Check_ACDE_bounds {noncompliance}

Bounds for the Average Controlled Direct Effect (ACDE).

Description

The empirical bounds for the Average Controlled Direct Effect (ACDE) within the principal strata of Always Takers and Never Takers, under the assumption of monotonicity (no Defiers). These are equivalent to an empirical check of the Instrumental Variable (IV) inequalities (see references below).

Usage

Check_ACDE_bounds(n_y0x0z0, n_y1x0z0 = NA, n_y0x1z0 = NA, n_y1x1z0 = NA,
  n_y0x0z1 = NA, n_y1x0z1 = NA, n_y0x1z1 = NA, n_y1x1z1 = NA,
  iv.ineqs = FALSE)

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.

iv.ineqs

Whether to return the empirical bounds or the IV inequalities (TRUE).

Value

The empirical bounds for the ACDE among Always Takers and Never Takers, or the empirical IV inequalities.

References

Richardson, T. S., Evans, R. J., & Robins, J. M. (2011). Transparent parameterizations of models for potential outcomes. Bayesian Statistics, 9, 569-610.

A. Balke and J. Pearl. (1997). Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association, 1171-1176.

Examples

Check_ACDE_bounds(99, 1027, 30, 233, 84, 935, 31, 422)
Check_ACDE_bounds(c(99, 1027, 30, 233, 84, 935, 31, 422))
Check_ACDE_bounds(99, 1027, 30, 233, 84, 935, 31, 422, iv.ineqs=TRUE)
Check_ACDE_bounds(c(99, 1027, 30, 233, 84, 935, 31, 422), iv.ineqs=TRUE)