What is the positivity assumption?
Positivity requires a nonzero probability of each treatment for every covariate pattern in the target population. In finite data, poor overlap is the practical warning: comparable treated and untreated people become rare.
Try it in the experiment
Start with the visual support experiment: common, rare, or impossible comparisons →
- Compare the groups under moderate treatment selection.
- Switch to strong selection.
- Inspect the propensity distributions, clipped probabilities, and effective sample sizes.
Extreme weights concentrate information in a few observations, while outcome models rely more heavily on extrapolation. AIPW combines the two approaches; it does not manufacture comparisons that the data do not contain.