R/svyrmpg.R

In DjalmaPessoa/convey: Income Concentration Analysis with Complex Survey Samples

#' Relative median poverty gap
#'
#' Estimate the difference between the at-risk-of-poverty threshold (\code{arpt}) and the median of incomes less than the \code{arpt} relative to the \code{arpt}.
#'
#'
#' @param formula a formula specifying the income variable
#' @param design a design object of class \code{survey.design} or class \code{svyrep.design} from the \code{survey} library.
#' @param quantiles income quantile, usually .5 (median)
#' @param percent fraction of the quantile, usually .60
#' @param na.rm Should cases with missing values be dropped?
#' @param thresh return the poverty poverty threshold
#' @param poor_median return the median income of poor people
#' @param ... future expansion
#'
#' @details you must run the \code{convey_prep} function on your survey design object immediately after creating it with the \code{svydesign} or \code{svrepdesign} function.
#'
#' @return Object of class "\code{cvystat}", which are vectors with a "\code{var}" attribute giving the variance and a "\code{statistic}" attribute giving the name of the statistic.
#'
#' @author Djalma Pessoa and Anthony Damico
#'
#' @seealso \code{\link{svyarpt}}
#'
#' @references Guillaume Osier (2009). Variance estimation for complex indicators
#' of poverty and inequality. \emph{Journal of the European Survey Research
#' Association}, Vol.3, No.3, pp. 167-195,
#' ISSN 1864-3361, URL \url{https://ojs.ub.uni-konstanz.de/srm/article/view/369}.
#'
#' Jean-Claude Deville (1999). Variance estimation for complex statistics and estimators:
#' linearization and residual techniques. Survey Methodology, 25, 193-203,
#' URL \url{https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X19990024882}.
#'
#' @keywords survey
#'
#' @examples
#'
#' library(survey)
#' library(laeken)
#' data(eusilc) ; names( eusilc ) <- tolower( names( eusilc ) )
#'
#' # linearized design
#' des_eusilc <- svydesign( ids = ~rb030 , strata = ~db040 ,  weights = ~rb050 , data = eusilc )
#' des_eusilc <- convey_prep( des_eusilc )
#'
#' svyrmpg( ~eqincome , design = des_eusilc, thresh = TRUE )
#'
#' # replicate-weighted design
#' des_eusilc_rep <- as.svrepdesign( des_eusilc , type = "bootstrap" )
#' des_eusilc_rep <- convey_prep( des_eusilc_rep )
#'
#' svyrmpg( ~eqincome , design = des_eusilc_rep, thresh = TRUE )
#'
#' \dontrun{
#'
#' # linearized design using a variable with missings
#' svyrmpg( ~ py010n , design = des_eusilc )
#' svyrmpg( ~ py010n , design = des_eusilc , na.rm = TRUE )
#' # replicate-weighted design using a variable with missings
#' svyrmpg( ~ py010n , design = des_eusilc_rep )
#' svyrmpg( ~ py010n , design = des_eusilc_rep , na.rm = TRUE )
#'
#' # database-backed design
#' library(RSQLite)
#' library(DBI)
#' dbfile <- tempfile()
#' conn <- dbConnect( RSQLite::SQLite() , dbfile )
#' dbWriteTable( conn , 'eusilc' , eusilc )
#'
#' dbd_eusilc <-
#' 	svydesign(
#' 		ids = ~rb030 ,
#' 		strata = ~db040 ,
#' 		weights = ~rb050 ,
#' 		data="eusilc",
#' 		dbname=dbfile,
#' 		dbtype="SQLite"
#' 	)
#'
#' dbd_eusilc <- convey_prep( dbd_eusilc )
#'
#' svyrmpg( ~ eqincome , design = dbd_eusilc )
#'
#' dbRemoveTable( conn , 'eusilc' )
#'
#' dbDisconnect( conn , shutdown = TRUE )
#'
#' }
#'
#' @export
svyrmpg <-
  function(formula, design, ...) {
    if (length(attr(terms.formula(formula) , "term.labels")) > 1)
      stop(
        "convey package functions currently only support one variable in the `formula=` argument"
      )

    UseMethod("svyrmpg", design)

  }


#' @rdname svyrmpg
#' @export
svyrmpg.survey.design <-
  function(formula,
           design,
           quantiles = 0.5,
           percent = 0.6,
           na.rm = FALSE,
           thresh = FALSE,
           poor_median = FALSE,
           ...) {
    if (is.null(attr(design, "full_design")))
      stop(
        "you must run the ?convey_prep function on your linearized survey design object immediately after creating it with the svydesign() function."
      )


