian Linear Regression	-1118.7	49.4

The full hierarchical model significantly outperforms simpler alternatives.

💡 Technical Highlights

Advanced Features

• Population weighting: sigma ~ scale(log(TOT_POP)) accounts for county size differences
• Convergence optimisation: adapt_delta = 0.95 ensures stable sampling
• Comprehensive diagnostics: Multiple posterior predictive checks validate model assumptions

Computational Details

• Sampling: 4 chains × 4000 iterations (2000 warmup)
• Convergence: All R̂ ≈ 1.00
• Effective samples: High ESS across all parameters

🔮 Future Extensions

Methodological Improvements

• Informative priors: Especially for sparsely sampled states
• Non-linear models: Investigate interaction effects and threshold behaviors
• Alternative distributions: Beta regression for bounded proportions

Additional Analyses

• Causal inference: Instrumental variables or natural experiments
• Temporal dynamics: Panel data across multiple elections
• Mechanism exploration: Mediation analysis through economic factors

📚 Dependencies

Core Packages

• brms (≥2.19.0) - Bayesian modeling
• ggplot2 (≥3.4.0) - Visualisation
• dplyr (≥1.1.0) - Data manipulation
• rstan (≥2.26.0) - Stan interface

Full dependency list available in requirements.txt

🤝 Contributing

Contributions are welcome! Please feel free to:

• Report bugs or issues
• Suggest methodological improvements
• Add additional analyses
• Improve documentation

📜 License

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

---

*This analysis demonstrates advanced Bayesian statistical modeling techniques applied to contemporary political and pub