R/FromAlphaToRE_function.R

In gpapadog/Interference: Causal inference with interference for realistic regimes

#' Function that calculates the random effect that corresponds to a specific
#' average probability of treatment.
#' 
#' @param alpha Target average probability of treatment. Numberic in 0 - 1.
#' @param lin_pred Linear predictor for the probability of treatment among the
#' remaining units. Includes intercept and fixed effects.
#' @param alpha_re_bound The lower and upper end of the values for bi we will
#' look at. Defaults to 10, meaning we will look between - 10 and 10.
#' 
FromAlphaToRE <- function(alpha, lin_pred, alpha_re_bound = 10) {
  
  alpha_re_bound <- abs(alpha_re_bound)

  r <- optimise(f = AlphaToBi, lower = - 1 * alpha_re_bound,
                upper = alpha_re_bound, alpha = alpha, lin_pred = lin_pred)
  r <- r$minimum
  if (alpha_re_bound - abs(r) < 0.1) {
    warning(paste0('bi = ', r, ', alpha_re_bound = ', alpha_re_bound))
  }
  return(r)
}

AlphaToBi <- function(b, alpha, lin_pred) {
  exp_lin_pred <- exp(lin_pred)
  r <- abs(mean(exp_lin_pred / (exp_lin_pred + exp(- b))) - alpha)
  return(r)
}