%0 Journal Article
%T Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models.
%A Schultheiss C
%A Bühlmann P
%A Yuan M
%J J Am Stat Assoc
%V 119
%N 546
%D 2024
%M 38974187
%F 4.369
%R 10.1080/01621459.2022.2157728
%X 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. Supplementary materials for this article are available online.