Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. Existing methods require observational data from a number of sufficiently different environments, which is rarely available. In this work, we consider a structural equation model where the target variable is described by a generalized linear model conditional on its parents. Under this setting, we characterize the causal model via Pearson risk invariance, leading to a computational strategy for searching the causal model among all possible models. Crucially, for generalized linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment. Applications range from classical Poisson/logistic regression association studies, now seen through a causal lens, to relational event models for dynamic network data. The method is implemented in the R package causalreg.
