R/Abadie-Imbens-SE.R

In MatchItSE: Calculates SE for Matched Samples from 'MatchIt'

#' Abadie Imben's Standard Error for the ATT
#'
#' Calculate the SE for the ATT with Abadie & Imben's method.
#'
#' @param obj MatchIt Object
#' @param Y Response Vector
#' @return SE for the ATT of \code{Y}
#' @references
#' Abadie, A., Drukker, D., Herr, J.L. & Imbens, G. (2004).Implementing matching estimators for average treatment effects in Stata. The Stata Jorunal (4), pp. 290 - 311.
#'
#' @examples
#' \dontrun{
#'   library(MatchIt)
#'   data("lalonde")
#'   m.out  <- matchit(treat ~ educ + black, data = lalonde)
#'   att(obj = m.out, Y = lalonde$re78)
#'   abadie_imbens_se(obj = m.out, Y = lalonde$re78)
#' }
#' @export
abadie_imbens_se <- function(obj, Y){
  stopifnot(methods::is(obj, "matchit"))
  tt <- obj$treat
  ww <- obj$weights
  mm <- as.matrix(obj$match.matrix[ww[tt == 1] > 0, ])
  nm <- rownames(obj$X)
  nt <- sum(ww > 0 & tt == 1)  # Count treated
  #nc <- sum(ww > 0 & tt == 0)  # Count control
  tau.hat <- att(obj, Y)
  if (ncol(mm) > 1){
    yi <- Y[match(rownames(mm), nm)]
    yl <- sapply(1:ncol(mm), function(j){ Y[match(mm[,j], nm)] })
    sigma.t <- sum(rowMeans( (yi - yl - tau.hat)^2, na.rm = T)/(2*nt))
    #scale.sample.t <- (nt + sum(as.vector(table(mm))^2))/(nt^2)
    scale.sample.t <- (nt + cppKMsqSum(mm, unique(mm[!is.na(mm)]), 1/rowSums(!is.na(mm))))/(nt^2)
  } else {
    yi <- Y[match(rownames(mm), nm)]  # Response treated
    yl <- Y[match(mm[,1], nm)]  # Response control
    sigma.t <- sum( ((yi - yl - tau.hat)^2) / (2*nt) )  # Formula 10ff
    scale.sample.t <- (nt + sum(as.vector(table(mm[,1]))^2))/(nt^2)
    #scale.sample.t <- sum((c(rep(1,nt), as.vector(table(mm[,1])))^2)/(nt^2)) # Formula 5 | geht effizienter (rep usw)
  }
  return( sqrt(scale.sample.t * sigma.t) )
}