7.5 Covariates: Endogenous selection bias

  • Talent T, Beauty B, Hollywood success Y (Elwert and Winship 2014b, 36)
    • Talent T → Beauty B
    • Asume talent and beauty are unrelated (no causal relationship)
    • Assume both T and B separately cause success Y: T → Y ← B
    • Hollywood success Y is a collider variable (common outcome of T and B)

  • Endogenous selection bias if conditioning on/controlling for collider (Elwert and Winship 2014b, 36)
    • Given success (Y = 1), i.e., looking at subset of successful Hollywood actors
      • …knowing that non-talented person (T = 0) is successful actor implies that the person must be beautiful (B = 1)
      • …knowing that non-beautiful person (B = 0) is a successful actor implies that the person must be talented (T = 1)
    • In subsets of Hollywood success (Y = 1 or 0) there is a correlation between T and B
    • conditioning on collider (y) creates spurious association between beauty and talent (spurious association is endogenous selectionbias).

  • Difficult to grasp…32

References

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

  1. “The reason is that humans tend to associate dependence with causation. Accordingly, they assume (wrongly) that statistical dependence between two variables can only exist if there is a causal mechanism that generate such dependence;” (Pearl, Glymour, and Jewell 2016, 44)↩