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Angrist Evans Data

Description

Angrist Evans Data

Usage

AE

Format

A data frame with 209,133 rows and 8 columns.

worked

indicator for whether worked in the previous year

hours

weekly hours worked in the previous year

morekids

indicator for having more than two children vs. exactly two children.

samesex

indicator for the first two children having the same sex (male-male or female-female)

yob

the year the woman was born

black

indicator that mother is Black

hisp

indicator that mother is Hispanic

other

indicator that mother is neither Black nor Hispanic

Source

Derived from Angrist and Evans (1998, The American Economic Review).

(Alternative) Defining single splines basis functions, withinteractions

Description

This function returns a numerically integrable functioncorresponding to a single splines basis function. It was notimplemented because it was slower than using the function from thesplines2 package.

Usage

altDefSplinesBasis(splineslist, j, l, v = 1)

Arguments

Value

a vectorized function corresponding to a single splinesbasis function that can be numerically integrated.

Auxiliary function: extract arguments from function in string form

Description

Auxiliary function to extract arguments from a function that is instring form.

Usage

argstring(string)

Arguments

Value

string of arguments.

Audit procedure

Description

This is the wrapper for running the entire audit procedure. Thisfunction sets up the LP/QCQP problem of minimizing criterion. forthe set of IV-like estimands, while satisfying boundedness andmonotonicity constraints declared by the user. Rather than enforcethat boundedness and monotonicity hold across the entire support ofcovariates and unobservables, this procedure enforces theconditions over a grid of points. This grid corresponds to the setof values the covariates can take, and a set of values of theunobservable term. The size of this grid is specified by the userin the function arguments. The procedure first estimates the boundswhile imposing the shape constraints for an initial subset ofpoints in the grid. The procedure then goes on to check ('audit')whether the constraints are satisfied over the entire grid. Anypoint where either the boundedness or monotonicity constraints areviolated are incorporated into the initial grid, and the process isrepeated until the audit no longer finds any violations, or untilsome maximum number of iterations is reached.

Usage

audit(  data,  uname,  m0,  m1,  pm0,  pm1,  splinesobj,  vars_mtr,  terms_mtr0,  terms_mtr1,  vars_data,  initgrid.nu = 20,  initgrid.nx = 20,  audit.nx = 2500,  audit.nu = 25,  audit.add = 100,  audit.max = 25,  audit.tol,  audit.grid = NULL,  m1.ub,  m0.ub,  m1.lb,  m0.lb,  mte.ub,  mte.lb,  m1.ub.default = FALSE,  m0.ub.default = FALSE,  mte.ub.default = FALSE,  m1.lb.default = FALSE,  m0.lb.default = FALSE,  mte.lb.default = FALSE,  m0.dec = FALSE,  m0.inc = FALSE,  m1.dec = FALSE,  m1.inc = FALSE,  mte.dec = FALSE,  mte.inc = FALSE,  equal.coef0,  equal.coef1,  sset,  gstar0,  gstar1,  orig.sset = NULL,  orig.criterion = NULL,  criterion.tol = 1e-04,  solver,  solver.options,  solver.presolve,  solver.options.criterion,  solver.options.bounds,  rescale = TRUE,  smallreturnlist = FALSE,  noisy = TRUE,  debug = FALSE)

Arguments

Value

a list. Included in the list are estimates of the treatmenteffect bounds; the minimum violation of observationalequivalence of the set of IV-like estimands; the list ofmatrices and vectors defining the LP/QCQP problem; the points usedto generate the audit grid, and the points where the shapeconstraints were violated.

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are providedsSet <- list()## Declare MTR formulasformula0 = ~ 1 + uformula1 = ~ 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))## If splines are interacted with other variables, the## 'interactSplines' should be used.## splinesList <- interactSplines(splinesobj = splinesList,##                               m0 = formula0,##                               m1 = formula1,##                               data = data,##                               uname = 'u')## Construct MTR polynomialspolynomials0 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)polynomials1 <- polyparse(formula = formula1,                 data = dtm,                 uname = u,                 as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(intercept, d),                          treat = d,                          list = FALSE)## Generate target gamma momentstargetGamma <- 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 estimandssSet <- genSSet(data = dtm,                sset = sSet,                sest = ivEstimates,                splinesobj = splinesList,                pmodobj = propensityObj$phat,                pm0 = polynomials0,                pm1 = polynomials1,                ncomponents = 2,                scount = 1,                yvar = "ey",                dvar = "d",                means = TRUE)## Perform audit procedure and return boundsaudit(data = dtm,      uname = u,      m0 = formula0,      m1 = formula1,      pm0 = polynomials0,      pm1 = polynomials1,      splinesobj = splinesList,      vars_data = colnames(dtm),      vars_mtr = "u",      terms_mtr0 = "u",      terms_mtr1 = "u",      sset = sSet$sset,      gstar0 = targetGamma$gstar0,      gstar1 = targetGamma$gstar1,      m0.inc = TRUE,      m1.dec = TRUE,      m0.lb = 0.2,      m1.ub = 0.8,      audit.max = 5,      solver = "lpSolveAPI")

Spline basis function of order 1

Description

This function is the splines basis function of order 1. Thisfunction was coded in accordance to Carl de Boor's set of notes onsplines, "B(asic)-Spline Basics".

Usage

bX(x, knots, i)

Arguments

Value

scalar.

Obtaining TE bounds

Description

This function estimates the bounds on the target treatmenteffect. The LP model must be passed as an environment variable,under the entry$model. SeelpSetup.

Usage

bound(  env,  sset,  solver,  solver.options,  noisy = FALSE,  smallreturnlist = FALSE,  rescale = FALSE,  debug = FALSE)

Arguments

Value

a list containing the bounds on the treatment effect; thecoefficients on each term in the MTR associated with the upperand lower bounds, for both counterfactuals; the optimizationstatus to the maximization and minimization problems; the LPproblem that the optimizer solved.

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are providedsSet <- list()## Declare MTR formulasformula0 = ~ 1 + uformula1 = ~ 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 polynomialspolynomials0 <- polyparse(formula = formula0,                          data = dtm,                          uname = u,                          as.function = FALSE)polynomials1 <- polyparse(formula = formula1,                          data = dtm,                          uname = u,                           as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(intercept, d),                          treat = d,                          list = FALSE)## Generate target gamma momentstargetGamma <- 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 estimandssSet <- 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 $sset is requiredsSet <- sSet$sset## Define additional upper- and lower-bound constraints for the LP## problemA <- 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")

Construct confidence intervals for treatment effects under partialidentification

Description

This function constructs the forward and backward confidenceintervals for the treatment effect under partial identification.

Usage

boundCI(bounds, bounds.resamples, n, m, levels, type)

Arguments

Value

iftype is 'forward' or 'backward', then thecorresponding type of confidence interval for each level isreturned. The output is in the form of a matrix, with each rowcorresponding to a level. Iftype is 'both', then a listis returned. One element of the list is the matrix of backwardconfidence intervals, and the other element of the list is thematrix of forward confidence intervals.

Construct p-values for treatment effects under partialidentification

Description

This function estimates the p-value for the treatment effect underpartial identification. p-values corresponding to forward andbackward confidence intervals can be returned.

Usage

boundPvalue(bounds, bounds.resamples, n, m, type)

Arguments

Value

Iftype is 'forward' or 'backward', a scalar p-valuecorresponding to the type of confidence interval isreturned. Iftype is 'both', a vector of p-valuescorresponding to the forward and backward confidence intervalsis returned.

Check polynomial form of the u-term

Description

This function ensures that the unobservable term enters into theMTR in the correct manner. That is, it enters as a polynomial.

Usage

checkU(formula, uname)

Arguments

Value

If the unobservable term is entered correctly into theformula, thenNULL is returned. Otherwise, the vector ofincorrect terms is returned.

Auxiliary function: test if object is a formula

Description

Auxiliary function to test if an object is a formula. Warnings aresuppressed.

Usage

classFormula(obj)

Arguments

Value

boolean expression.

Auxiliary function: test if object is a list

Description

Auxiliary function to test if an object is a list. Warnings aresuppressed.

Usage

classList(obj)

Arguments

Value

boolean expression.

Combining the boundedness and monotonicity constraint objects

Description

This function simply combines the objects associated with theboundedness constraints and the monotonicity constraints.

