  Selection bias is ubiquitous in real-world data, and can lead to misleading
results if not dealt with properly. We introduce a conditioning operation on
Structural Causal Models (SCMs) to model latent selection from a causal
perspective. We show that the conditioning operation transforms an SCM with the
presence of an explicit latent selection mechanism into an SCM without such
selection mechanism, which partially encodes the causal semantics of the
selected subpopulation according to the original SCM. Furthermore, we show that
this conditioning operation preserves the simplicity, acyclicity, and linearity
of SCMs, and commutes with marginalization. Thanks to these properties,
combined with marginalization and intervention, the conditioning operation
offers a valuable tool for conducting causal reasoning tasks within causal
models where latent details have been abstracted away. We demonstrate by
example how classical results of causal inference can be generalized to include
selection bias and how the conditioning operation helps with modeling of
real-world problems.
