Module 3: Binary Outcomes and Why OLS Fails

Module 3: Binary Outcomes and Why OLS Fails

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Health research often focuses on binary outcomes such as disease versus no disease, admitted versus not admitted, and survived versus did not survive. A central lesson from the logistic regression notes is that OLS can produce fitted values below 0 or above 1, which makes no sense when the quantity of interest is a probability.

This module uses that problem to motivate the move from OLS to logistic and related models. The key point is practical: binary outcomes require a model that respects the probability scale.

Why this matters

  • Linear predictions can fall outside the range of valid probabilities.
  • Binary outcomes violate the logic of a simple linear fit.
  • This is why logistic regression is not optional but appropriate.

STATA illustration

regress hiqual avg_ed
predict yhat

logit hiqual avg_ed
predict phat

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