Usage

combinemonobound(bdA, monoA)

Arguments

Value

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

Construct constant function

Description

This function constructs another function that returns aconstant. It is used for constructing weight/knot functions.

Usage

constructConstant(x)

Arguments

Value

a function.

Minimizing violation of observational equivalence

Description

Given a set of IV-like estimates and the set of matrices/vectorsdefining an LP problem, this function minimizes the violation ofobservational equivalence under the L1 norm. The LP model must bepassed as an environment variable, under the entry$model.SeelpSetup.

Usage

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

Arguments

Value

A list including the minimum violation of observationalequivalence, the solution to the LP problem, and the status ofthe solution.

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are providedsSet <- list()## Declare MTR formulasformula0 = ~ 1 + uformula1 = ~ 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 polynomialspolynomials0 <- polyparse(formula = formula0,                          data = dtm,                          uname = u,                          as.function = FALSE)polynomials1 <- polyparse(formula = formula1,                          data = dtm,                          uname = u,                           as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(intercept, d),                          treat = d,                          list = FALSE)## Generate target gamma momentstargetGamma <- 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 estimandssSet <- 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 $sset is requiredsSet <- sSet$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 criterionlpSetupCriterion(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)obseqMincat("The minimum criterion is",  obseqMin$obj, "\n")

Generating design matrices

Description

This function generates the design matrix given an IVspecification.

Usage

design(formula, data, subset, treat, orig.names)

Arguments

Value

Three matrices are returned: one for the outcome variable,Y; one for the second stage covariates, X; and one for thefirst stage covariates, Z.

Examples

dtm <- ivmte:::gendistMosquito()design(formula = ey ~ d | z,           data = dtm,           subset = z %in% c(1, 2))

Auxiliary function: extracting columns by component names

Description

Auxiliary function to extract columns from a matrix based on columnnames.

Usage

extractcols(M, components)

Arguments

Format result for display

Description

This function simply takes a number and formats it for beingdisplayed. Numbers less than 1 in absolute value are rounded to 6significant figure. Numbers larger than

Usage

fmtResult(x)

Arguments

Value

A scalar.

Evaluate a particular function

Description

This function evaluates a single function in a list of functions.

Usage

funEval(fun, values = NULL, argnames = NULL)

Arguments

Value

the output of the function evaluated.

Generate basis matrix for splines

Description

The user can declare that the unobservable enters into the MTRs inthe form of splines. This function generates the basis matrix forthe splines. The specifications for the spline must be passed asthe$splineslist object generated byremoveSplines. Note that this function does notaccount for any interactions between the splines and thecovariates. Interactions can be added simply by sweeping the basismatrix by a vector for the values of the covariates.

Usage

genBasisSplines(splines, x, d = NULL)

Arguments

Value

a matrix. The number of rows is equal to the length ofx, and the number of columns depends on thespecifications of the spline. The name of each column takes thefollowing form: "u[d]S[j].[b]", where "u" and "S" are fixed andstand for "unobservable" and "Splines" respectively. "[d]" willbe either 0 or 1, depending on the treatment status. "[j]" willbe an integer indicating which element of the listsplines the column pertains to. "[b]" will be an integerreflect which component of the basis the column pertains to.

Estimating expectations of terms in the MTR (gamma objects)

Description

This function generates the gamma objects defined in the paper,i.e. each additive term in E[md], where md is a MTR.

Usage

genGamma(  monomials,  lb,  ub,  multiplier = 1,  subset = NULL,  means = TRUE,  late.rows = NULL)

Arguments

Value

Ifmeans = TRUE, then the function returns a vectorof the additive terms in Gamma (i.e. the expectation is over D,X, Z, and u). Ifmeans = FALSE, then the functionreturns a matrix, where each row corresponds to an observation,and each column corresponds to an additive term in E[md | D, X,Z] (i.e. only the integral with respect to u is performed).

Examples

dtm <- ivmte:::gendistMosquito()## Declare MTR formulaformula0 = ~ 1 + u## Construct MTR polynomialspolynomials0 <- polyparse(formula = formula0,                data = dtm,                uname = u,                as.function = FALSE)## Construct propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate gamma moments, with S-weight equal to its default value## of 1genGamma(monomials = polynomials0,         lb = 0,         ub = propensityObj$phat)

Generate Gamma moments for splines

Description

The user can declare that the unobservable enters into the MTRs inthe form of splines. This function generates the gamma moments forthe splines. The specifications for the spline must be passed as anelement generated byremoveSplines. This functionaccounts for the interaction between covariates and splines.

Usage

genGammaSplines(  splinesobj,  data,  lb,  ub,  multiplier = 1,  subset,  d = NULL,  means = TRUE,  late.rows = NULL)

Arguments

Value

a matrix, corresponding to the splines being integratedover the region specified bylb andub,accounting for the interaction terms. The number of rows isequal to the number of rows indata. The number ofcolumns depends on the specifications of the spline. The nameof each column takes the following form: "u[d]S[j].[b]", where"u" and "S" are fixed and stand for "unobservable" and"Splines" respectively. "[d]" will be either 0 or 1, dependingon the treatment status. "[j]" will be an integer indicatingwhich element of the listsplines the column pertainsto. "[b]" will be an integer reflect which component of thebasis the column pertains to.

Generating the Gamma moments for splines, for 'testthat'

Description

This function generates the Gamma moments for a given set ofweights. This funciton is written specifically for tests.

Usage

genGammaSplinesTT(distr, weight, zvars, u1s1, u0s1, u0s2, target = FALSE, ...)

Arguments

Value

vector, the Gamma moments associated withweight.

Function to generate gamma moments for 'testthat'

Description

This function generates the gamma moments from a population leveldata set. This is specifically constructed to carry out tests.

Usage

genGammaTT(data, s0, s1, lb, ub)

Arguments

Value

list, contains the vectors of the Gamma moments for controland treated observations.

Generating moments/data for IV-like estimands

Description

This function takes in the IV estimate and its IV-likespecification, and generates a list containing the correspondingIV-like point estimate, and the corresponding moments (gammas) thatwill enter into the constraint matrix of the LP problem. If theoptionmeans = FALSE, then the data are not averaged togenerate the gamma moments and may be used for GMM. The functionrequires the user to provide a list (i.e. the list the pointestimates and moments corresponding to other IV-likespecifications; or an empty list) to append these point estimatesand moments to.

Usage

genSSet(  data,  sset,  sest,  splinesobj,  pmodobj,  pm0,  pm1,  ncomponents,  scount,  subset_index,  means = TRUE,  yvar,  dvar,  noisy = TRUE,  ivn = NULL,  redundant = NULL)

Arguments

Value

A list containing the point estimate for the IV regression,and the expectation of each monomial term in the MTR.

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are provided)sSet <- list()## Declare MTR formulasformula1 = ~ 1 + uformula0 = ~ 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 polynomialspolynomials0 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)polynomials1 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(d),                          treat = d,                          list = FALSE)## Construct S-set, which contains the coefficients and weights## corresponding to various IV-like estimandsgenSSet(data = dtm,        sset = sSet,        sest = ivEstimates,        splinesobj = splinesList,        pmodobj = propensityObj$phat,        pm0 = polynomials0,        pm1 = polynomials1,        ncomponents = 1,        scount = 1)

Generating target MTR moments

Description

This function estimates the moment of each MTR term under thetarget weight.

Usage

genTarget(  treat,  m0,  m1,  target,  target.weight0,  target.weight1,  target.knots0,  target.knots1,  late.Z,  late.from,  late.to,  late.X,  eval.X,  genlate.lb,  genlate.ub,  data,  splinesobj,  pmodobj,  pm0,  pm1,  noisy = TRUE)

Arguments

Value

A list containing either the vectors of gamma moments forD = 0 andD = 1, or a matrix of individual gammavalues forD = 0 andD = 1. Additoinally, twovectors are returned.xindex0 andxindex1 listthe variables that interact with the unobservableu inm0 andm1.uexporder0 anduexporder1 lists the exponents of the unobservableu in each term it appears in.

