# Goodness-of-Fit Tests for Linear Non-Gaussian Structural Equation Models

arXiv: https://arxiv.org/abs/2311.04585 · HTML: https://mlsanity.com/paper/2311.04585/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2023.

## Built on by (most cited first, 4 of 4)

- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)
- [Linear Regression Beyond Covariance: Latent Slope Spectra from Higher-Order Cumulants](https://mlsanity.com/paper/2610.17772/) (2026)

## Abstract (arXiv)

The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations identifiable. One prominent assumption is that the joint distribution of the observed variables follows a linear non-Gaussian structural equation model. In this paper, we develop novel goodness-of-fit tests that assess the validity of this assumption in the basic setting without latent confounders as well as in extension to linear models that incorporate latent confounders. Our approach involves testing algebraic relations among second and higher moments that hold as a consequence of the linearity of the structural equations. Specifically, we show that the linearity implies rank constraints on matrices and tensors derived from moments. For a practical implementation of our tests, we consider a multiplier bootstrap method that uses incomplete U-statistics to estimate subdeterminants, as well as asymptotic approximations to the null distribution of singular values. The methods are illustrated, in particular, for the T"ubingen collection of benchmark data sets on cause-effect pairs.