R/ESS.R

In WeightIt: Weighting for Covariate Balance in Observational Studies

#' Compute effective sample size of weighted sample
#'
#' @description
#' Computes the effective sample size (ESS) of a weighted sample, which
#' represents the size of an unweighted sample with approximately the same
#' amount of precision as the weighted sample under consideration.
#'
#' The ESS is calculated as \eqn{(\sum w)^2/\sum w^2}.
#'
#' @param w a vector of weights
#'
#' @seealso
#' [summary.weightit()]
#'
#' @references
#' McCaffrey, D. F., Ridgeway, G., & Morral, A. R. (2004).
#' Propensity Score Estimation With Boosted Regression for Evaluating Causal
#' Effects in Observational Studies. Psychological Methods, 9(4), 403–425. \doi{10.1037/1082-989X.9.4.403}
#'
#' Shook‐Sa, B. E., & Hudgens, M. G. (2020). Power and sample size for
#' observational studies of point exposure effects. Biometrics, biom.13405. \doi{10.1111/biom.13405}
#'
#' @examples
#'
#' library("cobalt")
#' data("lalonde", package = "cobalt")
#'
#' #Balancing covariates between treatment groups (binary)
#' (W1 <- weightit(treat ~ age + educ + married +
#'                   nodegree + re74, data = lalonde,
#'                 method = "glm", estimand = "ATE"))
#' summary(W1)
#' ESS(W1$weights[W1$treat == 0])
#' ESS(W1$weights[W1$treat == 1])

#' @export
ESS <- function(w) {
  sum(w)^2/sum(w^2)
}