In this article, I explain how to use backdoor criterion in the experimental setting to select good control variables, or, avoid selecting the bad ones, using Directed Acyclic Graphs (DAG). I started my own causal inference journey through potential outcomes model, which was introduced in my previous article. I just “discovered” DAG recently from taking Prof. Jason Roos’ amazing experimentation and causal inference class, and really like DAG as a framework to easily theorize and visualize a causal model. It facilitates the identification analysis by making variables included in the model and the assumptions made about the relationships between these variables salient. As a result, it also helps with identifying the confounding variables and analyzing how to de-confound.
I assume that the readers already understand the basics of DAG (if not, Scott Cunningham’s Causal Inference Mixtape is a helpful start), and I believe that the quickest way to get a grasp of the backdoor criterion is by means of examples. Therefore, I will proceed as follows: first, I will lay out the question we want to answer and provide the DAG representation for us to easily conceptualize it; Next, I will explain what backdoor criterion is and show how it should be carried out in our specific example; Last, I will run the example through simulated experiments.
The data science problem we want to solve is the following: we want to know what interventions can effectively influence people to behave more sustainably. To do so, we design randomized experiments with treatments aimed at encouraging people to reduce their electricity consumption. Let’s suppose that we have finished the first experiment in which we used monetary reward as the treatment (e.g., gift card). But we are wondering whether there is a cheaper way to achieve a similar or even larger effect by using behavioral interventions. Therefore, we design a second experiment in which we use information nudges as the treatment (e.g., treated participants will receive an email notification reminding them to reduce consumption with…