Examples

dtm <- ivmte:::gendistMosquito()## Declare MTR functionsformula1 = ~ 1 + uformula0 = ~ 1 + usplinesList = list(removeSplines(formula0), removeSplines(formula1))## Declare propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Construct MTR polynomialspolynomials0 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)polynomials1 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)## Generate target gamma momentsgenTarget(treat = "d",          m0 = ~ 1 + u,          m1 = ~ 1 + u,          target = "atu",          data = dtm,          splinesobj = splinesList,          pmodobj = propensityObj,          pm0 = polynomials0,          pm1 = polynomials1)

Generating list of target weight functions

Description

This function takes in the user-defined target weight functions andthe data set, and generates the weight functions for eachobservation.

Usage

genWeight(fun, fun.name, uname, data)

Arguments

Value

The weight function 'fun', where all arguments other thanthat of the unobserved variable are fixed according to thevector 'data'.

Generating the constraint matrix

Description

This function generates the component of the constraint matrix inthe LP/QCQP problem pertaining to the lower and upper bounds on the MTRsand MTEs. These bounds are declared by the user.

Usage

genboundA(  A0,  A1,  sset,  gridobj,  uname,  m0.lb,  m0.ub,  m1.lb,  m1.ub,  mte.lb,  mte.ub,  solution.m0.min = NULL,  solution.m1.min = NULL,  solution.m0.max = NULL,  solution.m1.max = NULL,  audit.tol,  direct = FALSE)

Arguments

Value

a constraint matrix for the LP/QCQP problem, the associatedvector of inequalities, and the RHS vector in the inequalityconstraint. The objects pertain only to the boundednessconstraints declared by the user.

Generate test distribution 1

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1 or 2, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 0 + u and m1 ~ 1 + u. All unobservablesu are integrated out.

Usage

gendist1(subN = 5, p1 = 0.4, p2 = 0.6)

Arguments

Value

a data.frame.

Generate test distribution 1 with errors

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1 or 2, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 0 + u and m1 ~ 1 + u.

Usage

gendist1e(N = 100, subN = 0.5, p1 = 0.4, p2 = 0.6, v0.sd = 0.5, v1.sd = 0.75)

Arguments

Value

a data.frame.

Generate test distribution 2

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1, 2, or 3, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 1 + u and m1 ~ 1 + u. All unobservablesu are integrated out.

Usage

gendist2(subN = 5, p1 = 0.4, p2 = 0.6, p3 = 0.8)

Arguments

Value

a data.frame.

Generate test distribution 3

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1 and 2, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 1 and m1 ~ 1. All unobservables u areintegrated out.

Usage

gendist3(subN = 5, p1 = 0.4, p2 = 0.6)

Arguments

Value

a data.frame.

Generate test distribution 3 with errors

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1 or 2, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 0 + u and m1 ~ 1 + u.

Usage

gendist3e(N = 100, subN = 0.5, p1 = 0.4, p2 = 0.6, v0.sd = 0.5, v1.sd = 0.75)

Arguments

Value

a data.frame.

Generate test distribution 4

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1, 2, and 3, and thedistribution of the values for the binary instrument isuniform. The MTRs are m0 ~ 1 and m1 ~ 1. All unobservables u areintegrated out.

Usage

gendist4(subN = 5, p1 = 0.4, p2 = 0.6, p3 = 0.8)

Arguments

Value

a data.frame.

Generate test distribution 5 (has errors and a covariate)

Description

This function generates a data set for testing purposes. There is asingle instrument that takes on values of 1 or 2, and thedistribution of the values for the binary instrument isuniform. The MTRs are both of the form m ~ 1 + x + u.

Usage

gendist5e(N = 100, subN = 0.5, p1 = 0.4, p2 = 0.6, v0.sd = 1, v1.sd = 1.55)

Arguments

Value

a data.frame.

Generate test distribution 6 (has errors and a covariate)

Description

This function generates a data set for testing purposes. There is asingle instrument that is uniformly distributed over [0, 1]. TheMTRs are both of the form m ~ 1 + x + x:u.

Usage

gendist6e(N = 100, v0.sd = 1, v1.sd = 1.55)

Arguments

Value

a data.frame.

Generate basic data set for testing

Description

This code generates population level data to test the estimationfunction. This is a simpler dataset, one in which we can moreeasily estimate a correctly specified model. The data presentedbelow will have already integrated over the # unobservable termsU, where U | X, Z ~ Unif[0, 1].

Usage

gendistBasic()

Value

a list of two data.frame objects. One is the distributionof the simulated data, the other is the full simulated dataset.

Generate test data set with covariates

Description

This code generates population level data to test the estimationfunction. This data includes covariates. The data generated willhave already integrated over the unobservable terms U, where U | X,Z ~ Unif[0, 1].

Usage

gendistCovariates()

Value

a list of two data.frame objects. One is the distributionof the simulated data, the other is the full simulated dataset.

Generate mosquito data set

Description

This code generates the population level data in Mogstad, Santos,Torgovitsky (2018), i.e. the mosquito data set used as the runningexample.

Usage

gendistMosquito()

Value

data.frame.

Generate test data set with splines

Description

This code generates population level data to test theestimation function. This data set incorporates splines in theMTRs.

Usage

gendistSplines()

Details

The distribution of the data is as follows

| ZX/Z | 0 1_______|___________-1 | 0.1 0.1|X 0 | 0.2 0.2|1 | 0.1 0.2

The data presented below will have already integrated over theunobservable terms U, and U | X, Z ~ Unif[0, 1].

The propensity scores are generated according to the model

p(x, z) = 0.5 - 0.1 * x + 0.2 * z

| Zp(X,Z) | 0 1_______|___________-1 | 0.6 0.8|X 0 | 0.5 0.7|1 | 0.4 0.6

The lowest common multiple of the first table is 12. The lowestcommon multiple of the second table is 84. It turns out that 840 *5 = 4200 observations is enough to generate the population dataset, such that each group has a whole-number of observations.

The MTRs are defined as follows:

y1 ~ beta0 + beta1 * x + uSpline(degree = 2,knots = c(0.3, 0.6),intercept = FALSE)

The coefficients (beta1, beta2), and the coefficients on thesplines, will be defined below.

y0 = x : uSpline(degree = 0,knots = c(0.2, 0.5, 0.8),intercept = TRUE)+ uSpline(degree = 1,knots = c(0.4),intercept = TRUE)+ beta3 * I(u ^ 2)

The coefficient beta3, and the coefficients on the splines, will bedefined below.

Value

a list of two data.frame objects. One is the distributionof the simulated data, the other is the full simulated dataset.

Auxiliary function: generating basis vectors

Description

Auxiliary function to generate standard basis vectors.

Usage

genej(pos, length)

Arguments

Value

Vector containing 1 in a single position, and 0 elsewhere.

Generating the grid for the audit procedure

Description

This function takes in a matrix summarizing the support of thecovariates, as well as set of points summarizing the support of theunobservable variable. A Cartesian product of the subset of thesupport of the covariates and the points in the support of theunobservable generates the grid that is used for the auditprocedure.

Usage

gengrid(index, xsupport, usupport, uname)

Arguments

Value

a list containing the grid used in the audit; a vectormapping the elements in the support of the covariates toindex.

Generate components of the monotonicity constraints

Description

This function generates the matrix and vectors associated with themonotonicity constraints declared by the user. It takes in a gridof the covariates on which the shape constraints are defined, and thencalculates the values of the MTR and MTE over the grid. Thematrices characterizing the monotonicity conditions can then beobtained by taking first differences over the grid of theunobservable term, within each set of values in the grid ofcovariate values.

Usage

genmonoA(  A0,  A1,  sset,  uname,  gridobj,  gstar0,  gstar1,  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

Value

constraint matrix for the LP/QCQP problem. The matrix pertainsonly to the monotonicity conditions on the MTR and MTE declaredby the user.

Generating monotonicity and boundedness constraints

Description

This is a wrapper function generating the matrices and vectorsassociated with the monotonicity and boundedness constraintsdeclared by the user. Since this function generates all thecomponents required for the shape constraints, it is also thefunction that performs the audit. That is, MTR coefficients arepassed, then this function will verify whether they satisfy theshape constraints.

Usage

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

Value

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

Auxiliary function: extract X and Z covariates from a formula

Description

Auxiliary function that takes in a two-sided formula, and extractsthe variable names of either the covariates or instruments. Thefunction returns an error if the formula includes a variable called'intercept'.

