Exposure positivity under Bernoulli assignment

The probability that all d neighbours are treated is \(p^d \to 0\) and the Horvitz-Thompson weight \(1/p^d \to \infty\) (Research.P3.Exposure.exposure_prob_tendsto_zero, ht_weight_unbounded).

Usage

morie_exposure_positivity(p, degrees)

Arguments

p

Treatment probability in (0, 1).

degrees

Neighbourhood sizes.

Value

A data frame: degree, prob_all_treated, ht_weight.

References

Wager S (2024). Causal Inference: A Statistical Learning Approach, ch. 11-12.

Examples

morie_exposure_positivity(p = 0.5, degrees = c(1, 5, 10, 30))
#>   degree prob_all_treated  ht_weight
#> 1      1     5.000000e-01          2
#> 2      5     3.125000e-02         32
#> 3     10     9.765625e-04       1024
#> 4     30     9.313226e-10 1073741824