# Generate Pseudo-Responses Based on Conditional Quantile Regression Models 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. ```r augX(raw.data, length.out = 200, txVec, moCondQuant_0, moCondQuant_1, nlCondQuant_0 = FALSE, nlCondQuant_1 = FALSE, start_0 = NULL, start_1 = NULL, clnodes) ``` ## Arguments - `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. ## Returns It returns a list object, consisting of the following elements: 1. `y.a.0`, the vector of estimated individual level pseudo outcomes, given the treatment is 0; 2. `y.a.1`, the vector of estimated individual level pseudo outcomes, given the treatment is 1; 3. `nlCondQuant_0`, logical, indicating whether the `y.a.0` is generated based on a nonlinear conditional quantile model. 4. `nlCondQuant_1`, logical, indicating whether the `y.a.1` is generated based on a nonlinear conditional quantile model. ## Details 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 $u0$th quantile of this observation were treatment level 0 is applied via the conditional $u0$th 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. ## Examples ```r 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) ``` ## References Rdpack::insert_ref(key="wang2017quantile",package="quantoptr")

augX function