An introduction to Causal Modelling

2025-06-19

AI Summary

This paper bridges the theoretical and practical gap between the potential outcomes framework and causal graphical models. Addressing core causal inference problems—including counterfactual reasoning, treatment effect identification, and estimation—the work systematically unifies potential outcomes, causal diagrams, d-separation, the backdoor criterion, single-world intervention graphs (SWIGs), and structural equation models, offering the first coherent account of their logical interconnections. Methodologically, it proposes a robust identification strategy grounded in propensity score estimation and inverse probability weighting, augmented with sandwich standard errors for valid statistical inference. The key contribution is a pedagogically transparent, operationally feasible framework that lowers the barrier to integrating these two dominant causal paradigms. By harmonizing conceptual rigor with practical applicability, the paper provides applied researchers with an accessible yet theoretically sound entry point into modern causal inference. (149 words)

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments and potential outcomes. We discuss causal effect measures-including average treatment effects on the treated and on the untreated-and choices of effect scales for binary outcomes. We derive identification in randomized experiments under exchangeability and consistency, and extend to stratification and blocking designs. We present inverse probability weighting with propensity score estimation and robust inference via sandwich estimators. Finally, we introduce causal graphs, d-separation, the backdoor criterion, single-world intervention graphs, and structural equation models, showing how graphical and potential-outcome approaches complement each other. Emphasis is placed on clear notation, intuitive explanations, and practical examples for applied researchers.

Problem

• Introduces modern causal modeling integrating potential outcomes and graphical methods
• Discusses causal effect measures and identification in randomized experiments
• Explains causal graphs and how graphical and potential-outcome approaches complement

Innovation

• Integrates potential outcomes and graphical methods
• Uses inverse probability weighting with propensity scores
• Combines causal graphs with structural equation models