Usage

getXZ(fm, inst = FALSE, terms = FALSE, components = FALSE)

Arguments

Value

vector of variable names.

GMM estimate of TE under point identification

Description

If the user sets the argumentpoint = TRUE in the functionivmte, then it is assumed that the treatment effectparameter is point identified. The observational equivalencecondition is then set up as a two-step GMM problem. Solving thisGMM problem recovers the coefficients on the MTR functions m0 andm1. Combining these coefficients with the target gamma momentsallows one to estimate the target treatment effect.

Usage

gmmEstimate(  sset,  gstar0,  gstar1,  center = NULL,  subsetList = NULL,  n = NULL,  redundant = NULL,  identity = FALSE,  nMoments,  splines,  noisy = TRUE)

Arguments

Value

a list containing the point estimate of the treatmenteffects, and the MTR coefficient estimates. The momentconditions evaluated at the solution are also returned, alongwith the J-test results. However, if the optioncenteris passed, then the moment conditions and J-test are centered(this is to perform the J-test via bootstrap).

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are providedsSet <- list()## Declare MTR formulasformula1 = ~ 0 + uformula0 = ~ 0 + 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 polynomialspolynomials0 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)polynomials1 <- polyparse(formula = formula0,                 data = dtm,                 uname = u,                 as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(intercept, d),                          treat = d,                          list = FALSE)## Generate target gamma momentstargetGamma <- 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 estimandssSet <- genSSet(data = dtm,                sset = sSet,                sest = ivEstimates,                splinesobj = splinesList,                pmodobj = propensityObj$phat,                pm0 = polynomials0,                pm1 = polynomials1,                ncomponents = 2,                scount = 1,                yvar = "ey",                dvar = "d",                means = FALSE)## Obtain point estimates using GMMgmmEstimate(sset = sSet$sset,            gstar0 = targetGamma$gstar0,            gstar1 = targetGamma$gstar1)

Update splines object with list of interactions

Description

Certain interactions between factor variables and splines should bedropped to avoid collinearity. Albeit collinearity in the MTRspecification will not impact the bounds, it can substantiallyimpact how costly it is to carry out the estimation. What thisfunction does is map each spline to a temporary variable. A designmatrix is then constructed using these temporary variables in placethe splines. If an interaction involving one of the temporaryvariables is dropped, then one knows to also drop the correspondinginteraction with the spline. Note that only interaction terms needto be omitted, so one does not need to worry about the formulacontained in removeSplines$formula.

Usage

interactSplines(splinesobj, m0, m1, data, uname)

Arguments

Value

An updated version ofsplinesobj.

Auxiliary function: check if string is command

Description

Auxiliary function to check if a string is in fact a command, butin string form.

Usage

isfunctionstring(string)

Arguments

Value

boolean expression.

Obtaining IV-like specifications

Description

This function estimates the IV-like estimands, as well as generatesthe weights associated with the IV-like specifications.

Usage

ivEstimate(  formula,  data,  subset,  components,  treat,  list = FALSE,  order = NULL)

Arguments

Value

Returns a list containing the matrices of IV-likespecifications forD = 0 andD = 1; and theestimates of the IV-like estimands.

Examples

dtm <- ivmte:::gendistMosquito()ivEstimate(formula = ey ~ d | z,           data = dtm,           components = l(d),           treat = d,           list = FALSE)

Instrumental Variables: Extrapolation by Marginal Treatment Effects

Description

This function provides a general framework for using the marginaltreatment effect (MTE) to extrapolate. The model is the same binarytreatment instrumental variable (IV) model considered by Imbens andAngrist (1994) (doi:10.2307/2951620) and Heckman and Vytlacil(2005) (doi:10.1111/j.1468-0262.2005.00594.x). The framework onwhich this function is based was developed by Mogstad, Santos andTorgovitsky (2018) (doi:10.3982/ECTA15463). See also the recentsurvey paper on extrapolation in IV models by Mogstad andTorgovitsky (2018)(doi:10.1146/annurev-economics-101617-041813). A detaileddescription of the module and its features can be found inSheaand Torgovitsky (2021).

Usage

ivmte(  data,  target,  late.from,  late.to,  late.X,  genlate.lb,  genlate.ub,  target.weight0 = NULL,  target.weight1 = NULL,  target.knots0 = NULL,  target.knots1 = NULL,  m0,  m1,  uname = u,  m1.ub,  m0.ub,  m1.lb,  m0.lb,  mte.ub,  mte.lb,  m0.dec,  m0.inc,  m1.dec,  m1.inc,  mte.dec,  mte.inc,  equal.coef,  ivlike,  components,  subset,  propensity,  link = "logit",  treat,  outcome,  solver,  solver.options,  solver.presolve,  solver.options.criterion,  solver.options.bounds,  lpsolver,  lpsolver.options,  lpsolver.presolve,  lpsolver.options.criterion,  lpsolver.options.bounds,  criterion.tol = 1e-04,  initgrid.nx = 20,  initgrid.nu = 20,  audit.nx = 2500,  audit.nu = 25,  audit.add = 100,  audit.max = 25,  audit.tol,  rescale,  point,  point.eyeweight = FALSE,  bootstraps = 0,  bootstraps.m,  bootstraps.replace = TRUE,  levels = c(0.99, 0.95, 0.9),  ci.type = "backward",  specification.test = TRUE,  noisy = FALSE,  smallreturnlist = FALSE,  debug = FALSE)

Arguments

Details

When the function is used to estimate bounds, andstatistical inference is not performed, the function returnsthe following objects.

audit.count

the number of audits required until there wereno more violations; or the number of audits performed before the auditprocedure was terminated.

audit.criterion

the minimum criterion.

audit.grid

a list containing the points used to define the auditgrid, as well as a table of points where the shape constraints wereviolated.

bounds

a vector with the estimated lower and upper bounds ofthe target treatment effect.

call.options

a list containing all the model specifications andcall options generating the results.

gstar

a list containing the estimate of the weighted meansfor each component in the MTRs. The weights are determined by thetarget parameter declared intarget, or the weights definedbytarget.weight1,target.knots1,target.weight0,target.knots0.

gstar.coef

a list containing the coefficients on the treatedand control group MTRs.

gstar.weights

a list containing the target weights used toestimategstar.

result

a list containing the LP/QCQP model, and the full outputfrom solving the problem.

solver

the solver used in estimation.

moments

the number of elements in the S-set used to generateachieve (partial) identification.

propensity

the propensity score model. If a variable is fedto thepropensity argument when callingivmte, thenthe returned object is a list containing the name of variable givenby the user, and the values of that variable used in estimation.

s.set

a list of all the coefficient estimates and weightscorresponding to each element in the S-set.

splines.dict

a list including the specifications of eachspline declared in each MTR.

messages

a vector of character strings logging the output ofthe estimation procedure.

Ifbootstraps is greater than 0, then statistical inferencewill be performed and the output will additionally contain thefollowing objects.

bootstraps

the number of bootstraps.

bootstraps.failed

the number of bootstraps that failed (e.g.due to collinearity) and had to be repeated.

bounds.bootstraps

the estimates of the bounds from everybootstrap draw.

bounds.ci

forward and/or backward confidence intervals forthe bound estimates at the levels specified inlevels.

bounds.se

bootstrap standard errors on the lower and upperbound estimates.

p.value

p-value for the estimated bounds. p-values areconstructed by finding the level at which the confidence intervalno longer contains 0.

propensity.ci

confidence interval for coefficient estimatesof the propensity score model.

propensity.se

standard errors for the coefficient estimatesof the propensity score model.

specification.p.value

p-value from a specification test.The specification test is only performed if the minimum criterionis not 0.

Ifpoint = TRUE andbootstraps = 0, then pointestimation is performed using two-step GMM. The output will containthe following objects.

j.test

test statistic and results from the asymptotic J-test.

moments

a vector. Each element is the GMM criterion for eachmoment condition used in estimation.

mtr.coef

coefficient estimates for the MTRs.

point.estimate

point estimate of the treatment effect.

redundant

indexes for the moment conditions (i.e. elementsin the S set) that were linearly independent and could be dropped.

