Suppose you want to estimate whether encouraging side-quest engagement increases in-game purchases. A correlation between engagement and purchases cannot answer that question on its own: player skill or time spent playing might affect both. A causal directed acyclic graph (DAG) makes proposed cause-and-effect relationships explicit before estimation. Each node is a variable; a directed edge points from a proposed cause to a variable it affects. The graph is acyclic: its arrows do not form a directed loop. section 11.2 section 13.1.1
Build the graph around the causal question, not merely around available predictors:
- Identify the treatment and outcome, then add plausible common causes. For side-quest engagement and purchases, these include player skill and time spent playing. section 11.2
- Add other variables according to their proposed causal roles. Group assignment and customization level may serve as instruments; total inventory is a collider and can introduce bias if handled as an ordinary adjustment variable. section 11.2
- Check the assumptions behind each arrow with domain knowledge. A DAG states what is proposed to cause what; observed correlation alone does not establish an arrow. section 13.1.1
Why the arrows matter for fairness
A loan dataset might show higher rejection rates for men for two different reasons: advertising attracted less-qualified male applicants, or loan officers penalized men. A DAG distinguishes these proposed routes to the same statistical disparity. Removing gender from a training table does not, by itself, remove patterns carried by proxies such as names. section 1.3.4
Listing 11.1 Build the causal DAG
import pygraphviz as pgv #1
from IPython.display import Image #2
causal_graph = """
digraph {
"Prior Experience" -> "Player Skill Level";
"Prior Experience" -> "Time Spent Playing";
"Time Spent Playing" -> "Player Skill Level";
"Guild Membership" -> "Side-quest Engagement";
"Guild Membership" -> "In-game Purchases";
"Player Skill Level" -> "Side-quest Engagement";
"Player Skill Level" -> "In-game Purchases";
"Time Spent Playing" -> "Side-quest Engagement";
"Time Spent Playing" -> "In-game Purchases";
"Side-quest Group Assignment" -> "Side-quest Engagement";
"Customization Level" -> "Side-quest Engagement";
"Side-quest Engagement" -> "Won Items";
"Won Items" -> "In-game Purchases";
"Won Items" -> "Total Inventory";
"In-game Purchases" -> "Total Inventory";
}
""" #3
G = pgv.AGraph(string=causal_graph) #3
G.draw('/tmp/causal_graph.png', prog='dot') #4
Image('/tmp/causal_graph.png') #5
The Graphviz DOT listing makes the gaming model concrete: each arrow declares a proposed causal relationship, and PyGraphviz loads the specification for visualization. section 11.2
In an effect-estimation workflow, the DAG is the model used for identification, not the estimate itself. A valid backdoor adjustment set blocks all backdoor paths; front-door and instrumental-variable approaches require different assumptions. The graph can also anchor a structural causal model, which adds functions describing how parent variables determine each modeled variable. An arrow can express a causal assumption, but it cannot by itself express a claim such as linearity. section 11.7 section 10.1.2
