R/makeRandomDataT.R
In benkeser/haltmle.sim: Simulation study for HAL-TMLE
#' makeRandomData
#'
#' Simulate a random data generating distribution. See Details to see how it's done.
#'
#'
#' Draw random data generating distribution. The code simulates as follows: \cr
#' Simulate W \itemize{
#' \item Choose \code{D}, a random number of covariates from Uniform(1,maxD)
#' \item Randomly choose \code{d1}, the distribution for first covariate, from \code{distW.uncor}
#' \item Call \code{paste0(d1,".Parm")} (which is assumed to exist in the global environment) to get parameters for \code{d1}
#' \item Call \code{d1} with parameters chosen in previous step to generate first covariate
#' \item Randomly choose \code{d2}, the distribution for second covariate, from \code{c(distW.uncor, distW.cor)} (now including correlated distributions).
#' \item Call \code{paste0(d2,".Parm")} to get parameters for \code{d2}
#' \item Call \code{d2} with parameters chosen in previous step and first covariate (to possibly induce correlation with previous covariate) to generate second covariate.
#' \item Continue until \code{maxD} is reached.
#' }
#'
#' Simulating A \itemize{
#' \item Draw \code{MG1}, a random number of main terms for propensity score, from Uniform(1,maxD)
#' \item For \code{i} = 1,...,\code{MG1}, draw \code{f} a random function from \code{funcG0.uni}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Call \code{f} with \code{x = W[,i]} to generate \code{i}-th main term.
#' \item If \code{D > 1}, draw \code{MG2}, a random number of bivariate interactions for propensity, from Uniform(1,\code{MG1-1})
#' \item For \code{i} = 1,...,\code{MG2}, draw \code{f} a random function from \code{funcG0.biv}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j} and \code{k}, two random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k]} to generate \code{i}-th bivariate interaction term.
#' \item If \code{D > 2}, draw \code{MG3}, a random number of trivariate interactions for propensity, from Uniform(1,\code{MG2-1})
#' \item For \code{i} = 1,...,\code{MG3}, draw \code{f} a random function from \code{funcG0.tri}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j},\code{k},\code{l}, three random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k], x3 = W[,l]} to generate \code{i}-th trivariate interaction term.
#' \item Sum together all main, bivariate, and trivariate terms to get the logit propensity score.
#' \item Divide the logit propensity score by 1.01 until the minimum propensity score is bigger than \code{minG0}.
#' \item Draw A from Bernoulli distribution with conditional probability equal to the adjusted propensity score.
#' }
#'
#' Simulating Y \itemize{
#' \item Draw \code{MQ1}, a random number of main terms for outcome regression score, from Uniform(2,maxD)
#' \item For \code{i} = 1,...,\code{MQ1}, draw \code{f} a random function from \code{funcQ0.uni}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Call \code{f} with \code{x = AW[,i]} to generate \code{i}-th main term, where AW is matrix with first column A, other columns W.
#' \item If \code{D > 1}, draw \code{MQ2}, a random number of bivariate interactions for outcome regression, from Uniform(1,\code{MQ1-1})
#' \item For \code{i} = 1,...,\code{MQ2}, draw \code{f} a random function from \code{funcQ0.biv}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j} and \code{k}, two random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k]} to generate \code{i}-th bivariate interaction term.
#' \item If \code{D > 2}, draw \code{MQ3}, a random number of trivariate interactions for propensity, from Uniform(1,\code{MQ2-1})
#' \item For \code{i} = 1,...,\code{MQ3}, draw \code{f} a random function from \code{funcQ0.tri}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j},\code{k},\code{l}, three random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k], x3 = W[,l]} to generate \code{i}-th trivariate interaction term.
#' \item Sum together all main, bivariate, and trivariate terms to get the conditional mean outcome, \code{Q0}.
#' \item Draw \code{errf}, arandom function from \code{errY} from which to draw errors
#' \item Call \code{paste0(errf,"Parm"} (assumed to exist) to generate random parameters for error distribution.
#' \item Call \code{errf} with randomly chosen parameters to draw \code{e}, an error for the outcome.
#' \item Let \code{Y = Q0 + e}.
#' }
#'
#' @param n A \code{numeric} sample size
#' @param maxD A \code{numeric} indicating maximum number of covariates
#' @param distW.uncor A \code{vector} of \code{characters} that are functions in the global environment that
#' generate covariates. These functions should have an associated parameter function with \code{"Parm"} added
#' to the end of their name. See the format of the functions provided to understand their structure.
#' @param distW.cor Same as above, but generates a correlated covariate
#' @param funcG0.uni A \code{vector} of \code{characters} that are functions in the global environment that
#' are used to generate main terms for logit of the propensity score.
#' @param funcG0.biv Ditto above, but for bivariate functions.
#' @param funcG0.tri Ditto above, but for trivariate functions.
#' @param funcQ0.uni Ditto \code{funcG0.uni}, but for the outcome regression
#' @param funcQ0.biv Ditto
#' @param funcQ0.tri Ditto
#' @param errY A \code{vector} of \code{characters} that are functions in the global environment that
#' are used to generate error terms for the outcome regression.
#' @param minG0 The minimum value for the propensity score (default 0.01).