Ifpoint = TRUE andbootstraps is not 0, thenpoint estimation is performed using two-step GMM, and additionalstatistical inference is performed using the bootstrap samples.The output will contain the following additional objects.

bootstraps

the number of bootstraps.

bootstraps.failed

the number of bootstraps that failed (e.g.due to collinearity) and had to be repeated.

j.test

test statistic and result from the J-test performedusing the bootstrap samples.

j.test.bootstraps

J-test statistic from each bootstrap.

mtr.bootstraps

coefficient estimates for the MTRs fromeach bootstrap sample. These are used to construct the confidenceintervals and standard errors for the MTR coefficients.

mtr.ci

confidence intervals for each MTR coefficient.

mtr.se

standard errors for each MTR coefficient estimate.

p.value

p-value for the treatment effect point estimateestimated using the bootstrap.

point.estimate.bootstraps

treatment effect point estimatefrom each bootstrap sample. These are used to construct theconfidence interval, standard error, and p-value for the treatmenteffect.

point.estimate.ci

confidence interval for the treatmenteffect.

point.estimate.se

standard error for the treatment effectestimate.

propensity.ci

confidence interval for the coefficients inthe propensity score model, constructed using the bootstrap.

propensity.se

standard errors for the coefficient estimatesof the propensity score model.

Value

Returns a list of results from throughout the estimationprocedure. This includes all IV-like estimands; the propensityscore model; bounds on the treatment effect; the estimatedexpectations of each term in the MTRs; the components andresults of the LP/QCQP problem.

Examples

dtm <- ivmte:::gendistMosquito()ivlikespecs <- c(ey ~ d | z,                 ey ~ d | factor(z),                 ey ~ d,                 ey ~ d | factor(z))jvec <- l(d, d, d, d)svec <- l(, , , z %in% c(2, 4))ivmte(ivlike = ivlikespecs,      data = dtm,      components = jvec,      propensity = d ~ z,      subset = svec,      m0 = ~  u + I(u ^ 2),      m1 = ~  u + I(u ^ 2),      uname = u,      target = "att",      m0.dec = TRUE,      m1.dec = TRUE,      bootstraps = 0,      solver = "lpSolveAPI")

Single iteration of estimation procedure from Mogstad, Torgovitsky,Santos (2018)

Description

This function estimates the treatment effect parameters, followingthe procedure described in Mogstad, Santos and Torgovitsky (2018)(doi:10.3982/ECTA15463). A detailed description of the module andits features can be found inSheaand Torgovitsky (2021). However, this is not the main function ofthe module. Seeivmte for the main function. Forexamples of how to use the package, see the vignette, which isavailable on the module'sGitHub page.

Usage

ivmteEstimate(  data,  target,  late.Z,  late.from,  late.to,  late.X,  eval.X,  genlate.lb,  genlate.ub,  target.weight0,  target.weight1,  target.knots0 = NULL,  target.knots1 = NULL,  m0,  m1,  uname = u,  m1.ub,  m0.ub,  m1.lb,  m0.lb,  mte.ub,  mte.lb,  m0.dec,  m0.inc,  m1.dec,  m1.inc,  mte.dec,  mte.inc,  equal.coef,  ivlike,  components,  subset,  propensity,  link = "logit",  treat,  solver,  solver.options,  solver.presolve,  solver.options.criterion,  solver.options.bounds,  criterion.tol = 0.01,  initgrid.nx = 20,  initgrid.nu = 20,  audit.nx = 2500,  audit.nu = 25,  audit.add = 100,  audit.max = 25,  audit.tol,  audit.grid = NULL,  rescale = TRUE,  point = FALSE,  point.eyeweight = FALSE,  point.center = NULL,  point.redundant = NULL,  bootstrap = FALSE,  count.moments = TRUE,  orig.sset = NULL,  orig.criterion = NULL,  vars_y,  vars_mtr,  terms_mtr0,  terms_mtr1,  vars_data,  splinesobj,  splinesobj.equal,  noisy = TRUE,  smallreturnlist = FALSE,  debug = FALSE,  environments)

Arguments

Details

The treatment effects parameters the user can choose from are theATE, ATT, ATU, LATE, and generalized LATE. The user is required toprovide a polynomial expression for the marginal treatmentresponses (MTR), as well as a set of regressions.

There are two approaches to estimating the treatment effectparameters. The first approach restricts the set of MTRcoefficients on each term of the MTRs to be consistent with theregression estimates from the specifications passed throughivlike. The bounds on the treatment effect parametercorrespond to finding coefficients on the MTRs that maximize theiraverage difference. If the model is point identified, then GMM isused for estimation. Otherwise, the function solves an LPproblem. The second approach restricts the set of MTR coefficientsto fit the conditional mean of the outcome variable. If the modelis point identified, then constrained least squares is used forestimation. Otherwise, the function solves a QCQP.

The estimation procedure relies on the propensity to take uptreatment. The propensity scores can either be estimated as part ofthe estimation procedure, or the user can specify a variable in thedata set already containing the propensity scores.

Constraints on the shape of the MTRs and marginal treatment effects(MTE) can be imposed by the user. Specifically, bounds andmonotonicity restrictions are permitted. These constraints arefirst enforced over a subset of points in the data. An iterativeaudit procedure is then performed to ensure the constraints holdmore generally.

Value

Returns a list of results from throughout the estimationprocedure. This includes all IV-like estimands; the propensityscore model; bounds on the treatment effect; the estimatedexpectations of each term in the MTRs; the components andresults of the LP/QCQP problem.

ivmte Simulated Data

Description

ivmte Simulated Data

Usage

ivmteSimData

Format

A data frame with 5,000 rows and 14 columns.

y

binary outcome variable

d

binary treatment variable

z

instrument that takes the value 0, 1, 2, or 3

x

covariate x that takes integer values from 1 to 10

Source

Simulated — see code in data/ivmteSimData.R.

Listing subsets and components

Description

This function allows the user to declare a list of variable namesin non-character form and subsetting conditions. This is used toensure clean entry of arguments into thecomponents andsubset arguments of the function. When selecting componentsto include in the S set, selecting the intercept term and factorvariables requires special treatment. To select the intercept term,include in the vector of variable names, ‘intercept’. If the thefactorized counterpart of a variablex = 1, 2, 3 is includedin the IV-like specifications viafactor(x), the user canselect the coefficients for specific factors by declaring thecomponentsfactor(x)-1, factor(x)-2, factor(x)-3.

Usage

l(...)

Arguments

Value

list.

Examples

components <- l(d, x1, intercept, factor(x)-2)subsets <- l(, z %in% c(2, 4))

Constructing LP problem

Description

If the user passes IV-like moments to the function, then thefunction constructs the components of the LP problem. If no IV-likemoments are passed, then the function constructs the linearconstraints of the QCQP problem. Note that the LP/QCQP model willbe saved inside an environment variable, which is to be passedthrough the argumentenv. This is done for efficient use ofmemory. The environmentenv is supposed to already contain alist under the entry$mbobj containing the matrices definingthe shape constraints. This list of shape constraints$mbobjshould contain three entries corresponding to a system of linearequations of the formAx <=> b:mbA, the matrixdefining the constraints,A;mbs, a vector indicatingwhether a row inmbA is an equality or inequality constraint(for Gurobi and MOSEK, use '<=', '>=', '='; for CPLEX,use 'L', 'G', and 'E');mbrhs, a vector of the right handside values defining the constraint of the form i.e. the vectorb. Depending on the linear programming solver used, thisfunction will return different output specific to the solver.

Usage

lpSetup(  env,  sset,  orig.sset = NULL,  equal.coef0 = NULL,  equal.coef1 = NULL,  shape = TRUE,  direct = FALSE,  rescale = TRUE,  solver)

Arguments

Value

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

Examples

dtm <- ivmte:::gendistMosquito()## Declare empty list to be updated (in the event multiple IV like## specifications are providedsSet <- list()## Declare MTR formulasformula0 = ~ 1 + uformula1 = ~ 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 polynomialspolynomials0 <- polyparse(formula = formula0,                          data = dtm,                          uname = u,                          as.function = FALSE)polynomials1 <- polyparse(formula = formula1,                          data = dtm,                          uname = u,                           as.function = FALSE)## Generate propensity score modelpropensityObj <- propensity(formula = d ~ z,                            data = dtm,                            link = "linear")## Generate IV estimatesivEstimates <- ivEstimate(formula = ey ~ d | z,                          data = dtm,                          components = l(intercept, d),                          treat = d,                          list = FALSE)## Generate target gamma momentstargetGamma <- 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 estimandssSet <- 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 $sset is requiredsSet <- sSet$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")

Configure LP environment for obtaining the bounds

Description

This function sets up the LP model so that the bounds can beobtained. The LP model must be passed as an environment variable,under the entry$model. SeelpSetup.

