Graphical Models for Quasi-experimental Designs

Abstract

Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand and, thus, warrant a causal interpretation of the estimated effect. In this article, we discuss and compare the identifying assumptions of quasi-experiments using causal graphs. The increasing complexity of the causal graphs as one switches from an RCT to RD, IV, or PS designs reveals that the assumptions become stronger as the researcher's control over treatment selection diminishes. We introduce limiting graphs for the RD design and conditional graphs for the latent subgroups of com-pliers, always takers, and never takers of the IV design, and argue that the PS is a collider that offsets confounding bias via collider bias.

Keywords: causal graphs; causal inference; directed acyclic graphs; instrumental variables; matching design; propensity scores; randomized experiment; regression discontinuity design; structural causal model.

Conflict of interest statement

Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1.

Causal graph of an observational study: complete and stylized representation.

Figure 2.

Data generating graph of a randomized controlled trial.

Figure 3.

Causal graphs of a regression discontinuity (RD) design. (A) Data generating graph. (B) Limiting graph for A = aC ± ε with ε ⟶ 0.

Figure 4.

Data generating graph of an instrumental variable design.

Figure 5.

Data generating IV graphs for (A) compliers, (B) always takers and never takers, and (C) compliers, always takers and never takers together (i.e., no defiers).

Figure 6.

IV graphs for (A) compliers and (B) compliers, always takers, and never takers together (i.e., no defiers).

Figure 7.

Causal graph of the randomized controlled trial with noncompliance.

Figure 8.

Causal graphs for the fuzzy regression discontinuity (RD) design. (A) Data generating graph. (B) Limiting graph for A = aC ± ε with ε ⟶ 0.

Figure 9.

Causal graphs for a matching design (with constant matching ratio).(A) Data generating directed acyclic graph. (B) Computation of match indicator S.(C) Conditioning on the match indicator S. (D) The independence structure after matching (S = 1).

Figure 10.

Causal graphs for propensity score designs. (A) Data generating directed acyclic graph. (B) Computation of the propensity score (PS). (C) Conditioning on the PS. (D) The independence structure after PS adjustment.