🧠 Causal Inference with Data: Beyond Correlation
Correlation tells us that two variables move together, but it does not imply causation. Causal inference aims to answer “What happens to Y if I change X?”, not just “Are X and Y related?”
1️⃣ Understand the Key Concepts
Correlation: Measures statistical association; symmetric; does not imply causality.
Causation: Changing X produces a change in Y; asymmetric; requires assumptions or experimental design.
Confounder: A variable that influences both X and Y, creating spurious correlation.
Treatment/Intervention (X): The variable you manipulate.
Outcome (Y): The variable you measure to assess effect.
Example:
X = Hours of study
Y = Exam score
Confounder = Prior knowledge (affects both hours studied and scores)
2️⃣ Establishing Causal Relationships
A. Randomized Controlled Trials (RCTs)
Gold standard for causality.
Random assignment ensures confounders are balanced.
Feasible in medicine or online experiments, often not in observational data.
B. Observational Data Methods
When RCTs are impossible, we rely on assumptions and statistical methods:
Regression Adjustment
Adjust for confounders in linear/logistic regression.
Example:
import statsmodels.api as sm
X = data[['study_hours', 'prior_knowledge']]
y = data['exam_score']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
print(model.summary())
Propensity Score Matching
Estimate probability of treatment given confounders.
Match treated and untreated units with similar scores.
Reduces confounding bias.
Instrumental Variables (IV)
Find a variable (instrument) that affects X but not Y directly, except through X.
Common in economics when randomization is impossible.
Difference-in-Differences (DiD)
Compares treated vs. control groups before and after intervention.
Removes time-invariant confounding.
Regression Discontinuity Design
Exploits cutoff-based assignment to treatment (e.g., scholarships given for scores above 90).
3️⃣ Causal Graphs (Directed Acyclic Graphs, DAGs)
Visual tool to represent causal assumptions.
Nodes = variables; edges = causal effect.
Helps identify confounders, mediators, and colliders.
Example DAG:
PriorKnowledge → StudyHours → ExamScore
PriorKnowledge → ExamScore
To estimate effect of StudyHours on ExamScore, adjust for PriorKnowledge.
Python library: causalgraphicalmodels
from causalgraphicalmodels import CausalGraphicalModel
dag = CausalGraphicalModel(
nodes=['PriorKnowledge', 'StudyHours', 'ExamScore'],
edges=[
('PriorKnowledge', 'StudyHours'),
('PriorKnowledge', 'ExamScore'),
('StudyHours', 'ExamScore')
]
)
dag.draw()
4️⃣ Modern Causal Inference with Python
Libraries
DoWhy – Combines causal graphs + statistical estimation
EconML – Heterogeneous treatment effect estimation
CausalML – Uplift modeling and causal effect estimation
Example with DoWhy:
import dowhy
from dowhy import CausalModel
import pandas as pd
data = pd.read_csv("study_data.csv")
model = CausalModel(
data=data,
treatment='StudyHours',
outcome='ExamScore',
common_causes=['PriorKnowledge']
)
# Identify causal effect
identified_estimand = model.identify_effect()
# Estimate effect using linear regression
estimate = model.estimate_effect(identified_estimand, method_name="backdoor.linear_regression")
print(estimate.value)
5️⃣ Assumptions Matter
Causal inference is assumption-driven:
Ignorability (No Unmeasured Confounders)
Positivity (Each treatment has non-zero probability)
Stable Unit Treatment Value Assumption (SUTVA)
Violating these assumptions can bias causal estimates, even if correlation exists.
6️⃣ From Correlation to Actionable Insights
Correlation: “StudyHours and ExamScore move together.”
Causal Inference: “Increasing study hours by 1 hour increases exam score by 5 points (after adjusting for PriorKnowledge).”
The latter allows policy decisions, interventions, and predictions.
7️⃣ Practical Workflow
Define question: “What is the causal effect of X on Y?”
Draw causal DAG; identify confounders and mediators
Choose method (regression, matching, IV, DiD)
Check assumptions
Estimate effect and test robustness (sensitivity analysis)
Interpret results carefully: causality depends on assumptions
✅ Summary
Step Goal
Correlation Explore associations
DAGs Represent causal assumptions
Confounder adjustment Reduce bias
Estimation methods Backdoor adjustment, propensity scores, IV, DiD
Sensitivity analysis Test robustness
Decision making Use causal estimates for interventions
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