Usage

lpSetupBound(  env,  g0,  g1,  sset,  criterion.tol,  criterion.min,  solver,  setup = TRUE)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Configure LP environment for minimizing the criterion

Description

This function sets up the objective function for minimizing thecriterion. The LP model must be passed as an environment variable,under the entry$model. SeelpSetup.

Usage

lpSetupCriterion(env, sset)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Configure LP environment for specification testing

Description

This function re-centers various objects in the LP environment sothat a specification test can be performed via the bootstrap. TheLP model must be passed as an environment variable, under the entry$model. SeelpSetup.

Usage

lpSetupCriterionBoot(  env,  sset,  orig.sset,  orig.criterion,  criterion.tol = 0,  setup = TRUE)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Generate equality constraints

Description

This function generates the linear constraints to ensure thatcertain MTR coefficients are constant across the treatment andcontrol group.

Usage

lpSetupEqualCoef(equal.coef0, equal.coef1, ANames)

Arguments

Value

A list, containing the matrix of linear equalityconstraints, a vector of equal signs, and a vector of 0s.

Configure LP environment for diagnostics

Description

This function separates the shape constraints from the LPenvironment. That way, the model can be solved without any shapeconstraints, which is the primary cause of infeasibility. This isdone in order to check which shape constraints are causing themodel to be infeasible. The LP model must be passed as anenvironment variable, under the entry$model. SeelpSetup.

Usage

lpSetupInfeasible(env, sset)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Configure LP environment to be compatible with solvers

Description

This alters the LP environment so the model will be compatible withspecific solvers. The LP model must be passed as an environmentvariable, under the entry$model. SeelpSetup.

Usage

lpSetupSolver(env, solver)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Function to generate integral of m0 and m1

Description

Function carries out integral for a polynomial of degree 3.

Usage

mInt(ub, lb, coef)

Arguments

Value

scalar.

Check magnitude of real number

Description

This function returns the order of magnitude of a a number.

Usage

magnitude(x)

Arguments

Value

An integer indicating the order of magnitude.

Convert matrix into triplet form

Description

This function converts matrices into triplet form for Mosek. Thisis required in order to declare quadratic programming problems andsecond-order cone programming problems.

Usage

matrixTriplets(mat, lower = TRUE)

Arguments

Value

A list containing vectors of row and column indexes, andmatrix values.

Auxiliary function: modifying calls

Description

This function can be used to modify calls in several ways.

Usage

modcall(call, newcall, newargs, keepargs, dropargs)

Arguments

Value

New call object.

Construct pre-meaned moment matrix

Description

This function constructs the matrix to be fed into the GMMestimator to construct the moment conditions.

Usage

momentMatrix(sset, gn0, gn1, subsetList = NULL, n = NULL)

Arguments

Value

matrix whose column means can be used to carry out the GMMestimation.

Integrating and evaluating monomials

Description

Analytically integrates monomials and evalates them at a givenpoint. It is assumed that there is no constant multiplying themonomial.

Usage

monoIntegral(u, exp)

Arguments

Value

scalar or vector, depending on whatu is.

Check if custom weights are negations of each other

Description

This function checks whether the user-declared weights for treatedand control groups are in fact negations of each other. This isproblematic for the GMM procedure when accounting for estimationerror of the target weights.

Usage

negationCheck(  data,  target.knots0,  target.knots1,  target.weight0,  target.weight1,  N = 20)

Arguments

Value

boolean. If the weights are negations of each other,TRUE is returned.

OLS weights

Description

Function generating the S-weights for OLS estimand, with controls.

Usage

olsj(X, X0, X1, components, treat, order = NULL)

Arguments

Value

A list of two vectors: one is the weight for D = 0, theother is the weight for D = 1.

Function to parse options for CPLEX

Description

This function constructs a list of options to be parsed whensolver is set tocplexapi.

Usage

optionsCplexAPI(options)

Arguments

Value

list, each element being the command to evaluate toimplement an option.

Function to parse a single set of options for CPLEX

Description

This function constructs a string to be parsed whensolveris set tocplexapi.

Usage

optionsCplexAPISingle(name, vector)

Arguments

Value

string, the command to be evaluated to implement a singleoption.

Function to extract feasibility tolerance from CPLEX options

Description

This function parses through the user-submitted CPLEX options todetermine what the feasibility tolerance is. This tolerance canthen be used for the audit. If the user does not set the CPLEXfeasibility tolerance, then a default value of1e-06 isreturned.

Usage

optionsCplexAPITol(options)

Arguments

Value

scalar, the level to set the audit tolerance at.

Function to parse options for Gurobi

Description

This function constructs a list of options to be parsed whensolver is set toGurobi. This function reallyimplements some default values, and accounts for thedebugoption.

Usage

optionsGurobi(options, debug)

Arguments

Value

list, the set of options declared by the user, includingsome additional default values (if not assigned by the user)and accounting fordebug.

Function to parse options for lp_solve

Description

This function constructs a list of options to be parsed whensolver is set tolpsolveapi. The options permittedare those that can be set vialpSolveAPI::lp.control, andshould be passed as a named list (e.g.list(epslevel ="tight")).

Usage

optionsLpSolveAPI(options)

Arguments

Value

string, the command to be evaluated to implement theoptions.

Function to parse options for Gurobi

Description

This function constructs a list of options to be parsed whensolver is set toRmosek. This function reallyimplements the default feasibility tolerances.

Usage

optionsRmosek(options, debug)

Arguments

Value

list, the set of options declared by the user, includingsome additional default values.

Correct boolean expressions in terms lists

Description

This function takes a vector of terms and places parentheses aroundboolean expressions.

Usage

parenthBoolean(termsList)

Arguments

Value

character vector.

Auxiliary function: generate all permutations of a vector

Description

This function generates every permutation of the elements in avector.

Usage

permute(vector)

Arguments

Value

a list of all the permutations ofvector.

Auxiliary function: generate all permutation orderings

Description

This function generates every permutation of the first n naturalnumbers.

Usage

permuteN(n)

Arguments

Value

a list of all the permutations of the first n naturalnumbers.

Obtaining IV-like estimands

Description

This function performs TSLS to obtain the estimates for the IV-likeestimands.

Usage

piv(  Y,  X,  Z,  lmcomponents = NULL,  weights = NULL,  order = NULL,  excluded = TRUE)

Arguments

Value

vector of select coefficient estimates.

Function to multiply polynomials

Description

This function takes in two vectors characterizing polynomials. Itthen returns a vector characterizing the product of the twopolynomials.

Usage

polyProduct(poly1, poly2)

Arguments

Value

vector, characterizing the product of the two polynomialscharacterizedpoly1 andpoly2.

Parsing marginal treatment response formulas

Description

This function takes in an MTR formula, and then parses the formulasuch that it becomes a polynomial in the unobservableu. Itthen breaks these polynomials into monomials, and then integrateseach of them with respect tou. Each integral corresponds toE[md | D, X, Z].

Usage

polyparse(  formula,  data,  uname = "u",  env = parent.frame(),  as.function = FALSE)

Arguments

Value

A list (of lists) of monomials corresponding to theoriginal MTR (for each observation); a list (of lists) of theintegrated monomials; a vector for the degree of each of theoriginal monomials in the MTR; and a vector for the names ofeach variable entering into the MTR (notex^2 + x hasonly one term,x).

Examples

dtm <- ivmte:::gendistMosquito()## Declare MTR functionsformula1 = ~ 1 + uformula0 = ~ 1 + u## Construct MTR polynomialspolynomials0 <- polyparse(formula = formula0,                          data = dtm,                          uname = u,                          as.function = FALSE)polynomials1 <- polyparse(formula = formula0,                          data = dtm,                          uname = u,                          as.function = FALSE)

Calulating population mean

Description

Given a distribution, this function calculates the population meanfor each term in a formula.

