Manski worst-case bounds

With treatment left NULL, bounds the mean of a partially observed outcome (Manski 2007, eq. 2.4 applied to the mean): the missing part is set to each end of the support in turn, so the interval has width \((K_1 - K_0) P(\mathrm{missing})\). With a binary treatment, bounds the average treatment effect by his eq. (7.6), each potential outcome being unobserved for those who received the other treatment.

Usage

morie_bndest(y, observed, support, treatment = NULL)

Arguments

y

Outcomes.

observed

Logical vector of observed outcomes; ignored (and may be NULL) when treatment is supplied.

support

Length-2 vector c(K0, K1) with K0 < K1, the assumed outcome support.

treatment

Optional binary 0/1 treatment.

Value

For the mean: a list with lower, upper, width, p_observed, identified, width_identity, assumptions, n, method. For the ATE: ate_lower, ate_upper, ate_width, y1_bounds, y0_bounds, p_treated, contains_zero, width_identity, identified, n, method.

References

Manski, C. F. (2007). Identification for Prediction and Decision. Harvard University Press, Sections 2.1 and 7.1.

Examples

set.seed(1)
morie_bndest(y = rnorm(40), observed = rbinom(40, 1, 0.7), support = c(-3, 3))
#> $lower
#> [1] -0.7850038
#> 
#> $upper
#> [1] 1.014996
#> 
#> $width
#> [1] 1.8
#> 
#> $p_observed
#> [1] 0.7
#> 
#> $identified
#> [1] FALSE
#> 
#> $width_identity
#> [1] "(K1 - K0)(1 - P(obs)) exactly"
#> 
#> $assumptions
#> [1] "the outcome's support alone; nothing about WHY data are missing"
#> 
#> $n
#> [1] 40
#> 
#> $method
#> [1] "Manski worst-case bounds on a partially observed mean"
#>