Causal Models with Constraints

Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations we want to study both causal and non-causal relationships between a single set of variables; this cannot be done in a standard causal model. For example, a standard causal model cannot talk simultaneously about the level of high-density lipoprotein cholesterol (H DL), the level of low-density lipoprotein cholesterol (LDL), and the level of total cholesterol (T OT), although this seems quite natural. One can imagine a situation where we only have data regarding the level of total cholesterol, even though our causal model may say that certain health conditions depend on the amount of LDL. The problem is that standard causal models allow simultaneous interventions to all variables in the model. But we cannot intervene to simultaneously setLDL to120 mg/dL,HDL to70, andTOT to 180, for that is logically inconsistent! In this example, the variables have a part-whole relationship, rather than a causal relationship.