#' @param pos (1-2*pos)100\% of pscores fall withing minG0 and 1- minG0, default is .005
#' @param skewage default is c(-1,1). random add a skewing constant to the logit(pscores)
#' @return An object of class \code{"makeRandomData"} with the following entries
#' \item{W}{A matrix of covariates}
#' \item{A}{A vector of binary treatments}
#' \item{Y}{A vector of continuously valued outcome}
#' \item{distW}{A list containing relevant information needed to reproduce data sets}
#' \item{fnG0}{A list of lists containing relevant information needed to reproduce data sets}
#' \item{fnQ0}{A list of lists containing relevant information needed to reproduce data sets}
#' \item{distErrY}{A list containing relevant information needed to reproduce data sets}
#' \item{divideLogitG0}{A numeric of the scaling factor for the propensity}
#' @export
makeRandomDataT <- function(n,
maxD = 2,
D = NULL,
minObsA = 30,
func.distW = c("uniformW","normalW","bernoulliW","binomialW","gammaW",
"normalWCor","bernoulliWCor","uniformWCor", "gammaPointMassW",
"binomialFracW","normalPointMassW"),
funcG0.uni = c("linUni","polyUni","sinUni","jumpUni","pLogisUni",
"dNormUni","qGammaUni","dNormMixUni","cubicSplineUni",
"linSplineUni"),
funcG0.biv = c("linBiv","polyBiv","sinBiv","jumpBiv",
"dNormAddBiv","dNormMultBiv","polyJumpBiv",
"sinJumpBiv","dNormMultJumpBiv","linSplineBiv"),
funcG0.tri = c("linTri", "polyTri", "sinTri", "jumpTri",
"linJump2Tri","linJump1Tri","polyJump2Tri",
"polyJump1Tri","sinJump2Tri","sinJump1Tri",
"dNormAddTri","dNormMultTri","dNormMultJump2Tri",
"dNormMultJump1Tri","pLogisAddTri"),
funcG0.quad = c("linQuad", "polyQuad", "sinQuad", "jumpQuad",
"linJump2Quad","linJump1Quad","polyJump2Quad",
"polyJump1Quad","sinJump2Quad","sinJump1Quad",
"dNormAddQuad","dNormMultQuad","dNormMultJump2Quad",
"dNormMultJump1Quad","pLogisAddQuad"),
funcQ0.uni = c("linUni","polyUni","sinUni","jumpUni","pLogisUni",
"dNormUni","qGammaUni","dNormMixUni","cubicSplineUni",
"linSplineUni"),
funcQ0.biv = c("linBiv","polyBiv","sinBiv","jumpBiv",
"dNormAddBiv","dNormMultBiv","polyJumpBiv",
"sinJumpBiv","dNormMultJumpBiv","linSplineBiv"),
funcQ0.tri = c("linTri", "polyTri", "sinTri", "jumpTri",
"linJump2Tri","linJump1Tri","polyJump2Tri",
"polyJump1Tri","sinJump2Tri","sinJump1Tri",
"dNormAddTri","dNormMultTri","dNormMultJump2Tri",
"dNormMultJump1Tri","pLogisAddTri"),
funcQ0.quad = c("linQuad", "polyQuad", "sinQuad", "jumpQuad",
"linJump2Quad","linJump1Quad","polyJump2Quad",
"polyJump1Quad","sinJump2Quad","sinJump1Quad",
"dNormAddQuad","dNormMultQuad","dNormMultJump2Quad",
"dNormMultJump1Quad","pLogisAddQuad"),
errY = c("normalErr","uniformErr","gammaErr","normalErrAW","uniformErrAW"),
minG0 = 1e-3,
minR2 = 0.01, maxR2 = 0.99, pos = .005, skewing = c(-1,1),
...) {
# draw random number of covariates
if(!is.null(maxD)){
D <- sample(1:maxD, 1)
}
#----------------------------------------------------------------------
# Simulate W
#----------------------------------------------------------------------
# initialize empties
N = 1e5
W <- matrix(nrow = N, ncol = D)
distW <- vector(mode = "list", length = D)
for(d in 1:D){
# randomly sample distribution
if(d==1){
# sample distribution
thisD <- sample(func.distW, 1)
# generate parameters
thisParm <- do.call(paste0(thisD,"Parm"), args = list(W = NULL))
# generate covariate
W[,d] <- do.call(thisD, args = c(list(n=N, W = NULL), thisParm))
}else{
# sample distribution
thisD <- sample(func.distW, 1)
# generate parameters
thisParm <- do.call(paste0(thisD,"Parm"), args = list(W = data.frame(W[,1:(d-1),drop=FALSE])))
# generate covariate
W[,d] <- do.call(thisD, args = c(list(n=N, W = data.frame(W[,1:(d-1),drop=FALSE])), thisParm))
}
# save distributions
distW[[d]]$fn <- thisD; distW[[d]]$parm <- thisParm
}
#----------------------------------------------------------------------
# Simulate propensity
#----------------------------------------------------------------------
# draw random number of main terms
Mg1 <- sample(1:D, 1)
# draw random number of two-way interaction terms
Mg2 <- sample(0:D, 1)
# but Mg2 cannot be greater than the total number of combos
Mg2 <- ifelse(D > 1, min(Mg2, gamma(D+1)/gamma(3)/gamma(D-1)), 0)
# draw random number of three-way interaction terms
Mg3 <- sample(0:D, 1)
Mg3 <- ifelse(D > 2, min(Mg3, gamma(D+1)/gamma(4)/gamma(D-2)), 0)
# draw random number of four-way interaction terms
Mg4 <- sample(0:D, 1)
Mg4 <- ifelse(D > 3, min(Mg4, gamma(D+1)/gamma(5)/gamma(D-3)), 0)
# univariate
if(Mg1 > 0){
uniG0 = lapply(1:Mg1, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.uni, 1)
