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Advancing Causal Inference: A Nonparametric Approach to ATE and CATE Estimation with Continuous Treatments

Hugo Gobato Souto, Francisco Louzada Neto

Abstract

This paper introduces a generalized ps-BART model for the estimation of Average Treatment Effect (ATE) and Conditional Average Treatment Effect (CATE) in continuous treatments, addressing limitations of the Bayesian Causal Forest (BCF) model. The ps-BART model's nonparametric nature allows for flexibility in capturing nonlinear relationships between treatment and outcome variables. Across three distinct sets of Data Generating Processes (DGPs), the ps-BART model consistently outperforms the BCF model, particularly in highly nonlinear settings. The ps-BART model's robustness in uncertainty estimation and accuracy in both point-wise and probabilistic estimation demonstrate its utility for real-world applications. This research fills a crucial gap in causal inference literature, providing a tool better suited for nonlinear treatment-outcome relationships and opening avenues for further exploration in the domain of continuous treatment effect estimation.

Advancing Causal Inference: A Nonparametric Approach to ATE and CATE Estimation with Continuous Treatments

Abstract

This paper introduces a generalized ps-BART model for the estimation of Average Treatment Effect (ATE) and Conditional Average Treatment Effect (CATE) in continuous treatments, addressing limitations of the Bayesian Causal Forest (BCF) model. The ps-BART model's nonparametric nature allows for flexibility in capturing nonlinear relationships between treatment and outcome variables. Across three distinct sets of Data Generating Processes (DGPs), the ps-BART model consistently outperforms the BCF model, particularly in highly nonlinear settings. The ps-BART model's robustness in uncertainty estimation and accuracy in both point-wise and probabilistic estimation demonstrate its utility for real-world applications. This research fills a crucial gap in causal inference literature, providing a tool better suited for nonlinear treatment-outcome relationships and opening avenues for further exploration in the domain of continuous treatment effect estimation.
Paper Structure (24 sections, 20 equations, 54 figures, 36 tables)

This paper contains 24 sections, 20 equations, 54 figures, 36 tables.

Table of Contents

  1. Key Words
  2. Introduction
  3. ps-BART for Continuous Treatments
  4. Experimental Design
  5. Data Generating Processes (DGPs) for Model Evaluation
  6. Evaluation Metrics and Approach
  7. Results and Analysis
  8. 1st Set of DGPs
  9. $\alpha=1$
  10. $\alpha=2$
  11. $\alpha=4$
  12. $\alpha=8$
  13. Conclusion
  14. 2nd Set of DGPs
  15. Specification 1
  16. ...and 9 more sections

Figures (54)

  • Figure 1: BCF ATE and CATE Functions Estimation for N=100 (for CATE, an Example of a Random $\mathbf{x_i}$ of a Random Simulation is used)
  • Figure 2: ps-BART ATE and CATE Functions Estimation for N=100 (for CATE, an Example of a Random $\mathbf{x_i}$ of a Random Simulation is used)
  • Figure 3: BCF ATE and CATE Functions Estimation for N=250 (for CATE, an Example of a Random $\mathbf{x_i}$ of a Random Simulation is used)
  • Figure 4: ps-BART ATE and CATE Functions Estimation for N=250 (for CATE, an Example of a Random $\mathbf{x_i}$ of a Random Simulation is used)
  • Figure 5: BCF ATE and CATE Functions Estimation for N=500 (for CATE, an Example of a Random $\mathbf{x_i}$ of a Random Simulation is used)
  • ...and 49 more figures