1d:T79b,# Estimate the Gini's mean difference/mean absolute difference(MAD) for a Given Treatment Regime Estimate the MAD if the entire population follows a treatment regime indexed by the given parameters. This function supports the `IPWE_MADopt` function. ```r abso_diff_est(beta, x, y, a, prob, Cnobs) ``` ## Arguments - `beta`: a vector indexing the treatment regime. It indexes a linear treatment regime: $$ d(x)= I\{\beta_0 + \beta_1 x_1 + ... + \beta_k x_k > 0\}.d(x)= I{\beta_0 + \beta_1*x_1 + ... + \beta_k*x_k > 0}. $$ - `x`: a matrix of observed covariates from the sample. Notice that we assumed the class of treatment regimes is linear. This is important that columns in `x` matches with `beta`. - `y`: a vector, the observed responses from a sample - `a`: a vector of 0s and 1s, the observed treatments from a sample - `prob`: a vector, the propensity scores of getting treatment 1 in the samples - `Cnobs`: A matrix with two columns, enumerating all possible combinations of pairs of indexes. This can be generated by `combn(1:n, 2)`, where `n` is the number of unique observations. ## Examples ```r library(stats) GenerateData.MAD <- function(n) { x1 <- runif(n) x2 <- runif(n) tp <- exp(-1+1*(x1+x2))/(1+exp(-1+1*(x1+x2))) a<-rbinom(n = n, size = 1, prob=tp) error <- rnorm(length(x1)) y <- (1 + a*0.3*(-1+x1+x2<0) + a*-0.3*(-1+x1+x2>0)) * error return(data.frame(x1=x1,x2=x2,a=a,y=y)) } n <- 500 testData <- GenerateData.MAD(n) logistic.model.tx <- glm(formula = a~x1+x2, data = testData, family=binomial) ph <- as.vector(logistic.model.tx$fit) Cnobs <- combn(1:n, 2) abso_diff_est(beta=c(1,2,-1), x=model.matrix(a~x1+x2, testData), y=testData$y, a=testData$a, prob=ph, Cnobs = Cnobs) ``` ## References Rdpack::insert_ref(key="wang2017quantile",package="quantoptr") ## See Also The function `IPWE_MADopt` is based on this function.

abso_diff_est function