Higher-order least squares: assessing partial goodness of fit of linear causal models

Abstract

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings.

References in corpus (9)

• On asymptotically optimal confidence regions and tests for high-dimensional models
• Statistical significance in high-dimensional linear models
• Causal Discovery with Continuous Additive Noise Models
• Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (2013)
• Causal discovery of linear acyclic models with arbitrary distributions
• Goodness of fit tests for high-dimensional linear models
• Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (2008)
• Cyclic Causal Discovery from Continuous Equilibrium Data
• Spectral Deconfounding via Perturbed Sparse Linear Models