Counterfactuals and Relevant Terms
Source:vignettes/articles/theoretical-scaffolding.Rmd
theoretical-scaffolding.RmdIntroduction
Questions of causality predominate throughout the natural and social sciences (Pearl 2009). However, observational data are limited in their ability to demonstrate causality because “…one can never observe the potential outcome under the treatment state for those observed in the control state, and one can never observe the potential outcome under the control state for those observed in the treatment state” (Morgan and Winship 2015, 45). Holland (1986) describes this as the fundamental problem of causal inference. The counterfactual model provides approaches for inferring causal relationships from observational data. This article provides a concise explanation of its ideas and applications.
The Counterfactual Model
(what is the counterfactual model? what are its basic principals? focused on the aspects which are encoded in DAGs)
The back-door adjustment criterion has two main components:
- ``…conditioning on variables that lie on back-door paths can be an effective strategy to identify a causal effect’’ (Morgan and Winship 2015, 116).
- ``…if a set of conditioning variables blocks all back-door paths, the analyst must then varify that no variables within the conditioning set block the causal effect of interest or otherwise mistakenly adjust it away’’ (Morgan and Winship 2015, 117).
Essentially, researchers should condition on only the set of variables that enables them to close back-door paths.
SUTVA: “SUTVA is simply the a priori assumption that the value of Y for unit when exposed to treatment will be the same no matter what mechanism is used to assign treatment to unit and no matter what treatnebts the other units receive” (Morgan and Winship 2015, 48).
On ceteris paribus assumptions: “When a facile ceteris paribus assumption is invoked to relieve the analyst from having to discuss other contrasts that are nearly certain to occur at the same time, the posited causal states may be open to the charge that they are too improbable or ill-defined to justify the pursuit of a causal analysis based on a causal analysis based on them” (Morgan and Winship 2015, 43).
Misapplications of Counterfactuals
(look at kitchen sink regressions and table 2 fallacies) Covariate adjustment is a common method for inferring causality from observational data. Many empirical practitioners use covariate adjustment to reduce variance in the outcome of interest, under the assumption that larger adjustment sets will increase precision. An extensive and growing body of literature identifies the shortcomings of this approach. Indiscriminate adjustment may lead to collider bias and the improper representation and causal interpretation of multivariate models’ control variables lead to the table 2 fallacy. The following subsection explains those pitfalls.
Causal Graphs
(what are DAGs? define elements.) The Basic Elements of Causal Graphs:
- “Causal effects are represented by directed edges → (i.e., single-headed arrows), such that an edge from one node to another signifies that the variable at the origin of the directed edge causes the variable at the terminus. These ‘directed’ edges are what give graphs composed of nodes and single-headed arrows the general label of ‘directed graphs’” (Morgan and Winship 2015, 79–80).
- “A path in any sequence of edges pointing in any direction that connects one variable to another’’ (Morgan and Winship 2015, 80).
- “A directed path is a path in which all edges point in the same direction” (Morgan and Winship 2015, 80).
- “A variable is a descendant of another variable if it can be reached by a direct path” (Morgan and Winship 2015, 80).
- “Most importantly, for directed paths of length one, as in A→B, the variable is the parent while the variable is the child” (Morgan and Winship 2015, 80).