# draw random column of W
wCol <- sample(1:ncol(W), 1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x = W[,wCol]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = wCol))
})
M1 = vapply(1:Mg1, FUN = function(m) {
thisF = uniG0[[m]]$fn
wCols = uniG0[[m]]$whichColsW
thisParm = uniG0[[m]]$parm
do.call(thisF, args = c(list(x = W[,wCols[1]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
uniG0 <- NULL
M1 = NULL
}
# two-way interactions
if(Mg2 > 0 & D > 1){
# all two-way column combinations
comb <- as.matrix(combn(D,2))
# randomly sample Mg2 two-way interactions without replacement
combCols <- sample(1:ncol(comb),Mg2,replace = TRUE)
bivG0 = lapply(1:Mg2, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.biv, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]], x2 = W[,theseCols[2]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M2 = vapply(1:Mg2, FUN = function(m) {
thisF = bivG0[[m]]$fn
theseCols = bivG0[[m]]$whichColsW
thisParm = bivG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]], x2 = W[,theseCols[2]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
bivG0 <- NULL
M2 = NULL
}
#trivariate
if(Mg3 > 0 & D > 2){
# all three way choices of columns
comb <- as.matrix(combn(D, 3))
# randomly sample Mg3 three-way interactions without replacement
combCols <- sample(1:ncol(comb),Mg3,replace = TRUE)
triG0 = lapply(1:Mg3, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.tri, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M3 = vapply(1:Mg3, FUN = function(m) {
thisF = triG0[[m]]$fn
theseCols = triG0[[m]]$whichColsW
thisParm = triG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
triG0 <- NULL
M3 = NULL
}
# quadravariate
if(Mg4 > 0 & D > 3){
# empty list
quadG0 <- vector(mode="list",length=Mg4)
# all four way choices of columns
comb <- as.matrix(combn(D, 4))
# randomly sample Mg3 four-way interactions without replacement
combCols <- sample(1:ncol(comb), Mg4, replace = TRUE)
quadG0 = lapply(1:Mg4, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.quad, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]],
x4 = W[,theseCols[4]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M4 = vapply(1:Mg4, FUN = function(m) {
thisF = quadG0[[m]]$fn
theseCols = quadG0[[m]]$whichColsW
thisParm = quadG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]],
x4 = W[,theseCols[4]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
quadG0 <- NULL
M4 = NULL
}
M = list(M1, M2, M3, M4)
notnull = !unlist(lapply(M, is.null))
M = do.call(cbind, M[notnull])
# center the distribution--skewing to be controlled next
M_c = apply(M, MARGIN = 2, FUN = function(col) col - mean(col))
# skew randomly according to skewing argument
logitg0 = rowSums(as.matrix(M_c))
skewage = runif(1, skewing[1],skewing[2])
# (1 - 2pos)*100% of all data is within positivity range so not truncating everything
tol = TRUE
its = 0
while (tol & its < 20) {
tol = mean(plogis(.8^its*logitg0 + .8^its*skewage) < minG0) > pos |
mean(plogis(.8^its*logitg0 + .8^its*skewage) > (1 - minG0)) >
pos
its = its + 1
}
logitg0 = .8^its*logitg0 + .8^its*skewage
# truncate for positivity violations
logitg0[plogis(logitg0) < minG0] <- qlogis(minG0)
logitg0[plogis(logitg0) > 1 - minG0] <- qlogis(1 - minG0)
# chosen rows at random from W:
Wrows = sample(1:N,n)
W = as.matrix(W[Wrows,])
# choose corresponding logitg0
logitg0 = logitg0[Wrows]
# simulate A
A <- rbinom(n, 1, plogis(logitg0))
# matrix with A and W
AW <- cbind(A, W)
#----------------------------------------------------------------------
# Simulate Y
#----------------------------------------------------------------------
# draw random number of main terms between 0 and D + 1, where we set
# no minimum, which allows there to be cases of just pure noise
MQ1 <- sample(0:(D+1), 1)
# draw random number of two-way interaction terms
MQ2 <- sample(0:(D+1), 1)
# but Mg2 cannot be greater than the total number of combos
MQ2 <- ifelse(D > 0, min(MQ2, gamma(D+2)/gamma(3)/gamma(D)), 0)
# draw random number of three-way interaction terms
MQ3 <- sample(0:(D+1), 1)
MQ3 <- ifelse(D > 1, min(MQ3, gamma(D+2)/gamma(4)/gamma(D-1)), 0)
# draw random number of four-way interaction terms
MQ4 <- sample(0:(D+1), 1)
MQ4 <- ifelse(D > 2, min(MQ4, gamma(D+2)/gamma(5)/gamma(D-2)), 0)
# MQ1 <- round(runif(1, -0.5, D + 1.5))
#
# # draw random number of interaction terms
# MQ2 <- round(runif(1, -0.5, D + 1.5))
# MQ3 <- round(runif(1, -0.5, D + 1.5))
# MQ4 <- round(runif(1, -0.5, D + 1.5))
# empty
Q0 <- rep(0, n)
# main terms
# empty
if(MQ1 > 0){