Usage

popmean(formula, distribution, density = "f")

Arguments

Value

vector, the means for each term informula.

Print results

Description

This function uses the print method on the ivmte return list.

Usage

## S3 method for class 'ivmte'print(x, ...)

Arguments

Value

basic set of results.

Estimating propensity scores

Description

This function estimates the propensity of taking up treatment. Theuser can choose from fitting a linear probability model, a logitmodel, or a probit model. The function can also be used to generatea table of propensity scores for a given set of covariates andexcluded variables. This was incorporated to account for the LATEbeing a target parameter. Specifically, if the argumentformula is the name of a variable indata, but thetarget parameter is not the LATE, then no propensity model isreturned. If the target parameter is the LATE, then then thepropensity model is simply the empirical distribution of propensityscores in the data conditioned on the set of covariates declared inlate.X andlate.Z.

Usage

propensity(formula, data, link = "logit", late.Z, late.X, env = parent.frame())

Arguments

Value

A vector of propensity scores for each observation, as wellas a 'model'. If the user inputs a formula characterizing themodel for taking up treatment, then thelm/glmobject is returned. If the user declares a variable in the dataset to be used as the propensity score, then adata.frame containing the propensity score for eachvalue of the covariates in the probability model is returned.

Examples

dtm <- ivmte:::gendistMosquito()## Declaring a probability model.propensity(formula = d ~ z,               data = dtm,               link = "linear")## Declaring a variable to be used insteadpropensity(formula = ~ pz,               data = dtm,               link = "linear")

Constructing QCQP problem

Description

This function is only used when the direct MTR regression procedureis used. This function simply constructs the quadratic constraint,and adds it to the LP problem defined by the linear optimization problemfor the bounds and the linear shape constraints.

Usage

qpSetup(env, sset, rescale = TRUE)

Arguments

Constructing QCQP problem for bounding

Description

This function is only used when the direct MTR regression procedureis used. This function simply constructs the quadratic constraint,and adds it to the LP problem defined by the linear optimization problemfor the bounds and the linear shape constraints.

Usage

qpSetupBound(  env,  g0,  g1,  criterion.tol,  criterion.min,  rescale = FALSE,  setup = TRUE)

Arguments

Value

A list of matrices and vectors necessary to define an LPproblem for Gurobi or MOSEK.

Configure QCQP problem to find minimum criterion

Description

This function sets up the objective function for minimizing thecriterion. The QCQP model must be passed as an environment variable,under the entry$model. SeeqpSetup.

Usage

qpSetupCriterion(env)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Configure QP environment for diagnostics

Description

This function separates the shape constraints from the QPenvironment. That way, the model can be solved without any shapeconstraints, which is the primary cause of infeasibility. This isdone in order to check which shape constraints are causing themodel to be infeasible. The QP model must be passed as anenvironment variable, under the entry$model. SeelpSetup.

Usage

qpSetupInfeasible(env, rescale)

Arguments

Value

Nothing, as this modifies an environment variable to savememory.

Separating splines from MTR formulas

Description

This function separates out the function callsuSpline() anduSplines() potentially embedded in the MTR formulas from therest of the formula. The terms involving splines are treatedseparately from the terms that do not involve splines when creatingthe gamma moments.

Usage

removeSplines(formula, env = parent.frame())

Arguments

Value

a list containing two objects. One object isformulabut with the spline components removed. The second object is alist. The name of each element is theuSpline()/uSplines() command, and the elementsare a vector of the names of covariates that were interactedwith theuSpline()/uSplines() command.

Examples

## Declare and MTR with a sline component.m0 = ~ x1 + x1 : uSpline(degree = 2,                          knots = c(0.2, 0.4)) +            x2 : uSpline(degree = 2,                          knots = c(0.2, 0.4)) +            x1 : x2 : uSpline(degree = 2,                               knots = c(0.2, 0.4)) +            uSpline(degree = 3,                     knots = c(0.2, 0.4),                     intercept = FALSE)## Now separate the spline component from the non-spline componentremoveSplines(m0)

Function to implement rescaling procedure

Description

This function rescales the matrix of covariates used in the directregression to improve the conditioning number and the stability ofthe estimation procedure.

Usage

rescaleX(sset, dVec, drY, drN)

Arguments

Value

List of rescaled covariates.

Auxiliary function that converts an expression of variable namesinto a vector of strings.

Description

Auxiliary function that converts an expression of variable namesinto a vector of strings.

Usage

restring(vector, substitute = TRUE, command = "c")

Arguments

Value

A vector of variable names (strings).

Examples

a <- 4b <- 5ivmte:::restring(c(a, b), substitute = TRUE)ivmte:::restring(c(a, b), substitute = FALSE)

Generate Halton sequence

Description

This function generates a one dimensional Halton sequence.

Usage

rhalton(n, base = 2)

Arguments

Value

A sequence of randomly drawn numbers.

Running cplexAPI solver

Description

This function solves the LP problem using the cplexAPI package. Theobject generated bylpSetup is not compatible withthecplexAPI functions. This function adapts the object tosolve the LP problem. SeerunGurobi for additionalerror code labels.

Usage

runCplexAPI(model, lpdir, solver.options)

Arguments

Value

a list of the output from CPLEX. This includes theobjective value, the solution vector, and the optimizationstatus (status of1 indicates successful optimization).

Running Gurobi solver

Description

This function solves the LP/QCQP problem using the Gurobi package. Theobject generated bylpSetup is compatible with thegurobi function. SeerunCplexAPI foradditional error code labels.

Usage

runGurobi(model, solver.options)

Arguments

Value

a list of the output from Gurobi. This includes theobjective value, the solution vector, and the optimizationstatus (status of1 indicates successful optimization) .

Running lpSolveAPI

Description

This function solves the LP problem using thelpSolveAPIpackage. The object generated bylpSetup is notcompatible with thelpSolveAPI functions. This functionadapts the object to solve the LP problem. SeerunGurobi andrunCplexAPI foradditional error code labels.

Usage

runLpSolveAPI(model, modelsense, solver.options)

Arguments

Value

a list of the output fromlpSolveAPI. This includesthe objective value, the solution vector, and the optimizationstatus (status of1 indicates successful optimization).

Running Rmosek

Description

This function solves the LP/QCQP problem using theRmosekpackage. The object generated bylpSetup is notcompatible with theRmosek functions. This functionadapts the object to solve the LP problem. SeerunGurobi andrunCplexAPI foradditional error code labels.

Usage

runMosek(model, modelsense, solver.options, debug = FALSE)

Arguments

Value

a list of the output fromRmosek. This includesthe objective value, the solution vector, and the optimizationstatus (status of1 indicates successful optimization).

IV-like weighting function, OLS specification 1

Description

IV-like weighting function for OLS specification 1.

Usage

sOls1d(d, exx)

Arguments

Value

scalar.

IV-like weighting function, OLS specification 2

Description

IV-like weighting function for OLS specification 2.

Usage

sOls2d(x, d, exx)

Arguments

Value

scalar.

IV-like weighting function, OLS specification 3

Description

IV-like weighting function for OLS specification 3.

Usage

sOls3(x, d, j, exx)

Arguments

Value

scalar.

IV-like weighting function, OLS specifications

Description

IV-like weighting function for OLS specifications.

Usage

sOlsSplines(x = NULL, d, j, exx)

Arguments

Value

scalar.

IV-like weighting function, TSLS specification

Description

IV-like weighting function for TSLS specification.

Usage

sTsls(z, j, exz, pi)

Arguments

Value

scalar.

IV-like weighting function, TSLS specification

Description

IV-like weighting function for TSLS specification.

Usage

sTslsSplines(z, d, j, exz, pi)

Arguments

Value

scalar.

IV-like weighting function, Wald specification

Description

IV-like weighting function for OLS specification 2.

Usage

sWald(z, p.to, p.from, e.to, e.from)

Arguments

Value

scalar.

Select points from audit grid to add to the constraint grid

Description

This function selects which points from the audit grid should beincluded into the original grid. Both the constraint grid and auditgrid are represented as constraints in an LP/QCQP problem. Thisfunction selects which points in the audit grid (i.e. which rows inthe audit constraint matrix) should be added to the constraint grid(i.e. should be appended to the constraint matrix).

