Check_IV_ineqs {noncompliance}

Check of the Instrumental Variable (IV) inequalities.

Description

This checks whether the Instrumental Variable (IV) inequalities for a binary dataset have been satisfied empirically, assuming only Randomization and Exclusion Restriction for the principal strata of Always Takers and Never Takers. Monotonicity (no Defiers) is not assumed here.

Usage

Check_IV_ineqs(n_y0x0z0, n_y1x0z0 = NA, n_y0x1z0 = NA, n_y1x1z0 = NA,
  n_y0x0z1 = NA, n_y1x0z1 = NA, n_y0x1z1 = NA, n_y1x1z1 = NA,
  verbose = 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.

verbose

Whether to return all the IV inequalities (TRUE) or just a check that the inequalities have been satisfied empirically.

Value

A list of all the IV inequalities or a check of whether all the inequalities have been satisfied empirically.

References

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

B. Bonet. (2001). Instrumentality tests revisited. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 48-55.

Examples

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