uniQ0 <- vector(mode="list", length = MQ1)
for(m in 1:MQ1){
# randomly draw function
thisF <- sample(funcQ0.uni, 1)
# randomly draw column of AW
awCol <- sample(1:ncol(AW), 1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x = AW[,awCol]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x = AW[,awCol]), thisParm))
# save results
uniQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = awCol)
# add
Q0 <- Q0 + fOut
}
}else{
uniQ0 <- NULL
}
# two-way interactions
if(MQ2 > 0){
bivQ0 <- vector(mode="list",length=MQ2)
# all combinations of columns
comb <- as.matrix(combn(D+1,2))
# randomly sample columns
combCols <- sample(1:ncol(comb),MQ2, replace = TRUE)
for(m in 1:MQ2){
# what columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.biv,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]]),thisParm))
# save output
bivQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
bivQ0 <- NULL
}
# three-way interactions
if(MQ3 > 0 & D > 1){
# empty
triQ0 <- vector(mode="list",length=MQ3)
# all three-way column combinations
comb <- as.matrix(combn(D+1,3))
# randomly sample three choices of combinations without replacement
combCols <- sample(1:ncol(comb),MQ3, replace = TRUE)
for(m in 1:MQ3){
# columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.tri,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]], x3=AW[,theseCols[3]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]], x3=AW[,theseCols[3]]),thisParm))
# save output
triQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
triQ0 <- NULL
}
# four-way interactions
if(MQ4 > 0 & D > 2){
# empty
quadQ0 <- vector(mode="list",length=MQ4)
# all four-way column combinations
comb <- as.matrix(combn(D+1, 4))
# randomly sample four choices of combinations without replacement
combCols <- sample(1:ncol(comb), MQ4, replace = TRUE)
for(m in 1:MQ4){
# columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.quad,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"),
args = list(x1 = AW[,theseCols[1]],
x2 = AW[,theseCols[2]],
x3=AW[,theseCols[3]],
x4=AW[,theseCols[4]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]],
x2 = AW[,theseCols[2]],
x3=AW[,theseCols[3]],
x4=AW[,theseCols[4]]),thisParm))
# save output
quadQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
quadQ0 <- NULL
}
# Drawing an error function
# empty results
errYList <- vector(mode = "list")
# randomly draw error function
errFn <- sample(errY, 1)
# get parameters of error function
errParm <- do.call(paste0(errFn, "Parm"), args = list(AW = AW))
# evaluate error function
errOut <- do.call(errFn, args = c(list(AW=AW, n=n), errParm))
# save output
errYList$fn <- errFn; errYList$parm <- errParm
# make sure R2 is falling in proper range
ct <- 0
currR2 <- Inf
while(currR2 < minR2 | currR2 > maxR2){
ct <- ct + 1
if(currR2 > maxR2){
mult <- 1.1^ct
}else if(currR2 < minR2){
mult <- 1/1.1^ct
}
# compute Y
Y <- Q0 + errOut
out <- list(W = W, A = data.frame(A=A), Y = data.frame(Y=Y), distW = distW,
minG0 = minG0, minR2 = minR2, maxR2 = maxR2,
fnG0 = list(uni = uniG0, biv = bivG0, tri = triG0, quad = quadG0),
fnQ0 = list(uni = uniQ0, biv = bivQ0, tri = triQ0, quad = quadQ0), distErrY = errYList,
Q0 = Q0, g0 = plogis(logitg0), errMult = mult, funcG0.uni = funcG0.uni,
funcG0.biv = funcG0.biv, funcG0.tri = funcG0.tri, funcG0.quad = funcG0.quad,
funcQ0.uni = funcQ0.uni, funcQ0.biv = funcQ0.biv, funcQ0.tri = funcQ0.tri,
funcQ0.quad = funcQ0.quad, its = its, skewage = skewage)
class(out) <- "makeRandomData"
# get summary
bigObs <- remakeRandomData(n = 1e5, object = out)
currR2 <- 1 - mean((bigObs$Y - bigObs$Q0)^2)/var(bigObs$Y)
# cat("Current R2 = ", currR2)
}
return(out)
}
benkeser/haltmle.sim documentation built on May 12, 2019, noon
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#' makeRandomData
#'
#' Simulate a random data generating distribution. See Details to see how it's done.
#'
#'
#' Draw random data generating distribution. The code simulates as follows: \cr
#' Simulate W \itemize{
#' \item Choose \code{D}, a random number of covariates from Uniform(1,maxD)
#' \item Randomly choose \code{d1}, the distribution for first covariate, from \code{distW.uncor}
#' \item Call \code{paste0(d1,".Parm")} (which is assumed to exist in the global environment) to get parameters for \code{d1}
#' \item Call \code{d1} with parameters chosen in previous step to generate first covariate
#' \item Randomly choose \code{d2}, the distribution for second covariate, from \code{c(distW.uncor, distW.cor)} (now including correlated distributions).
