ACE_bounds {noncompliance}

Bounds for the Average Causal Effect (ACE).

Description

The empirical bounds for the Average Causal Effect (ACE), under the assumptions of the Instrumental Variable (IV) model.

Usage

ACE_bounds(n_y0x0z0, n_y1x0z0 = NA, n_y0x1z0 = NA, n_y1x1z0 = NA,
  n_y0x0z1 = NA, n_y1x0z1 = NA, n_y0x1z1 = NA, n_y1x1z1 = NA)

Arguments

n_y0x0z0

Number of individuals with Y=0, X=0, Z=0. Alternatively, a vector with elements (either counts, p(y, x , z) or p(y, x | z)) in the order of the arguments.

n_y1x0z0

Number of individuals with Y=1, X=0, Z=0.

n_y0x1z0

Number of individuals with Y=0, X=1, Z=0.

n_y1x1z0

Number of individuals with Y=1, X=1, Z=0.

n_y0x0z1

Number of individuals with Y=0, X=0, Z=1.

n_y1x0z1

Number of individuals with Y=1, X=0, Z=1.

n_y0x1z1

Number of individuals with Y=0, X=1, Z=1.

n_y1x1z1

Number of individuals with Y=1, X=1, Z=1.

Value

The empirical bounds for the ACE.

References

Richardson, T. S.; Robins, J. M. (2014). ACE Bounds; SEMs with Equilibrium Conditions. Statist. Sci. 29, no. 3, 363-366..

Examples

ACE_bounds(158, 14, 0, 0, 52, 12, 23, 78)
ACE_bounds(c(158, 14, 0, 0, 52, 12, 23, 78))
ACE_bounds(99, 1027, 30, 233, 84, 935, 31, 422)
ACE_bounds(c(99, 1027, 30, 233, 84, 935, 31, 422))