noncompliance (version 0.2.2)

ACE_bounds_posterior: Posterior bounds for the Average Causal Effect (ACE).

Description

The posterior bounds for the Average Causal Effect (ACE) is found based on a transparent reparametrization (see reference below), using a Dirichlet prior. A binary Instrumental Variable (IV) model is assumed here.

Usage

ACE_bounds_posterior(n_y0x0z0, n_y1x0z0 = NA, n_y0x1z0 = NA, n_y1x1z0 = NA, n_y0x0z1 = NA, n_y1x0z1 = NA, n_y0x1z1 = NA, n_y1x1z1 = NA, prior, num.sims = 1000)

Arguments

n_y0x0z0

Number of individuals with Y=0, X=0, Z=0. Alternatively, a vector with elements 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.

prior

Hyperparameters for the Dirichlet prior for p(y, x | z), in the order of the arguments.

num.sims

Number of Monte Carlo draws from the posterior.

Value

A data frame with the posterior bounds for the ACE, based only on sampled distributions (from the posterior) that satisfied the IV inequalites.

References

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

Examples

ACE_bounds_posterior(158, 14, 0, 0, 52, 12, 23, 78,
     prior = c( rep(1, 2), rep(0, 2), rep(1, 4)))
ACE_bounds_posterior(158, 14, 0, 0, 52, 12, 23, 78,
     prior = c( rep(1/2, 2), rep(0, 2), rep(1/4, 4)))
## Not run: 
# ace.bnds.lipid <- ACE_bounds_posterior(158, 14, 0, 0, 52, 12, 23, 78,
#      prior = c( rep(1, 2), rep(0, 2), rep(1, 4)), num.sims = 2e4)
# summary(ace.bnds.lipid) ## End(Not run)