#' \item Call \code{paste0(d2,".Parm")} to get parameters for \code{d2}
#' \item Call \code{d2} with parameters chosen in previous step and first covariate (to possibly induce correlation with previous covariate) to generate second covariate.
#' \item Continue until \code{maxD} is reached.
#' }
#'
#' Simulating A \itemize{
#' \item Draw \code{MG1}, a random number of main terms for propensity score, from Uniform(1,maxD)
#' \item For \code{i} = 1,...,\code{MG1}, draw \code{f} a random function from \code{funcG0.uni}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Call \code{f} with \code{x = W[,i]} to generate \code{i}-th main term.
#' \item If \code{D > 1}, draw \code{MG2}, a random number of bivariate interactions for propensity, from Uniform(1,\code{MG1-1})
#' \item For \code{i} = 1,...,\code{MG2}, draw \code{f} a random function from \code{funcG0.biv}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j} and \code{k}, two random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k]} to generate \code{i}-th bivariate interaction term.
#' \item If \code{D > 2}, draw \code{MG3}, a random number of trivariate interactions for propensity, from Uniform(1,\code{MG2-1})
#' \item For \code{i} = 1,...,\code{MG3}, draw \code{f} a random function from \code{funcG0.tri}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j},\code{k},\code{l}, three random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k], x3 = W[,l]} to generate \code{i}-th trivariate interaction term.
#' \item Sum together all main, bivariate, and trivariate terms to get the logit propensity score.
#' \item Divide the logit propensity score by 1.01 until the minimum propensity score is bigger than \code{minG0}.
#' \item Draw A from Bernoulli distribution with conditional probability equal to the adjusted propensity score.
#' }
#'
#' Simulating Y \itemize{
#' \item Draw \code{MQ1}, a random number of main terms for outcome regression score, from Uniform(2,maxD)
#' \item For \code{i} = 1,...,\code{MQ1}, draw \code{f} a random function from \code{funcQ0.uni}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Call \code{f} with \code{x = AW[,i]} to generate \code{i}-th main term, where AW is matrix with first column A, other columns W.
#' \item If \code{D > 1}, draw \code{MQ2}, a random number of bivariate interactions for outcome regression, from Uniform(1,\code{MQ1-1})
#' \item For \code{i} = 1,...,\code{MQ2}, draw \code{f} a random function from \code{funcQ0.biv}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j} and \code{k}, two random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k]} to generate \code{i}-th bivariate interaction term.
#' \item If \code{D > 2}, draw \code{MQ3}, a random number of trivariate interactions for propensity, from Uniform(1,\code{MQ2-1})
#' \item For \code{i} = 1,...,\code{MQ3}, draw \code{f} a random function from \code{funcQ0.tri}
#' \item Call \code{paste0(f,"Parm")} (assumed to exist) to generate parameters for \code{f}
#' \item Draw \code{j},\code{k},\code{l}, three random columns of \code{W}
#' \item Call \code{f} with \code{x1 = W[,j], x2 = W[,k], x3 = W[,l]} to generate \code{i}-th trivariate interaction term.
#' \item Sum together all main, bivariate, and trivariate terms to get the conditional mean outcome, \code{Q0}.
#' \item Draw \code{errf}, arandom function from \code{errY} from which to draw errors
#' \item Call \code{paste0(errf,"Parm"} (assumed to exist) to generate random parameters for error distribution.
#' \item Call \code{errf} with randomly chosen parameters to draw \code{e}, an error for the outcome.
#' \item Let \code{Y = Q0 + e}.
#' }
#'
#' @param n A \code{numeric} sample size
#' @param maxD A \code{numeric} indicating maximum number of covariates
#' @param distW.uncor A \code{vector} of \code{characters} that are functions in the global environment that
#' generate covariates. These functions should have an associated parameter function with \code{"Parm"} added
#' to the end of their name. See the format of the functions provided to understand their structure.
#' @param distW.cor Same as above, but generates a correlated covariate
#' @param funcG0.uni A \code{vector} of \code{characters} that are functions in the global environment that
#' are used to generate main terms for logit of the propensity score.
#' @param funcG0.biv Ditto above, but for bivariate functions.
#' @param funcG0.tri Ditto above, but for trivariate functions.
#' @param funcQ0.uni Ditto \code{funcG0.uni}, but for the outcome regression
#' @param funcQ0.biv Ditto
#' @param funcQ0.tri Ditto
#' @param errY A \code{vector} of \code{characters} that are functions in the global environment that
#' are used to generate error terms for the outcome regression.
#' @param minG0 The minimum value for the propensity score (default 0.01).
