R/z_score_fun.R

In m-allik/SocEpi: Health Inequality Analysis

#' z-scores
#'
#' \code{zscores} calculates standardized scores or z-scores, with a mean close to zero and standard deviation (sd)
#' close to one, for the variable given in \code{variable}.
#' The standardization uses a population weighted mean and standard deviation, which are calculated based on the
#' population distribution given by \code{population}.
#'
#' @param population Population counts.
#' @param variable Continuous deprivation measure, such as a percentage, to calculate the z-scores for.
#'
#' @return A list including the following:
#'  \item{z.score}{standardized score using weighted mean and sd}
#'  \item{w.mean}{weighted mean}
#'  \item{w.sd}{weighted standard deviation}
#'  \item{weight}{population weight}
#' @export
#'
#'
#' @examples
#' data <- dep_data
#'
#' # store all results in object z_oc
#' z_oc <- zscore(data$total_pop, data$pcnt_overcrowding)
#'
#' # extract z-score
#' data$z_overcrowd <- z_oc$z.score
#' mean(data$z_overcrowd) # mean of z-score
#' sd(data$z_overcrowd) # sd z-score
#'
#' # extract weighted mean and sd, compare weighted values to unweighted values
#' mean(data$pcnt_overcrowding)
#' z_oc$w.mean
#' sd(data$pcnt_overcrowding)
#' z_oc$w.sd
#'


zscore <- function(population, variable) {

  data <- data.frame(population, variable)

  # weights
  data$weight <- data$population/sum(data$population, na.rm = TRUE)

  # calculate weighted mean and sd
  w.mean <- sum(data$variable*data$weight, na.rm = TRUE)
  x <- ((data$variable - w.mean)^2)*data$weight
  w.sd <- sqrt(sum(x, na.rm = TRUE))

  # z-score
  data$z.score <- (data$variable - w.mean)/w.sd

  # cat("Weighted mean =", w.mean, "\n", "Weigted SD =", w.sd, "\n")

  output <- list("z.score" = data$z.score, "w.mean" = w.mean, "w.sd" = w.sd, "weight" = data$weight)
  #output <- cbind(w.mean, w.sd)
  return(output)

  }