ivmte (version 1.1.0)

obsEqMin: Minimizing violation of observational equivalence

Description

Given a set of IV-like estimates and the set of matrices/vectors defining an LP problem, this function minimizes the violation of observational equivalence under the L1 norm.

Usage

obsEqMin(sset, orig.sset = NULL, orig.criterion = NULL,
  criterion.tol = 0, lpobj, lpsolver, debug = FALSE)

Arguments

sset

A list of IV-like estimates and the corresponding gamma terms.

orig.sset

list, only used for bootstraps. The list caontains the gamma moments for each element in the S-set, as well as the IV-like coefficients.

orig.criterion

numeric, only used for bootstraps. The scalar corresponds to the minimum observational equivalence criterion from the original sample.

criterion.tol

tolerance for violation of observational equivalence, set to 0 by default.

lpobj

A list of matrices and vectors defining an LP problem.

lpsolver

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

debug

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

Value

A list including the minimum violation of observational equivalence, the solution to the LP problem, and the status of the solution.

Examples

# NOT RUN {
dtm <- ivmte:::gendistMosquito()

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

## Declare MTR formulas
formula1 = ~ 1 + u
formula0 = ~ 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 = formula0,
                 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,
                         point = FALSE)

## 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)

## 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
lpObject <- lpSetup(sset = sSet$sset,
                    mbA = A,
                    mbs = sense,
                    mbrhs = rhs,
                    lpsolver = "lpSolveAPI")

## Estimate the bounds
obsEqMin(sset = sSet$sset,
         lpobj = lpObject,
         lpsolver = "lpSolveAPI")

# }