#' @param pos (1-2*pos)100\% of pscores fall withing minG0 and 1- minG0, default is .005
#' @param skewage default is c(-1,1). random add a skewing constant to the logit(pscores)
#' @return An object of class \code{"makeRandomData"} with the following entries
#' \item{W}{A matrix of covariates}
#' \item{A}{A vector of binary treatments}
#' \item{Y}{A vector of continuously valued outcome}
#' \item{distW}{A list containing relevant information needed to reproduce data sets}
#' \item{fnG0}{A list of lists containing relevant information needed to reproduce data sets}
#' \item{fnQ0}{A list of lists containing relevant information needed to reproduce data sets}
#' \item{distErrY}{A list containing relevant information needed to reproduce data sets}
#' \item{divideLogitG0}{A numeric of the scaling factor for the propensity}
#' @export
makeRandomDataT <- function(n,
maxD = 2,
D = NULL,
minObsA = 30,
func.distW = c("uniformW","normalW","bernoulliW","binomialW","gammaW",
"normalWCor","bernoulliWCor","uniformWCor", "gammaPointMassW",
"binomialFracW","normalPointMassW"),
funcG0.uni = c("linUni","polyUni","sinUni","jumpUni","pLogisUni",
"dNormUni","qGammaUni","dNormMixUni","cubicSplineUni",
"linSplineUni"),
funcG0.biv = c("linBiv","polyBiv","sinBiv","jumpBiv",
"dNormAddBiv","dNormMultBiv","polyJumpBiv",
"sinJumpBiv","dNormMultJumpBiv","linSplineBiv"),
funcG0.tri = c("linTri", "polyTri", "sinTri", "jumpTri",
"linJump2Tri","linJump1Tri","polyJump2Tri",
"polyJump1Tri","sinJump2Tri","sinJump1Tri",
"dNormAddTri","dNormMultTri","dNormMultJump2Tri",
"dNormMultJump1Tri","pLogisAddTri"),
funcG0.quad = c("linQuad", "polyQuad", "sinQuad", "jumpQuad",
"linJump2Quad","linJump1Quad","polyJump2Quad",
"polyJump1Quad","sinJump2Quad","sinJump1Quad",
"dNormAddQuad","dNormMultQuad","dNormMultJump2Quad",
"dNormMultJump1Quad","pLogisAddQuad"),
funcQ0.uni = c("linUni","polyUni","sinUni","jumpUni","pLogisUni",
"dNormUni","qGammaUni","dNormMixUni","cubicSplineUni",
"linSplineUni"),
funcQ0.biv = c("linBiv","polyBiv","sinBiv","jumpBiv",
"dNormAddBiv","dNormMultBiv","polyJumpBiv",
"sinJumpBiv","dNormMultJumpBiv","linSplineBiv"),
funcQ0.tri = c("linTri", "polyTri", "sinTri", "jumpTri",
"linJump2Tri","linJump1Tri","polyJump2Tri",
"polyJump1Tri","sinJump2Tri","sinJump1Tri",
"dNormAddTri","dNormMultTri","dNormMultJump2Tri",
"dNormMultJump1Tri","pLogisAddTri"),
funcQ0.quad = c("linQuad", "polyQuad", "sinQuad", "jumpQuad",
"linJump2Quad","linJump1Quad","polyJump2Quad",
"polyJump1Quad","sinJump2Quad","sinJump1Quad",
"dNormAddQuad","dNormMultQuad","dNormMultJump2Quad",
"dNormMultJump1Quad","pLogisAddQuad"),
errY = c("normalErr","uniformErr","gammaErr","normalErrAW","uniformErrAW"),
minG0 = 1e-3,
minR2 = 0.01, maxR2 = 0.99, pos = .005, skewing = c(-1,1),
...) {
# draw random number of covariates
if(!is.null(maxD)){
D <- sample(1:maxD, 1)
}
#----------------------------------------------------------------------
# Simulate W
#----------------------------------------------------------------------
# initialize empties
N = 1e5
W <- matrix(nrow = N, ncol = D)
distW <- vector(mode = "list", length = D)
for(d in 1:D){
# randomly sample distribution
if(d==1){
# sample distribution
thisD <- sample(func.distW, 1)
# generate parameters
thisParm <- do.call(paste0(thisD,"Parm"), args = list(W = NULL))
# generate covariate
W[,d] <- do.call(thisD, args = c(list(n=N, W = NULL), thisParm))
}else{
# sample distribution
thisD <- sample(func.distW, 1)
# generate parameters
thisParm <- do.call(paste0(thisD,"Parm"), args = list(W = data.frame(W[,1:(d-1),drop=FALSE])))
# generate covariate
W[,d] <- do.call(thisD, args = c(list(n=N, W = data.frame(W[,1:(d-1),drop=FALSE])), thisParm))
}
# save distributions
distW[[d]]$fn <- thisD; distW[[d]]$parm <- thisParm
}
#----------------------------------------------------------------------
# Simulate propensity
#----------------------------------------------------------------------
# draw random number of main terms
Mg1 <- sample(1:D, 1)
# draw random number of two-way interaction terms
Mg2 <- sample(0:D, 1)
# but Mg2 cannot be greater than the total number of combos
Mg2 <- ifelse(D > 1, min(Mg2, gamma(D+1)/gamma(3)/gamma(D-1)), 0)
# draw random number of three-way interaction terms
Mg3 <- sample(0:D, 1)
Mg3 <- ifelse(D > 2, min(Mg3, gamma(D+1)/gamma(4)/gamma(D-2)), 0)
# draw random number of four-way interaction terms
Mg4 <- sample(0:D, 1)
