Compound-outcome worst-case bound

A composite endpoint is a fixed linear functional of its components, so the identification problem is the ordinary one for the scalar sum_k w_k y_k. The support of the composite is read off the realised composite values rather than combined component-wise, which keeps the interval sharp for the data at hand.

Usage

Bnscbo(y_components, D, X)

Arguments

y_components

Numeric matrix of outcome components, one row per unit.

D

Binary treatment indicator, coded 0/1.

X

Component weights, length equal to the number of columns.

Value

List with lower, upper, width, estimate, k, n.

Details

Formula: c_i = sum_k w_k y_ik, then the worst-case bound of Molinari (2021) equation (2.11) applied to c.

References

Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer, New York. Worst-case form as equation (2.11) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 17).

Examples

set.seed(1)
Bnscbo(y_components = matrix(rnorm(80), 40, 2), D = rbinom(40, 1, 0.5),
       X = c(0.5, 0.5))
#> $lower
#> [1] -1.603314
#> 
#> $upper
#> [1] 1.729015
#> 
#> $width
#> [1] 3.332329
#> 
#> $estimate
#> [1] 0.0628503
#> 
#> $k
#> [1] 2
#> 
#> $n
#> [1] 40
#> 
#> $method
#> [1] "Compound-outcome bound"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"