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

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))

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

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)

"Triangle" plot of the posterior bounds for the Average Causal Effect (ACE).

Description

Plot of the posterior upper bound for the Average Causal Effect (ACE) against the corresponding lower bound.

Usage

ACE_bounds_triangle.plot(bounds, title.txt)

Arguments

Value

A "triangle" plot.

Examples

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)))
ACE_bounds_triangle.plot(ace.bnds.lipid, "Bounds on ACE for Lipid Data")
## 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)
ACE_bounds_triangle.plot(ace.bnds.lipid, "Bounds on ACE for Lipid Data") 
## End(Not run)

Finds all column totals for Compliers and Never Takers under the sharp null for Compliers.

Description

Finds all compatible column totals for Compliers and Never Takers under the sharp null for Compliers, based on an observed dataset.

Usage

AllColTotalsH0_CONT(n_y0x0z0.H0, n_y1x0z0.H0, n_y0x0z1.H0, n_y1x0z1.H0,
  n_y0x1z1.H0, n_y1x1z1.H0)

Arguments

Value

A data.table with all possible combinations of the column totals for Compliers and Never Takers under the sharp null for Compliers.

Examples

AllColTotalsH0_CONT(158, 14, 52, 12, 23, 78)

Finite population sample space given an observed dataset.

Description

Sample space of all possibly observable datasets given an observed dataset, assuming only Compliers and Never Takers in the population.

Usage

AllPossiblyObsH0_CONT(n_y0x0z0, n_y1x0z0, n_y0x0z1, n_y1x0z1, n_y0x1z1,
  n_y1x1z1, findGLR = FALSE)

Arguments

Value

All possibly observable datasets in a data.table format.

Examples

AllPossiblyObsH0_CONT(16, 1, 5, 1, 2, 8)
AllPossiblyObsH0_CONT(16, 1, 5, 1, 2, 8, findGLR=TRUE)

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

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)

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

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)

Maximum Likelihood Estimate under the sharp null for Compliers.

Description

Find the maximum likelihood estimate of the 2 by 4 contingency table assuming only Compliers and Never Takers in the population, under the sharp null for Compliers and with the multivariate hypergeometric sampling distribution.

Usage

FindMLE_CONT_H0_hypergeoR(n_y0x0z0, n_y1x0z0, n_y0x0z1, n_y1x0z1, n_y0x1z1,
  n_y1x1z1)

Arguments

Value

The maximum likelihood under the sharp null for Compliers, and the corresponding (possibly non-unique) 2 by 4 contingency table.

Examples

FindMLE_CONT_H0_hypergeoR(158, 14, 52, 12, 23, 78)

Maximum Likelihood Estimate without assuming the sharp null for Compliers.

Description

Find the maximum likelihood estimate of the 2 by 4 contingency table assuming only Compliers and Never Takers in the population, with the multivariate hypergeometric sampling distribution.

Usage

FindMLE_CONT_H1_hypergeoR(n_y0x0z0, n_y1x0z0, n_y0x0z1, n_y1x0z1, n_y0x1z1,
  n_y1x1z1)

Arguments

Value

The maximum likelihood, and the corresponding (possibly non-unique) 2 by 4 contingency table.

Examples

FindMLE_CONT_H1_hypergeoR(158, 14, 52, 12, 23, 78)

Exact finite population p-values under the sharp null for Compliers.

Description

Find the exact population-specific p-values under the sharp null for Compliers, for each compatible population with only Compliers and Never Takers.

Usage

Get_pvalues_CONT(obs_y0x0z0, obs_y1x0z0, obs_y0x0z1, obs_y1x0z1, obs_y0x1z1,
  obs_y1x1z1, useGLR = FALSE, justexactp = TRUE, maxonly = TRUE)

Arguments

Value

Exact population-specific p-value(s) for a given observed dataset.

References

Loh, W. W., & Richardson, T. S. (2015). A Finite Population Likelihood Ratio Test of the Sharp Null Hypothesis for Compliers. In Thirty-First Conference on Uncertainty in Artificial Intelligence. [paper]

Examples

Get_pvalues_CONT(16, 1, 5, 1, 2, 8)
Get_pvalues_CONT(16, 1, 5, 1, 2, 8, TRUE, FALSE)
Get_pvalues_CONT(16, 1, 5, 1, 2, 8, TRUE, FALSE, FALSE)
Get_pvalues_CONT(158, 14, 52, 12, 23, 78)

Expand.grid using the data.table package.

Description

Expand.grid (expand.grid) using the data.table package, with up to 4 supplied vectors.

Usage

expand.grid.DT(seq1, seq2, seq3 = NA, seq4 = NA, col.names = NA)

Arguments

Value

A data.table with all possible combinations (Cartesian product) of the elements in the input vector sequences.

Examples

expand.grid.DT(1:10, 100:110)
expand.grid.DT(1:10, 100:110, col.names=c("A", "B"))
expand.grid.DT(1:10, 100:110, 11:13, 1:2)