augX: Generate Pseudo-Responses Based on Conditional Quantile...
In quantoptr: Algorithms for Quantile- And Mean-Optimal Treatment Regimes

Description Usage Arguments Details Value References Examples

This function supports the DR_Qopt function. For every observation, we generate pseudo-observations corresponding to treatment 0 and 1 respectively based on working conditional quantile models.

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augX(raw.data, length.out = 200, txVec, moCondQuant_0, moCondQuant_1,
  nlCondQuant_0 = FALSE, nlCondQuant_1 = FALSE, start_0 = NULL,
  start_1 = NULL, clnodes)

`raw.data`	A data frame, must contain all the variables that appear in `moCondQuant_0` and `moCondQuant_1`.
`length.out`	an integer greater than 1. If one of the conditional quantile model is set to be nonlinear, this argument will be triggered and we will fit `length.out` models across quantiles equally spaced between 0.001 and 0.999. The larger this value, the more refined the performance of this method. Default is 200.
`txVec`	a numeric vector of observed treatment levels coded 0L and 1L.
`moCondQuant_0`	A formula, used to specify the formula for the conditional quantile function when treatment = 0.
`moCondQuant_1`	A formula, used to specify the formula for the conditional quantile function when treatment = 1.
`nlCondQuant_0`	logical. When `nlCondQuant_0 = TRUE`, it is indicated that `moCondQuant_0` is nonlinear. The default value of this variable is `FALSE`.
`nlCondQuant_1`	logical. When `nlCondQuant_1 = TRUE`, it is indicated that `moCondQuant_1` is nonlinear. The default value of this variable is `FALSE`.
`start_0`	either a list object, providing the starting value in estimating the parameters in the nonlinear conditional quantile model, given that treatment=0. Default is `NULL`, corresponding to the case when `nlCondQuant_0=FALSE`.
`start_1`	either a list object, providing the starting value in estimating the parameters in the nonlinear conditional quantile model, given that treatment=0. Default is `NULL`, corresponding to the case when `nlCondQuant_1=FALSE`.
`clnodes`	Either a cluster object to enable parallel computation or `NULL`. If `NULL`, no parallel computation will be used.

This function implements the algorithm to generate individual level pseudo responses for two treatment levels respectively.

For each observation, two independent random variables from unif[0,1] are generated. Denote them by u0 and u1. Approximately, this function then estimates the u0th quantile of this observation were treatment level 0 is applied via the conditional u0th quantile regression. This estimated quantile will be the pseudo-response for treatment 0. Similarly, this function the pseudo-response for treatment 1 will be estimated and returned.

See the reference paper for a more formal explanation.

It returns a list object, consisting of the following elements:

y.a.0, the vector of estimated individual level pseudo outcomes, given the treatment is 0;
y.a.1, the vector of estimated individual level pseudo outcomes, given the treatment is 1;
nlCondQuant_0, logical, indicating whether the y.a.0 is generated based on a nonlinear conditional quantile model.
nlCondQuant_1, logical, indicating whether the y.a.1 is generated based on a nonlinear conditional quantile model.

\insertRef

wang2017quantilequantoptr

ilogit <- function(x) exp(x)/(1 + exp(x))
GenerateData.DR <- function(n)
{
  x1 <- runif(n,min=-1.5,max=1.5)
  x2 <- runif(n,min=-1.5,max=1.5)
  tp <- ilogit( 1 - 1*x1^2 - 1* x2^2)
  a <-rbinom(n,1,tp)
  y <- a * exp(0.11 - x1- x2) + x1^2 + x2^2 +  a*rgamma(n, shape=2*x1+3, scale = 1) +
       (1-a)*rnorm(n, mean = 2*x1 + 3, sd = 0.5)
  return(data.frame(x1=x1,x2=x2,a=a,y=y))
}
regimeClass = as.formula(a ~ x1+x2)
moCondQuant_0 = as.formula(y ~ x1+x2+I(x1^2)+I(x2^2))
moCondQuant_1 = as.formula(y ~ exp( 0.11 - x1 - x2)+ x1^2 + p0 + p1*x1
+ p2*x1^2 + p3*x1^3 +p4*x1^4 )
start_1 = list(p0=0, p1=1.5, p2=1, p3 =0,p4=0)

## Not run: 
n<-200
testdata <- GenerateData.DR(n)
fit1 <- augX(raw.data=testdata, txVec = testdata$a,
             moCondQuant_0=moCondQuant_0, moCondQuant_1=moCondQuant_1,
             nlCondQuant_0=FALSE,   nlCondQuant_1=TRUE,
             start_1=start_1, 
             clnodes=NULL)  
 
# How to use parallel computing in AugX(): ##
 
# on Mac OSX/linux
 clnodes <- parallel::makeForkCluster(nnodes =getOption("mc.cores",2))
 fit2 <- augX(raw.data=testdata, length.out = 5, txVec = testdata$a,
             moCondQuant_0=moCondQuant_0, moCondQuant_1=moCondQuant_1,
             nlCondQuant_0=FALSE,   nlCondQuant_1=TRUE,
             start_1=start_1, 
             clnodes=clnodes)  
  
# on Windows
 clnodes <- parallel::makeCluster(2, type="PSOCK")
 fit3 <- augX(raw.data=testdata, length.out = 5, txVec = testdata$a,
             moCondQuant_0=moCondQuant_0, moCondQuant_1=moCondQuant_1,
             nlCondQuant_0=FALSE,   nlCondQuant_1=TRUE,
             start_1=start_1, 
             clnodes=clnodes)  
 
## End(Not run)