# R/rif.R In ReneSchulenberg/test: Decomposition of (income) inequality

#### Documented in rif

#' @title Recentered influence function (RIF)
#'
#' @description Returns the (optional weighted) recentered influence function of a distributional
#' statistic.
#'
#' @details The RIF can be used as input for a RIF regression approach. RIF regressions are mostly
#' used to estimate the marginal effect of covariates on distributional statistics of income or
#' wealth.
#'
#' The RIF is calculated by adding the distributional statistic (quantile, gini or variance) to
#' the influence function. RIF is a numeric vector where each element corresponds to a particular
#' individual’s influence on the distributional statistic.
#'
#' @param x a numeric vector for which the recentered influence function is computed.
#' @param weights an optional vector of weigths of x to be used in the computation of the
#' recentered influence function. Should be NULL or a numeric vector.
#' @param method the distribution statistic for which the recentered influence function is
#' estimated. Options are "quantile", "gini" and "variance". Default is "quantile".
#' @param quantile quantile to be used when method "quantile" is selected. Must be a numeric
#' between 0 and 1. Default is 0.5 (median). Only a single quantile can be selected.
#' @param kernel a character giving the smoothing kernel to be used in method "quantile". Options
#' are "gaussian", "rectangular", "triangular", "epanechnikov", "biweight", "cosine"
#' or "optcosine". Default is "gaussian".
#'
#' @return A numeric vector of the recentered influence function of the selected distributional
#' statistic.
#'
#'
#' @examples
#' data(mex_inc_2008)
#'
#' #Recentered influence funtion of 20th quantile
#' rif_q20 <- rif(x=mex_inc_2008$income, weights=mex_inc_2008$factor, method="quantile",
#' quantile=0.2)
#'
#' #Recentered influence funtion of the gini coefficient
#' rif_gini <- rif(x=mex_inc_2008$income, weights=mex_inc_2008$factor, method="gini")
#'
#' @references
#' Firpo, S., N. Fortin and T. Lemieux (2009) Unconditional quantile regressions. \emph{Econometrica},
#' 77(3), p. 953-973.
#'
#' Heckley G, U.-G. Gerdtham U-G and G. Kjellsson (2016) A general method for decomposing the
#' causes of socioeconomic inequality in health. \emph{Journal of Health Economics},48, p. 89–106.
#'
#' Pereira, J. and A. Galego (2016) The drivers of wage inequality across Europe, a recentered
#' influence function regression approach, \emph{10th Annual Meeting of the Portuguese Economic
#' Journal}, University of Evora.
#'
#' @export

rif <- function(x, weights=NULL, method="quantile", quantile=0.5, kernel="gaussian"){

if (method=="quantile"){
df <- data.frame(x = as.numeric(x), w = as.numeric(weights))
df <- df[stats::complete.cases(df), ,drop = FALSE]
df[, "w"] <- df[, "w"]/sum(df[, "w"])
q <- Hmisc::wtd.quantile(x, weights=weights, probs=quantile, na.rm=TRUE)
d <- stats::density(df[,"x"],kernel=kernel, weights=df[, "w"])
dq <- stats::approx(d$x, d$y, q)\$y
RIF <- q + ((quantile - ifelse(x<q,1,0))/dq)
}
if (method=="gini"){
weights <- weights/sum(weights, na.rm=TRUE)
Xmean <- stats::weighted.mean(x,weights, na.rm=TRUE)
Xgini <- gini.wtd(x, weights=weights)

ord <- order(x)
x <- x[ord]
weights <- weights[ord]
p <- cumsum(weights)
GL <- cumsum(weights * x)

B2 <- (1-Xgini)*x/Xmean
C2 <- -2 * Xmean^(-1)*(x * (1 - p) + GL)
RIF_t <- 1+B2+C2
RIF <- RIF_t[order(ord)]
return(RIF)
}
if (method=="variance"){
weights <- weights/sum(weights, na.rm=TRUE)
Xmean <- stats::weighted.mean(x,weights, na.rm=TRUE)
RIF <- (x - Xmean)^2
}

return(RIF)
}

ReneSchulenberg/test documentation built on Feb. 6, 2018, 3:05 p.m.