Logit-shift a vector to have a specified mean

logit_shift.R

#' Logit-shift a vector to have a specified mean
#' 
#' Finds and applies a shift on the logit scale so that a vector has a chosen mean.
#' 
#' @param x The vector to shift
#' @param target The target mean, a single value between 0 and 1
#'
#' @returns A new vector with length matching `x`
#'
#' @references 
#' Rosenman, E. T., McCartan, C., & Olivella, S. (2023). Recalibration of Predicted 
#' Probabilities Using the "Logit Shift": Why Does It Work, and When Can It Be 
#' Expected to Work Well?. *Political Analysis*, 31(4), 651-661.
logit_shift = function(x, target) {
    diff = qlogis(mean(x)) - qlogis(target)
    bounds = if (diff > 0) c(-2*diff, 0) else c(0, -2*diff)   
    shift = uniroot(function(s) mean(plogis(qlogis(x) + s)) - target, bounds)$root
    plogis(qlogis(x) + shift)
}