LASSO Regression and Potential Outcomes Analysis for Causal Inference

A implementation of LASSO regression techniques for high-dimensional data analysis and potential outcomes modeling for randomized controlled trials.

Project Overview

Research Focus

This project analyzes female literacy rates across Indian districts using advanced statistical learning methods. The analysis employs both traditional econometric approaches and modern machine learning techniques to understand the determinants of educational outcomes and demonstrate causal inference methods.

Core Methodologies

1. LASSO Regression for Female Literacy Prediction

• Low-dimensional specification: Uses economic intuition to select key variables while avoiding highly correlated predictors (e.g., excluding male literacy and overall literacy)
• High-dimensional specification: Comprehensive feature engineering including interactions and polynomial terms, resulting in 400+ variables
• Regularization analysis: Complete LASSO path evaluation with cross-validation
• Performance metrics: Out-of-sample R² evaluation and feature selection assessment

2. Potential Outcomes and Causal Inference

• Randomized controlled trial simulation: Synthetic data generation for treatment effect analysis
• Average Treatment Effect (ATE) estimation: Multiple approaches including simple regression, LASSO-assisted, and randomization inference
• Variable selection: LASSO-guided covariate adjustment for improved causal estimates
• Balance assessment: Statistical tests for randomization validity

Repository Structure

Lasso_Potential_Outcomes_RCTs/
├── Python/                          # Python implementation
│   ├── scripts/
|   |   ├── comments.pdf                   # Answers for the comments section
│   │   ├── lasso_analysis.ipynb           # Female literacy LASSO analysis
│   │   └── potential_outcomes_rcts.ipynb  # Causal inference methods
│   ├── requirements.txt             # Python dependencies
│   ├── input/                       # Data directory
│   └── output/                      # Results and visualizations
├── R/                               # R implementation  
│   ├── scripts/
|   |   ├── comments.pdf                   # Answers for the comments section
│   │   ├── lasso_analysis.ipynb           # Female literacy LASSO analysis
│   │   └── potential_outcomes_rcts.ipynb  # Causal inference methods
│   ├── requirements.txt             # R package dependencies
│   ├── input/                       # Data directory
│   └── output/                      # Results and visualizations
├── Julia/                           # Julia implementation
│   ├── scripts/
|   |   ├── comments.pdf                   # Answers for the comments section
│   │   ├── lasso_analysis.ipynb           # Female literacy LASSO analysis
│   │   └── potential_outcomes_rcts.ipynb  # Causal inference methods
│   ├── requirements.txt             # Julia package dependencies
│   ├── input/                       # Data directory
│   └── output/                      # Results and visualizations
├── .gitignore                       # Version control exclusions
├── LICENSE                          # MIT License
└── README.md                        # This documentation

Technical Implementation Details

Task 1: Data Analysis and Visualization

• Dataset: District-wise literacy rates from Indian Census data (680 districts, 100 variables)
• Target variable: Female literacy rate (FEMALE_LIT)
• Exploratory analysis: Distribution analysis, missing value treatment, correlation assessment
• Visualization: Professional statistical graphics showing literacy distributions and relationships

Task 2: LASSO Regression Specifications

Low-Dimensional Model (Economic Intuition)

The low-dimensional specification follows economic theory and avoids multicollinearity by carefully selecting variables:

Selected Variables (5 features):

• GROWTHRATE: Population growth rate (demographic transition indicator)
• SEXRATIO: Sex ratio (gender equality proxy)
• ENR501: Schools with enrollment ≤ 50 (primary education access)
• TCH1: Primary school teachers (educational infrastructure)
• SCHTOT: Total number of schools (educational capacity)

Rationale: This specification avoids highly correlated variables such as male literacy and overall literacy rates, which would create multicollinearity issues. Instead, it focuses on underlying structural factors that influence educational outcomes through economic development, gender equality, and educational infrastructure channels.

High-Dimensional Model (Comprehensive Feature Engineering)

The high-dimensional specification maximizes predictive power through extensive feature engineering:

Feature Construction (400+ variables):

• Base variables: All available numeric variables (excluding highly correlated literacy measures)
• Interaction terms: All pairwise interactions between base variables
• Polynomial features: Squared terms for all continuous variables
• Result: ~400+ engineered features for LASSO selection

Purpose: This specification tests LASSO's ability to perform automatic feature selection in high-dimensional settings while maintaining predictive accuracy.

Task 3: Potential Outcomes Analysis

Experimental Design

• Synthetic RCT: 1000 observations with random treatment assignment
• Treatment effect: Simulated effect size with realistic noise structure
• Covariates: Four baseline variables (X1, X2, X3, X4) with known relationships

Estimation Methods

1. Simple regression: Y ~ D (naive treatment effect)
2. LASSO-assisted: Uses LASSO variable selection for covariate adjustment
3. Randomization inference: Permutation-based hypothesis testing

Statistical Computing Environments

Python Implementation

• Core libraries: scikit-learn, pandas, numpy, matplotlib, seaborn, statsmodels
• Features: Advanced data preprocessing, comprehensive visualization suite
• Strengths: Extensive machine learning ecosystem, excellent documentation

R Implementation

• Core libraries: glmnet, tidyverse, ggplot2, caret, broom
• Features: Native statistical computing, publication-quality graphics
• Strengths: Mature statistical packages, built-in hypothesis testing

Julia Implementation

• Core libraries: GLMNet.jl, DataFrames.jl, MLJ.jl, Plots.jl
• Features: High-performance computing, modern syntax
• Strengths: Speed optimization, growing ecosystem for scientific computing

Installation and Usage

Python Environment

cd Python/
pip install -r requirements.txt
jupyter notebook scripts/lasso_analysis.ipynb

R Environment

cd R/
# Install required packages using the requirements list
pip install -r requirements.txt  # For pip-style format
# OR use the R script: Rscript requirements.R
jupyter notebook scripts/lasso_analysis.ipynb

Julia Environment

cd Julia/
# Install packages from requirements.txt
julia -e 'using Pkg; [Pkg.add(split(line, ">=")[1]) for line in readlines("requirements.txt") if !startswith(line, "#") && !isempty(strip(line))]'
jupyter notebook scripts/lasso_analysis.ipynb

License

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

---

This repository demonstrates advanced statistical learning methods with emphasis on reproducible research, professional documentation, and cross-platform statistical computing for modern econometric and causal inference applications.