Rubin Causal Model: A Statistical Description of Causal Inference for Social Work Researchers

Significance. An important framework for causal inference in non-experimental settings that has seen recent use in social work research is the Rubin Causal Model or RCM. The RCM is frequently called a statistical model for causality because it is stated in precise statistical language. It proposes that each participant in an intervention study has one potential outcome for each treatment condition. For this reason the framework is often referred to as the potential outcomes model. The true measure of the effect of an intervention is ideally the difference between each of these participant’s potential outcomes. However, we can observe only one of the potential outcomes, the factual condition based on realized assignment. The other potential outcome is an unobserved counterfactual. This makes it impossible to estimate an individual treatment effect. Using three assumptions, we can approximate the individual treatment effect by taking the difference between the average outcomes in the treatment and comparison groups.

Content. The first two assumptions are necessary to define the average treatment effect (ATE). First, the treatment must be a manipulable characteristic. The standard for manipulability is not whether the characteristic will be manipulated, but whether it could be manipulated. Second, the stable unit treatment value assumption (SUTVA) stipulates that no participant can affect the potential outcome of another participant. The third assumption is that assignment is unrelated to the potential outcomes; i.e., assignment is unconfounded. Unconfoundedness comes in strong and weak flavors. The strong version rules out confounding without further conditioning; the weak rules out confounding after conditioning on observed covariates. Randomized designs are usually assumed to satisfy the strong condition. At best, non-randomized designs can only satisfy the weak.

The RCM has detractors. Manipulability requires that a participant could be in either treatment condition, but this may not be realistic in many non-randomized settings. SUTVA implies that emergent effects in treatment settings, for which the grouping of participants may be crucial, cannot occur. If these assumptions are unrealistic, we may not have potential outcomes to compare (manipulability fails) or we may have too many potential outcomes to compare (SUTVA fails). Other critiques have been offered by scholars such as Heckman and Pearl: the RCM relies heavily on randomization-as-metaphor which is not appropriate for many types of causal investigations; it is not an actual statistical model despite being expressed in statistical language; that it narrows the domain of acceptable causal questions; and that it does not address poor sample selection.

Implications. The RCM, despite these critiques, offers researchers a way to be explicit about the conditions being compared, and is widely used across many social science fields.  It can be extended to multi-valued treatments and can handle treatment effects that differ across participants. The potential outcomes can also be considered missing data or latent outcomes, making it possible to estimate causal treatment effects using these analytic techniques. Finally, it is compatible with the Campbell and Pearl frameworks despite important differences in scope and philosophy of causation.