bound {ivmte}

Obtaining TE bounds

Description

This function estimates the bounds on the target treatment effect. The LP model must be passed as an environment variable, under the entry $model. See lpSetup.

Usage

bound(
  env,
  sset,
  solver,
  solver.options,
  noisy = FALSE,
  smallreturnlist = FALSE,
  rescale = FALSE,
  debug = FALSE
)

Arguments

env

environment containing the matrices defining the LP problem.

sset

a list containing the point estimates and gamma components associated with each element in the S-set. This object is only used to determine the names of terms. If it is no submitted, then no names are provided to the solution vector.

solver

string, name of the package used to solve the LP problem.

solver.options

list, each item of the list should correspond to an option specific to the LP solver selected.

noisy

boolean, set to TRUE if optimization results should be displayed.

smallreturnlist

boolean, set to TRUE if the LP model should not be returned.

rescale

boolean, set to TRUE if the MTR components should be rescaled to improve stability in the LP/QP/QCP optimization.

debug

boolean, indicates whether or not the function should provide output when obtaining bounds. The option is only applied when solver = 'gurobi' or solver = 'rmosek'. The output provided is the same as what the Gurobi API would send to the console.

Value

a list containing the bounds on the treatment effect; the coefficients on each term in the MTR associated with the upper and lower bounds, for both counterfactuals; the optimization status to the maximization and minimization problems; the LP problem that the optimizer solved.

Examples

dtm <- ivmte:::gendistMosquito()

## Declare empty list to be updated (in the event multiple IV like
## specifications are provided
sSet <- list()

## Declare MTR formulas
formula0 = ~ 1 + u
formula1 = ~ 1 + u

## Construct object that separates out non-spline components of MTR
## formulas from the spline components. The MTR functions are
## obtained from this object by the function 'genSSet'.
splinesList = list(removeSplines(formula0), removeSplines(formula1))

## Construct MTR polynomials
polynomials0 <- polyparse(formula = formula0,
                          data = dtm,
                          uname = u,
                          as.function = FALSE)
polynomials1 <- polyparse(formula = formula1,
                          data = dtm,
                          uname = u,
                           as.function = FALSE)

## Generate propensity score model
propensityObj <- propensity(formula = d ~ z,
                            data = dtm,
                            link = "linear")

## Generate IV estimates
ivEstimates <- ivEstimate(formula = ey ~ d | z,
                          data = dtm,
                          components = l(intercept, d),
                          treat = d,
                          list = FALSE)

## Generate target gamma moments
targetGamma <- genTarget(treat = "d",
                         m0 = ~ 1 + u,
                         m1 = ~ 1 + u,
                         target = "atu",
                         data = dtm,
                         splinesobj = splinesList,
                         pmodobj = propensityObj,
                         pm0 = polynomials0,
                         pm1 = polynomials1)

## Construct S-set. which contains the coefficients and weights
## corresponding to various IV-like estimands
sSet <- genSSet(data = dtm,
                sset = sSet,
                sest = ivEstimates,
                splinesobj = splinesList,
                pmodobj = propensityObj$phat,
                pm0 = polynomials0,
                pm1 = polynomials1,
                ncomponents = 2,
                scount = 1,
                yvar = "ey",
                dvar = "d",
                means = TRUE)
## Only the entry $sset is required
sSet <- sSet$sset

## Define additional upper- and lower-bound constraints for the LP
## problem
A <- matrix(0, nrow = 22, ncol = 4)
A <- cbind(A, rbind(cbind(1, seq(0, 1, 0.1)),
                    matrix(0, nrow = 11, ncol = 2)))
A <- cbind(A, rbind(matrix(0, nrow = 11, ncol = 2),
                    cbind(1, seq(0, 1, 0.1))))
sense <- c(rep(">", 11), rep("<", 11))
rhs <- c(rep(0.2, 11), rep(0.8, 11))

## Construct LP object to be interpreted and solved by
## lpSolveAPI. Note that an environment has to be created for the LP
## object. The matrices defining the shape restrictions must be stored
## as a list under the entry \code{$mbobj} in the environment.
modelEnv <- new.env()
modelEnv$mbobj <- list(mbA = A,
                    mbs = sense,
                    mbrhs = rhs)
## Convert the matrices defining the shape constraints into a format
## that is suitable for the LP solver.
lpSetup(env = modelEnv,
        sset = sSet,
        solver = "lpsolveapi")
## Setup LP model so that it is solving for the bounds.
lpSetupBound(env = modelEnv,
             g0 = targetGamma$gstar0,
             g1 = targetGamma$gstar1,
             sset = sSet,
             criterion.tol = 0,
             criterion.min = 0,
             solver = "lpsolveapi")
## Declare any LP solver options as a list.
lpOptions <- optionsLpSolveAPI(list(epslevel = "tight"))
## Obtain the bounds.
bounds <- bound(env = modelEnv,
                sset = sSet,
                solver = "lpsolveapi",
                solver.options = lpOptions)
cat("The bounds are [",  bounds$min, ",", bounds$max, "].\n")