Description Usage Arguments Value Examples

If the user passes IV-like moments to the function, then the
function constructs the components of the LP problem. If no IV-like
moments are passed, then the function constructs the linear
constraints of the QCQP problem. Note that the LP/QCQP model will
be saved inside an environment variable, which is to be passed
through the argument `env`

. This is done for efficient use of
memory. The environment `env`

is supposed to already contain a
list under the entry `$mbobj`

containing the matrices defining
the shape constraints. This list of shape constraints `$mbobj`

should contain three entries corresponding to a system of linear
equations of the form `Ax <=> b`

: `mbA`

, the matrix
defining the constraints, `A`

; `mbs`

, a vector indicating
whether a row in `mbA`

is an equality or inequality constraint
(for Gurobi and MOSEK, use '<=', '>=', '='; for CPLEX,
use 'L', 'G', and 'E'); `mbrhs`

, a vector of the right hand
side values defining the constraint of the form i.e. the vector
`b`

. Depending on the linear programming solver used, this
function will return different output specific to the solver.

1 2 3 4 5 6 7 8 9 10 11 |

`env` |
environment containing the matrices defining the LP/QCQP problem. |

`sset` |
List of IV-like estimates and the corresponding gamma terms. |

`orig.sset` |
list, only used for bootstraps. The list contains the gamma moments for each element in the S-set, as well as the IV-like coefficients. |

`equal.coef0` |
character, name of terms in |

`equal.coef1` |
character, name of terms in |

`shape` |
boolean, default set to TRUE. Switch to determine whether or not to include shape restrictions in the LP/QCQP problem. |

`direct` |
boolean, set to |

`rescale` |
boolean, set to |

`solver` |
string, name of the package used to solve the LP/QCQP problem. |

A list of matrices and vectors necessary to define an LP/QCQP problem.

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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 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")
``` |

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