Mg4 <- ifelse(D > 3, min(Mg4, gamma(D+1)/gamma(5)/gamma(D-3)), 0)
# univariate
if(Mg1 > 0){
uniG0 = lapply(1:Mg1, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.uni, 1)
# draw random column of W
wCol <- sample(1:ncol(W), 1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x = W[,wCol]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = wCol))
})
M1 = vapply(1:Mg1, FUN = function(m) {
thisF = uniG0[[m]]$fn
wCols = uniG0[[m]]$whichColsW
thisParm = uniG0[[m]]$parm
do.call(thisF, args = c(list(x = W[,wCols[1]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
uniG0 <- NULL
M1 = NULL
}
# two-way interactions
if(Mg2 > 0 & D > 1){
# all two-way column combinations
comb <- as.matrix(combn(D,2))
# randomly sample Mg2 two-way interactions without replacement
combCols <- sample(1:ncol(comb),Mg2,replace = TRUE)
bivG0 = lapply(1:Mg2, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.biv, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]], x2 = W[,theseCols[2]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M2 = vapply(1:Mg2, FUN = function(m) {
thisF = bivG0[[m]]$fn
theseCols = bivG0[[m]]$whichColsW
thisParm = bivG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]], x2 = W[,theseCols[2]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
bivG0 <- NULL
M2 = NULL
}
#trivariate
if(Mg3 > 0 & D > 2){
# all three way choices of columns
comb <- as.matrix(combn(D, 3))
# randomly sample Mg3 three-way interactions without replacement
combCols <- sample(1:ncol(comb),Mg3,replace = TRUE)
triG0 = lapply(1:Mg3, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.tri, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M3 = vapply(1:Mg3, FUN = function(m) {
thisF = triG0[[m]]$fn
theseCols = triG0[[m]]$whichColsW
thisParm = triG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
triG0 <- NULL
M3 = NULL
}
# quadravariate
if(Mg4 > 0 & D > 3){
# empty list
quadG0 <- vector(mode="list",length=Mg4)
# all four way choices of columns
comb <- as.matrix(combn(D, 4))
# randomly sample Mg3 four-way interactions without replacement
combCols <- sample(1:ncol(comb), Mg4, replace = TRUE)
quadG0 = lapply(1:Mg4, FUN = function(m) {
# draw random function
thisF <- sample(funcG0.quad, 1)
# draw random column of W
theseCols <- comb[,combCols[m]]
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]],
x4 = W[,theseCols[4]]))
# call function with parameters
# save output in list
return(list(fn = thisF, parm = thisParm, whichColsW = theseCols))
})
M4 = vapply(1:Mg4, FUN = function(m) {
thisF = quadG0[[m]]$fn
theseCols = quadG0[[m]]$whichColsW
thisParm = quadG0[[m]]$parm
do.call(thisF, args = c(list(x1 = W[,theseCols[1]],
x2 = W[,theseCols[2]],
x3 = W[,theseCols[3]],
x4 = W[,theseCols[4]]),thisParm))
}, FUN.VALUE = rep(1,N))
} else {
quadG0 <- NULL
M4 = NULL
}
M = list(M1, M2, M3, M4)
notnull = !unlist(lapply(M, is.null))
M = do.call(cbind, M[notnull])
# center the distribution--skewing to be controlled next
M_c = apply(M, MARGIN = 2, FUN = function(col) col - mean(col))
# skew randomly according to skewing argument
logitg0 = rowSums(as.matrix(M_c))
skewage = runif(1, skewing[1],skewing[2])
# (1 - 2pos)*100% of all data is within positivity range so not truncating everything
tol = TRUE
its = 0
while (tol & its < 20) {
tol = mean(plogis(.8^its*logitg0 + .8^its*skewage) < minG0) > pos |
mean(plogis(.8^its*logitg0 + .8^its*skewage) > (1 - minG0)) >
pos
its = its + 1
}
logitg0 = .8^its*logitg0 + .8^its*skewage
# truncate for positivity violations
logitg0[plogis(logitg0) < minG0] <- qlogis(minG0)
logitg0[plogis(logitg0) > 1 - minG0] <- qlogis(1 - minG0)
# chosen rows at random from W:
Wrows = sample(1:N,n)
W = as.matrix(W[Wrows,])
# choose corresponding logitg0
logitg0 = logitg0[Wrows]
# simulate A
A <- rbinom(n, 1, plogis(logitg0))
# matrix with A and W
AW <- cbind(A, W)
#----------------------------------------------------------------------
# Simulate Y
#----------------------------------------------------------------------
# draw random number of main terms between 0 and D + 1, where we set
# no minimum, which allows there to be cases of just pure noise
MQ1 <- sample(0:(D+1), 1)
# draw random number of two-way interaction terms
MQ2 <- sample(0:(D+1), 1)
# but Mg2 cannot be greater than the total number of combos
MQ2 <- ifelse(D > 0, min(MQ2, gamma(D+2)/gamma(3)/gamma(D)), 0)
# draw random number of three-way interaction terms
MQ3 <- sample(0:(D+1), 1)
