criterionMin: Minimizing violation of observational equivalence
In ivmte: Instrumental Variables: Extrapolation by Marginal Treatment Effects

Description Usage Arguments Value Examples

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.

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

`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.

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

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")