# genmonoboundA: Generating monotonicity and boundedness constraints In ivmte: Instrumental Variables: Extrapolation by Marginal Treatment Effects

## Description

This is a wrapper function generating the matrices and vectors associated with the monotonicity and boundedness constraints declared by the user. Since this function generates all the components required for the shape constraints, it is also the function that performs the audit. That is, MTR coefficients are passed, then this function will verify whether they satisfy the shape constraints.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33``` ```genmonoboundA( pm0, pm1, support, grid_index, uvec, splinesobj, monov, uname, m0, m1, sset, gstar0, gstar1, m0.lb, m0.ub, m1.lb, m1.ub, mte.lb, mte.ub, m0.dec, m0.inc, m1.dec, m1.inc, mte.dec, mte.inc, solution.m0.min = NULL, solution.m1.min = NULL, solution.m0.max = NULL, solution.m1.max = NULL, audit.tol, direct ) ```

## Arguments

 `pm0` A list of the monomials in the MTR for d = 0. `pm1` A list of the monomials in the MTR for d = 1. `support` a matrix for the support of all variables that enter into the MTRs. `grid_index` a vector, the row numbers of `support` used to generate the grid preceding the audit. `uvec` a vector, the points in the interval [0, 1] that the unobservable takes on. `splinesobj` a list of lists. Each of the inner lists contains details on the splines declared in the MTRs. `monov` name of variable for which the monotonicity conditions applies to. `uname` name declared by user to represent the unobservable term in the MTRs. `m0` one-sided formula for marginal treatment response function for the control group. The formula may differ from what the user originally input in `ivmte`, as the spline components should have been removed. This formula is simply a linear combination of all covariates that enter into the original `m0` declared by the user in `ivmte`. `m1` one-sided formula for marginal treatment response function for the treated group. The formula may differ from what the user originally input in `ivmte`, as the spline components should have been removed. This formula is simply a linear combination of all covariates that enter into the original `m1` declared by the user in `ivmte`. `sset` a list containing the point estimates and gamma components associated with each element in the S-set. `gstar0` set of expectations for each terms of the MTR for the control group. `gstar1` set of expectations for each terms of the MTR for the control group. `m0.lb` scalar, lower bound on MTR for control group. `m0.ub` scalar, upper bound on MTR for control group. `m1.lb` scalar, lower bound on MTR for treated group. `m1.ub` scalar, upper bound on MTR for treated group. `mte.lb` scalar, lower bound on MTE. `mte.ub` scalar, upper bound on MTE. `m0.dec` boolean, indicating whether the MTR for the control group is monotone decreasing. `m0.inc` boolean, indicating whether the MTR for the control group is monotone increasing. `m1.dec` boolean, indicating whether the MTR for the treated group is monotone decreasing. `m1.inc` boolean, indicating whether the MTR for the treated group is monotone increasing. `mte.dec` boolean, indicating whether the MTE is monotone decreasing. `mte.inc` boolean, indicating whether the MTE is monotone increasing. `solution.m0.min` vector, the coefficients for the MTR for `D = 0` corresponding to the lower bound of the target parameter. If passed, this will initiate checks of shape constraints. `solution.m1.min` vector, the coefficients for the MTR for `D = 1` corresponding to the lower bound of the target parameter. If passed, this will initiate checks of shape constraints. `solution.m0.max` vector, the coefficients for the MTR for `D = 0` corresponding to the upper bound of the target parameter. If passed, this will initiate checks of shape constraints. `solution.m1.max` vector, the coefficients for the MTR for `D = 1` corresponding to the upper bound of the target parameter. If passed, this will initiate checks of shape constraints. `audit.tol` feasibility tolerance when performing the audit. By default to set to be equal `1e-06`. This parameter should only be changed if the feasibility tolerance of the solver is changed, or if numerical issues result in discrepancies between the solver's feasibility check and the audit. `direct` boolean, set to `TRUE` if the direct MTR regression is used.

## Value

a list containing a unified constraint matrix, unified vector of inequalities, and unified RHS vector for the boundedness and monotonicity constraints of an LP/QCQP problem.

ivmte documentation built on Sept. 17, 2021, 5:06 p.m.