MQ3 <- ifelse(D > 1, min(MQ3, gamma(D+2)/gamma(4)/gamma(D-1)), 0)
# draw random number of four-way interaction terms
MQ4 <- sample(0:(D+1), 1)
MQ4 <- ifelse(D > 2, min(MQ4, gamma(D+2)/gamma(5)/gamma(D-2)), 0)
# MQ1 <- round(runif(1, -0.5, D + 1.5))
#
# # draw random number of interaction terms
# MQ2 <- round(runif(1, -0.5, D + 1.5))
# MQ3 <- round(runif(1, -0.5, D + 1.5))
# MQ4 <- round(runif(1, -0.5, D + 1.5))
# empty
Q0 <- rep(0, n)
# main terms
# empty
if(MQ1 > 0){
uniQ0 <- vector(mode="list", length = MQ1)
for(m in 1:MQ1){
# randomly draw function
thisF <- sample(funcQ0.uni, 1)
# randomly draw column of AW
awCol <- sample(1:ncol(AW), 1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x = AW[,awCol]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x = AW[,awCol]), thisParm))
# save results
uniQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = awCol)
# add
Q0 <- Q0 + fOut
}
}else{
uniQ0 <- NULL
}
# two-way interactions
if(MQ2 > 0){
bivQ0 <- vector(mode="list",length=MQ2)
# all combinations of columns
comb <- as.matrix(combn(D+1,2))
# randomly sample columns
combCols <- sample(1:ncol(comb),MQ2, replace = TRUE)
for(m in 1:MQ2){
# what columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.biv,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]]),thisParm))
# save output
bivQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
bivQ0 <- NULL
}
# three-way interactions
if(MQ3 > 0 & D > 1){
# empty
triQ0 <- vector(mode="list",length=MQ3)
# all three-way column combinations
comb <- as.matrix(combn(D+1,3))
# randomly sample three choices of combinations without replacement
combCols <- sample(1:ncol(comb),MQ3, replace = TRUE)
for(m in 1:MQ3){
# columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.tri,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"), args = list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]], x3=AW[,theseCols[3]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]], x2 = AW[,theseCols[2]], x3=AW[,theseCols[3]]),thisParm))
# save output
triQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
triQ0 <- NULL
}
# four-way interactions
if(MQ4 > 0 & D > 2){
# empty
quadQ0 <- vector(mode="list",length=MQ4)
# all four-way column combinations
comb <- as.matrix(combn(D+1, 4))
# randomly sample four choices of combinations without replacement
combCols <- sample(1:ncol(comb), MQ4, replace = TRUE)
for(m in 1:MQ4){
# columns to use for this interaction
theseCols <- comb[,combCols[m]]
# randomly sample function
thisF <- sample(funcQ0.quad,1)
# get parameters
thisParm <- do.call(paste0(thisF,"Parm"),
args = list(x1 = AW[,theseCols[1]],
x2 = AW[,theseCols[2]],
x3=AW[,theseCols[3]],
x4=AW[,theseCols[4]]))
# call function with parameters
fOut <- do.call(thisF, args = c(list(x1 = AW[,theseCols[1]],
x2 = AW[,theseCols[2]],
x3=AW[,theseCols[3]],
x4=AW[,theseCols[4]]),thisParm))
# save output
quadQ0[[m]] <- list(fn = thisF, parm = thisParm, whichColsAW = theseCols)
# add
Q0 <- Q0 + fOut
}
}else{
quadQ0 <- NULL
}
# Drawing an error function
# empty results
errYList <- vector(mode = "list")
# randomly draw error function
errFn <- sample(errY, 1)
# get parameters of error function
errParm <- do.call(paste0(errFn, "Parm"), args = list(AW = AW))
# evaluate error function
errOut <- do.call(errFn, args = c(list(AW=AW, n=n), errParm))
# save output
errYList$fn <- errFn; errYList$parm <- errParm
# make sure R2 is falling in proper range
ct <- 0
currR2 <- Inf
while(currR2 < minR2 | currR2 > maxR2){
ct <- ct + 1
if(currR2 > maxR2){
mult <- 1.1^ct
}else if(currR2 < minR2){
mult <- 1/1.1^ct
}
# compute Y
Y <- Q0 + errOut
out <- list(W = W, A = data.frame(A=A), Y = data.frame(Y=Y), distW = distW,
minG0 = minG0, minR2 = minR2, maxR2 = maxR2,
fnG0 = list(uni = uniG0, biv = bivG0, tri = triG0, quad = quadG0),
fnQ0 = list(uni = uniQ0, biv = bivQ0, tri = triQ0, quad = quadQ0), distErrY = errYList,
Q0 = Q0, g0 = plogis(logitg0), errMult = mult, funcG0.uni = funcG0.uni,
funcG0.biv = funcG0.biv, funcG0.tri = funcG0.tri, funcG0.quad = funcG0.quad,
funcQ0.uni = funcQ0.uni, funcQ0.biv = funcQ0.biv, funcQ0.tri = funcQ0.tri,
funcQ0.quad = funcQ0.quad, its = its, skewage = skewage)
class(out) <- "makeRandomData"
# get summary
bigObs <- remakeRandomData(n = 1e5, object = out)
currR2 <- 1 - mean((bigObs$Y - bigObs$Q0)^2)/var(bigObs$Y)
# cat("Current R2 = ", currR2)
}
return(out)
}
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