criterionMin: Minimizing violation of observational equivalence

In jkcshea/ivmte: Instrumental Variables: Extrapolation by Marginal Treatment Effects

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. The LP model must be passed as an environment variable, under the entry $model. See lpSetup.

Usage

criterionMin(env, sset, solver, solver.options, rescale = FALSE, debug = FALSE)

Arguments

env	environment containing the matrices defining the LP problem.
sset	A list of IV-like estimates and the corresponding gamma terms.
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.
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 including the minimum violation of observational equivalence, the solution to the LP problem, and the status of the solution.

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.  The code below imposes a lower bound of 0.2 and upper
## bound of 0.8 on the MTRs.
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 will minimize the criterion
lpSetupCriterion(env = modelEnv,
                sset = sSet)
## Declare any LP solver options as a list.
lpOptions <- optionsLpSolveAPI(list(epslevel = "tight"))
## Minimize the criterion.
obseqMin <- criterionMin(env = modelEnv,
                         sset = sSet,
                         solver = "lpsolveapi",
                         solver.options = lpOptions)
obseqMin
cat("The minimum criterion is",  obseqMin$obj, "\n")

jkcshea/ivmte documentation built on Aug. 31, 2024, 6:44 p.m.