7.3 Covariates & Bias

• Important notion: Condition/control = FILTERING (Pearl, Glymour, and Jewell 2016, 8)

  • when we condition on X, we filter the data into subsets based on values of X (Pearl, Glymour, and Jewell 2016, 38)
    
  • See Data: (Empirical) Joint distributions
  • Idea will become more concrete in the lab…
    
    

• Remember.. fundamental objective: Estimate unbiased causal effect of D on Y
  
  

• Common-cause confounding bias (Elwert and Winship 2014b, 37)

  • D ← X → Y
  • results from failure to condition on a common cause (a confounder) of treatment and outcome
    
    

• Overcontrol/post-treatment bias

  • D → X → Y
  • results from conditioning on a variable on a causal path between treatment and outcome (Elwert and Winship 2014b, 35–36; Acharya, Blackwell, and Sen 2015, 1)
    
    

• Endogenous selection bias

  • D → X ← Y
    
  • Collider variable: A common outcome of D and Y
  • results from conditioning on a collider (or its descendant) on a non-causal path linking treatment and outcome
    
    

• Q: What does “bias can go in both directions” and “unbiased” mean? Example?

References

Acharya, Avidit, Matthew Blackwell, and Maya Sen. 2015. “Explaining Causal Findings Without Bias: Detecting and Assessing Direct Effects.” The American Political Science Review.

Elwert, Felix, and Christopher Winship. 2014b. “Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable.” Annu. Rev. Sociol. 40 (1): 31–53.

Pearl, Judea, Madelyn Glymour, and Nicholas P Jewell. 2016. Causal Inference in Statistics: A Primer. John Wiley & Sons.