# Direct and Indirect Effects

arXiv: https://arxiv.org/abs/1301.2300 · HTML: https://mlsanity.com/paper/1301.2300/

## Key facts

- Cited by 280 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2013.

## Built on by (most cited first, 30 of 280)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Post-hoc Interpretability for Neural NLP: A Survey](https://mlsanity.com/paper/2108.04840/) (2021)
- [Causal Analysis of Syntactic Agreement Mechanisms in Neural Language Models](https://mlsanity.com/paper/2106.06087/) (2021)
- [Towards Faithful Model Explanation in NLP: A Survey](https://mlsanity.com/paper/2209.11326/) (2022)
- [Counterfactual Attention Learning for Fine-Grained Visual Categorization and Re-identification](https://mlsanity.com/paper/2108.08728/) (2021)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Circuit Component Reuse Across Tasks in Transformer Language Models](https://mlsanity.com/paper/2310.08744/) (2023)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [Debiased Learning from Naturally Imbalanced Pseudo-Labels](https://mlsanity.com/paper/2201.01490/) (2022)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models](https://mlsanity.com/paper/2210.12023/) (2022)
- [Towards Vision-Language Mechanistic Interpretability: A Causal Tracing Tool for BLIP](https://mlsanity.com/paper/2308.14179/) (2023)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Large Language Models Share Representations of Latent Grammatical Concepts Across Typologically Diverse Languages](https://mlsanity.com/paper/2501.06346/) (2025)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Confidence Regulation Neurons in Language Models](https://mlsanity.com/paper/2406.16254/) (2024)
- [Demystifying Verbatim Memorization in Large Language Models](https://mlsanity.com/paper/2407.17817/) (2024)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)

## Abstract (arXiv)

The direct effect of one eventon another can be defined and measured byholding constant all intermediate variables between the two.Indirect effects present conceptual andpractical difficulties (in nonlinear models), because they cannot be isolated by holding certain variablesconstant. This paper shows a way of defining any path-specific effectthat does not invoke blocking the remainingpaths.This permits the assessment of a more naturaltype of direct and indirect effects, one thatis applicable in both linear and nonlinear models. The paper establishesconditions under which such assessments can be estimated consistentlyfrom experimental and nonexperimental data,and thus extends path-analytic techniques tononlinear and nonparametric models.