# Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables

arXiv: https://arxiv.org/abs/1612.03451 · HTML: https://mlsanity.com/paper/1612.03451/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2016.

## Built on by (most cited first, 6 of 6)

- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Identification in Tree-shaped Linear Structural Causal Models](https://mlsanity.com/paper/2203.01852/) (2022)
- [On the Complexity of Identification in Linear Structural Causal Models](https://mlsanity.com/paper/2407.12528/) (2024)
- [Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments](https://mlsanity.com/paper/2407.07933/) (2024)
- [Estimating Causal Effects in Gaussian Linear SCMs with Finite Data](https://mlsanity.com/paper/2601.04673/) (2026)
- [Efficient Symbolic Computations for Identifying Causal Effects](https://mlsanity.com/paper/2604.20516/) (2026)

## Abstract (arXiv)

We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification problem is concerned with the conditions under which causal parameters can be uniquely estimated from an observational, non-causal covariance matrix. In this paper, we provide an algorithm for the identification of causal parameters in linear structural models that subsumes previous state-of-the-art methods. In other words, our algorithm identifies strictly more coefficients and models than methods previously known in the literature. Our algorithm builds on a graph-theoretic characterization of conditional independence relations between auxiliary and model variables, which is developed in this paper. Further, we leverage this new characterization for allowing identification when limited experimental data or new substantive knowledge about the domain is available. Lastly, we develop a new procedure for model testing using AVs.