Usage

selectViolations(  diffVec,  audit.add,  lb0seq,  lb1seq,  lbteseq,  ub0seq,  ub1seq,  ubteseq,  mono0seq,  mono1seq,  monoteseq,  mbmap)

Arguments

Value

The audit grid is represented using a set of constraintmatrices. Each point in the audit grid corresponds to a set ofrows in the constraint matrices. The function simply returnsthe vector of row numbers for the points from the audit gridwhose corresponding constraints should be added to the originalLP/QCQP problem (i.e. the points to add to the original grid).

Integrating splines

Description

This function simply integrates the splines.

Usage

splineInt(ub, lb, knots, degree, intercept = FALSE)

Arguments

Value

vector, each component being the integral of a basis.

Constructing higher order splines

Description

This function recursively constructs the higher order splinesbasis. Note that the function does not take into consideration theorder of the final basis function. The dimensions of the inputsdicate this, and are updated in each iteration of therecursion. The recursion ends once the row number of argumentbmat reaches 1. This function was coded in accordance toCarl de Boor's set of notes on splines, "B(asic)-Spline Basics".

Usage

splineUpdate(x, bmat, knots, i, current.order)

Arguments

Value

vector, the evaluation of the spline at each value invectorx.

Evaluating splines basis functions

Description

This function evaluates the splines basis functions. Unlike thebSpline in thesplines2 package, this functionreturns the value of a single spline basis, rather than a vector ofvalues for all the spline basis functions.

Usage

splinesBasis(x, knots, degree, intercept = TRUE, i, boundary.knots = c(0, 1))

Arguments

Value

scalar.

Convert status code to string

Description

This function returns the status code specific to a solver.

Usage

statusString(status, solver)

Arguments

Value

Status specific to solver, e.g. 'OPTIMAL (2)'.

Auxiliary function: remove extraneous spaces

Description

Auxiliary function to remove extraneous spaces from strings.

Usage

subsetclean(string)

Arguments

Value

a string

Summarize results

Description

This function uses the summary method on the ivmte return list.

Usage

## S3 method for class 'ivmte'summary(object, ...)

Arguments

Value

summarized results.

Generate symmetric matrix

Description

Function takes in a vector of values, and constructs a symmetricmatrix from it. Diagonals must be included. The length of thevector must also be consistent with the number of "unique" entriesin the symmetric matrix. Note that entries are filled in along thecolumns (i.e. equivalent to byrow = FALSE).

Usage

symat(values)

Arguments

Value

matrix.

TSLS weights, with controls

Description

Function generating the S-weights for TSLS estimand, with controls.

Usage

tsls(X, Z, Z0, Z1, components, treat, order = NULL)

Arguments

Value

A list of two vectors: one is the weight for D = 0, theother is the weight for D = 1.

Spline basis function

Description

This function evaluates the splines that the user specifies whendeclaring the MTRs. This is to be used for auditing, namely whenchecking the boundedness and monotonicity conditions.

Usage

uSplineBasis(x, knots, degree = 0, intercept = TRUE)

Arguments

Value

a matrix, the values of the integrated splines. Each rowcorresponds to a value ofx; each column corresponds toa basis defined by the degrees and knots.

Examples

## Since the splines are declared as part of the MTR, you will need## to have parsed out the spline command. Thus, this command will be## called via eval(parse(text = .)). In the examples below, the## commands are parsed from the object \code{splineslist} generated## by \code{\link[MST]{removeSplines}}. The names of the elements in## the list are the spline commands, and the elements themselves are## the terms that interact with the splines.## Declare MTR functionm0 = ~ x1 + x1 : uSpline(degree = 2,                          knots = c(0.2, 0.4)) +    x2 : uSpline(degree = 2,                  knots = c(0.2, 0.4)) +    x1 : x2 : uSpline(degree = 2,                       knots = c(0.2, 0.4)) +    uSpline(degree = 3,             knots = c(0.2, 0.4),             intercept = FALSE)## Extract spline functions from MTR functionsplineslist <- removeSplines(m0)$splineslist## Declare points at which we wish to evaluate the spline functionsx <- seq(0, 1, 0.2)## Evaluate the splineseval(parse(text = gsub("uSpline\\(",                       "ivmte:::uSplineBasis(x = x, ",                        names(splineslist)[1])))eval(parse(text = gsub("uSpline\\(",                       "ivmte:::uSplineBasis(x = x, ",                       names(splineslist)[2])))

Integrated splines

Description

This function integrates out splines that the user specifies whendeclaring the MTRs. This is to be used when generating the gammamoments.

Usage

uSplineInt(x, knots, degree = 0, intercept = TRUE)

Arguments

Value

a matrix, the values of the integrated splines. Each rowcorresponds to a value ofx; each column corresponds toa basis defined by the degrees and knots.

Examples

## Since the splines are declared as part of the MTR, you will need## to have parsed out the spline command. Thus, this command will be## called via eval(parse(text = .)). In the examples below, the## commands are parsed from the object \code{splineslist} generated## by \code{\link[MST]{removeSplines}}. The names of the elements in## the list are the spline commands, and the elements themselves are## the terms that interact with the splines.## Declare MTR functionm0 = ~ x1 + x1 : uSpline(degree = 2,                          knots = c(0.2, 0.4)) +    x2 : uSpline(degree = 2,                  knots = c(0.2, 0.4)) +    x1 : x2 : uSpline(degree = 2,                       knots = c(0.2, 0.4)) +    uSpline(degree = 3,             knots = c(0.2, 0.4),             intercept = FALSE)## Separate the spline components from the MTR functionsplineslist <- removeSplines(m0)$splineslist## Delcare the points at which we wish to evaluate the integralsx <- seq(0, 1, 0.2)## Evaluate the splines integralseval(parse(text = gsub("uSpline\\(",                       "ivmte:::uSplineInt(x = x, ",                       names(splineslist)[1])))eval(parse(text = gsub("uSpline\\(",                       "ivmte:::uSplineInt(x = x, ",                       names(splineslist)[2])))

Auxiliary function that converts a vector of strings into anexpression containing variable names.

Description

Auxiliary function that converts a vector of strings into anexpression containing variable names.

Usage

unstring(vector)

Arguments

Value

An expression for the list of variable names that are notstrings.

Examples

ivmte:::unstring(c("a", "b"))

Auxiliary function: extracting elements from strings

Description

This auxiliary function extracts the (string) element in theposition argument of thevector argument.

Usage

vecextract(vector, position, truncation = 0)

Arguments

Value

A chracter/string.

Target weighting function, for ATT

Description

Target weighting function, for the ATT.

Usage

wAttSplines(z, d, ed)

Arguments

Value

scalar.

Target weight for ATE

Description

Function generates the target weight for the ATE.

Usage

wate1(data)

Arguments

Value

The bounds of integration over unobservableu, aswell as the multiplier in the weight.

Target weight for ATT

Description

Function generates the target weight for the ATT.

Usage

watt1(data, expd1, propensity)

Arguments

Value

The bounds of integration over unobservableu, aswell as the multiplier in the weight.

Target weight for ATU

Description

Function generates the target weight for the ATT.

Usage

watu1(data, expd0, propensity)

Arguments

Value

The bounds of integration over unobservableu, aswell as the multiplier in the weight.

Generating splines weights

Description

This function generates the weights required to construct splinesof higher order. This function was coded in accordance to Carl deBoor's set of notes on splines, "B(asic)-Spline Basics".

Usage

weights(x, knots, i, order)

Arguments

Value

scalar.

Target weight for generalized LATE

Description

Function generates the target weight for the generalized LATE,where the user can specify the interval of propensity scoresdefining the compliers.

Usage

wgenlate1(data, ulb, uub)

Arguments

Value

The bounds of integration over unobservableu, aswell as the multiplier in the weight.

Auxiliary function:which for lists

Description

Auxiliary function that makes it possible to usewhich witha list.

Usage

whichforlist(vector, obj)

Arguments

Value

a vector of positions where the elements invectorare equal toobj.

Target weight for LATE

Description

Function generates the target weight for the LATE, conditioned on aspecific value of the covariates.

Usage

wlate1(data, from, to, Z, model, X, eval.X)

Arguments

Value

The bounds of integration over unobservableu, aswell as the multiplier in the weight.