Linear Statistical Models for Causation: A Critical Review†

We review the basis for inferring causation by means of linear statistical models. Parameters should be stable under interventions, and so should error distributions. There are also statistical conditions that must be satisfied. Stability is difficult to establish a priori, and the statistical conditions are equally problematic. Therefore, causal relationships are seldom to be inferred from a data set by running regressions, unless there is substantial prior knowledge about the mechanisms that generated the data. Keywords: association; causation; latent variables; linear models; regression; structural equation models