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Understanding Causal Inference
  • A Guide to Causal Inference
  • Table of Contents
  • About-us
  • Preface
  • What is Causality?
  • Why bother with Causality?
  • Origin of Causality
  • Statistical Inference Vs Causal Inference
  • Decision-Making
  • Why we need Causality?
    • Leaders in the Industry
  • Key Causal Terms and FAQ
  • Assumptions
    • Causal Assumptions
  • Bias
    • Selection Bias
    • Correlation is not Causation
      • Simpsons Paradox
  • Causal Graphs
    • Colliders
    • Confounders
    • Mediators
    • Back Door Paths
    • Front Door Paths
    • Structural Causal Model
    • do-calculus
    • Graph Theory
    • Build your DAG
    • Testable Implications
    • Limitations of Causal Graphs
  • Counterfactuals
    • Potential Outcomes Framework
  • Modeling for Causal Inference
    • Experimental Data
      • Randomization
        • Problems with Randomization
        • A/B Testing
          • Experiment
    • Non-Experimental / Observational Data
      • Instrumental Variables
      • Weighting
        • Inverse Propensity Weighting
      • Propensity Score
      • Sensitivity Analysis
      • Regression Discontinuity
      • Matching
      • Stratification
        • Methods
        • Implications
  • Tools and Libraries
    • DoWhy
      • Do-Sampler
      • EconML
      • Workflow
    • Causal Graphical Models
    • CausalInference
    • Dagitty
    • Other Libraries
  • Limitations of Causal Inference
    • Fundamental Problem of Causal Inference
  • Real-World Implementations
  • What's Next
  • References
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  • ATE

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  1. Counterfactuals

Potential Outcomes Framework

Understanding the Causal Effects in Potential Outcomes Framework

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Last updated 4 years ago

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Potential Outcome Framework has helped in giving causal effects very precise definitions.

The Potential outcome is the outcome that would be observed if an individual is given a specific value of the treatment. It is the study of the effect of treatment at an individual level. For every Individual one can not simultaneously observe the 2 potential Outcomes, we can only observe one. Here, the unobserved outcome is called the "Counterfactual Outcome ".

Two possible treatments, T - Treatment received or not received(Placebo)

T∈{0,1}T ∈ \{0,1\}T∈{0,1}

Two possible outcomes, Y - the outcome is there or not there

{Yi(0),Yi(1)}\{Y_i (0) ,Y_i(1)\}{Yi​(0),Yi​(1)}

Note: Quantities we are trying to measure here is not observable!!

Example: What is the causal effect of doing a Master's degree and getting a high paying job?

  • Treatment: doing Master's (T=1) & not doing Master's (T=0)

  • Every individual person has 2 potential outcomes, Yt=0 & Yt=1 .

  • Yt=0 -> Potential Outcome when not doing Masters

  • Yt=1 -> Potential Outcome when doing Masters

ITE

**Individual Treatment Effect is the difference between the 2 potential outcomes for a particular individual. We cannot measure ICE as we would need counterfactual value for the individual.

ATE

Average Treatment Effect is the average difference between the 2 potential outcomes averaged over the entire population of interest. It is the population level average of the Individual Causal Effect(ICE).

  • Note: Even though an Individual Causal Effect is non zero, the Average causal effect can be Zero.

ICE=Y1−Y0ICE = Y1 - Y0ICE=Y1−Y0
ATE=E[Yi1]−E[Yi0]ATE = E[Yi1] - E[Yi0]ATE=E[Yi1]−E[Yi0]