Object Conditioning for Causal Inference

We describe and analyze a form of conditioning that is widely applied within social science and applied statistics but that is virtually unknown within causal graphical models. This approach, which we term object conditioning, can adjust for the effects of latent confounders and yet avoid the pitfall of conditioning on colliders. We describe object conditioning using plate models and show how its probabilistic implications can be explained using the property of exchangeability. We show that several seemingly obvious interpretations of object conditioning are insufficient to describe its probabilistic implications. Finally, we use object conditioning to describe and unify key aspects of a diverse set of techniques for causal inference, including within-subjects designs, difference-in-differences designs, and interrupted time-series designs.