R/calc_decompTheil_splinebins.R

In antrologos/tableInequality:

#' @export

calc_decompTheil_splinebins <- function(data_pnad, groups_theil, groups = NULL){

        if(is.null(groups)){
                data_pnad <- data_pnad %>%
                        mutate(ID = 1) %>%
                        arrange_at(c("ID", groups_theil, "min_faixa"))
        }else{
                data_pnad <- data_pnad %>%
                        unite(col = ID, groups) %>%
                        group_by_at(c("ID", groups_theil, "min_faixa")) %>%
                        summarise(
                                max_faixa = max(max_faixa),
                                n         = sum(n)) %>%
                        ungroup() %>%
                        arrange_at(c("ID", groups_theil, "min_faixa"))
        }

        data_split <- split(data_pnad, f = data_pnad$ID)

        interpolate <- function(data){
                interpolation <- binsmooth::splinebins(bEdges  = data$max_faixa,
                                                     bCounts = data$n)

                list(PDF = interpolation[[1]],
                     min = min(data$min_faixa),
                     max = interpolation$E)
        }

        calc_mean_from_pdf <- function(pdf_function, xmin, xmax){
                integrate(f = function(x) x*pdf_function(x), lower =  xmin, upper = xmax, subdivisions = 5000)$value
        }

        calc_theil_from_pdf <- function(pdf_function, xmean, xmin, xmax){
                theil_func <- function(x) (x/xmean)*log((x/xmean))

                theil <- integrate(f = function(x) theil_func(x)*pdf_function(x),
                                   lower =  0,
                                   upper = xmax, subdivisions = 5000)$value
                theil
        }

        calc_mean_and_theil_from_data <- function(data){
                interpolation <- interpolate(data)

                xmean          <- calc_mean_from_pdf(pdf_function = interpolation$PDF,
                                                     xmin          = interpolation$min,
                                                     xmax          = interpolation$max)

                theil         <- calc_theil_from_pdf(pdf_function = interpolation$PDF,
                                                     xmean        = xmean,
                                                     xmin         = interpolation$min,
                                                     xmax         = interpolation$max)
                tibble(mean = xmean, theil)
        }

        #data_i = data_split[[1]]
        calc_decompTheil <- function(data_i){

                data_i_split <- split(data_i, data_i[[groups_theil]])

                group_mean_theil  <- map(.x = data_i_split,
                                         .f = calc_mean_and_theil_from_data) %>%
                        rbindlist(idcol = TRUE)

                group_sizes    <- map(data_i_split, function(x) tibble(n = sum(x$n))) %>%
                        rbindlist(idcol = TRUE)

                group_results <- left_join(group_mean_theil, group_sizes) %>%
                        mutate(grand_mean = sum(n*mean)/sum(n),
                               share      = (n/sum(n))*(mean/grand_mean))

                between <- with(group_results, sum(share*log(mean/grand_mean)) )
                within  <- with(group_results, sum(theil*share))

                tibble(theil = between + within, between, within)

        }

        if(!any(c("multiprocess", "multicore", "multisession", "cluster") %in% class(plan()))){
                plan(multisession)
        }

        #calc_decompTheil(data_split[[1]])
        decompTheil_result <- future_map_dfr(.x = data_split,
                                             .f = calc_decompTheil,
                                             .progress = T)

        decompTheil_result <- bind_cols(tibble(ID = names(data_split)), decompTheil_result)

        if(is.null(groups)){
                decompTheil_result <- decompTheil_result %>%
                        dplyr::select(theil, between, within)
        }else{
                decompTheil_result <- decompTheil_result %>%
                        dplyr::select(ID, theil, between, within) %>%
                        separate(col = ID, into = groups, sep = "_")
        }

        decompTheil_result

}