    # if the class of the full_design attribute is just a TRUE, then the design is
    # already the full design.  otherwise, pull the full_design from that attribute.
    if ("logical" %in% class(attr(design, "full_design")))
      full_design <-
        design
    else
      full_design <- attr(design, "full_design")

    incvar <-
      model.frame(formula, design$variables, na.action = na.pass)[[1]]

    if (na.rm) {
      nas <- is.na(incvar)
      design$prob <- ifelse( nas , Inf , design$prob )
      incvar[ nas ] <- 0
    }

    incvec <-
      model.frame(formula, full_design$variables, na.action = na.pass)[[1]]

    if (na.rm) {
      nas <- is.na(incvec)
      full_design$prob <- ifelse( nas , Inf , full_design$prob )
      incvec[nas] <- 0
    }

    ARPT <-
      svyarpt(
        formula = formula,
        full_design,
        quantiles = quantiles,
        percent = percent,
        na.rm = na.rm
      )
    arpt <- coef(ARPT)
    linarpt <- attr(ARPT, "lin")

    POORMED <-
      svypoormed(
        formula = formula,
        design = design,
        quantiles = quantiles,
        percent = percent,
        na.rm = na.rm
      )
    medp <- coef(POORMED)
    linmedp <- attr(POORMED, "lin")

    MEDP <- list(value = medp, lin = linmedp)
    ARPT <- list(value = arpt, lin = linarpt)
    list_all <- list(ARPT = ARPT, MEDP = MEDP)

    # linearize RMPG
    RMPG <- contrastinf(quote((ARPT - MEDP) / ARPT) , list_all)
    rval <- RMPG$value
    infun <- unlist(RMPG$lin)

    # compute variance estimate
    varest <-
      survey::svyrecvar(
        infun / full_design$prob,
        full_design$cluster,
        full_design$strata,
        full_design$fpc,
        postStrata = full_design$postStrata
      )

    # format result
    varest <- as.matrix( varest )
    varest[ is.nan( varest ) ] <- NA
    colnames( varest ) <-
      rownames( varest ) <-
      names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]
    class(rval) <- c("cvystat" , "svystat")
    attr(rval , "var") <- varest
    attr(rval, "lin") <- infun
    attr(rval , "statistic") <- "rmpg"
    if (thresh)
      attr(rval, "thresh") <- arpt
    if (poor_median)
      attr(rval, "poor_median") <- medp

    rval
  }


#' @rdname svyrmpg
#' @export
svyrmpg.svyrep.design <-
  function(formula,
           design,
           quantiles = 0.5,
           percent = 0.6,
           na.rm = FALSE,
           thresh = FALSE,
           poor_median = FALSE,
           ...) {
    if (is.null(attr(design, "full_design")))
      stop(
        "you must run the ?convey_prep function on your replicate-weighted survey design object immediately after creating it with the svrepdesign() function."
      )

    # if the class of the full_design attribute is just a TRUE, then the design is
    # already the full design.  otherwise, pull the full_design from that attribute.
    if ("logical" %in% class(attr(design, "full_design"))) {
      full_design <- design
    } else full_design <- attr(design, "full_design")

    # collect full sample income data
    incvec <-
      model.frame( formula, full_design$variables, na.action = na.pass)[[1]]

    # treat missing
    if (na.rm) {
      nas <- is.na(incvec)
      full_design <- full_design[!nas, ]
      incvec <- incvec[!nas]
    }

    # collect domain income data
    incvar <-
      model.frame(formula, design$variables, na.action = na.pass)[[1]]

    # treat missing
    if (na.rm) {
      nas <- is.na(incvar)
      design <- design[!nas, ]
      incvar <- incvar[!nas]
    }

    # collect weights
    wsf <- weights(full_design, "sampling")
    names( incvec ) <- names( wsf ) <- rownames( full_design$variables )
    names( incvar ) <- names( wsf ) <- rownames( design$variables )
    ind <-  rownames( full_design$variables ) %in% rownames( design$variables )

    # compute estimate
    ws <- weights(design, "sampling")
    varname <- terms.formula( formula )[[2]]
    Rmpg_val <-
      ComputeRmpg(
        xf = incvec ,
        wf = wsf ,
        ind = ind ,
        quantiles = quantiles ,
        percent = percent ,
        varname = varname
      )
    rval <- Rmpg_val[3]

    # collect replicate weights
    wwf <- weights( full_design , "analysis" )

    # compute replicates
    qq <-
      apply( wwf , 2 , function( wi ) {
        suppressWarnings(
          ComputeRmpg( incvec ,
                       wi ,
                       ind = ind ,
                       quantiles = quantiles ,
                       percent = percent ,
                       varname = NULL )[3] )
      } )

    # compute variance
    if ( anyNA( qq ) ) {
      varest <- as.numeric( NA )
    } else varest <- survey::svrVar( qq ,
                                     design$scale ,
                                     design$rscales ,
                                     mse = design$mse ,
                                     coef = rval )

    # format result object
    varest <- as.matrix( varest )
    colnames(varest) <-
      rownames(varest) <-
      names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]
    class(rval) <- c("cvystat" , "svrepstat")
    attr(rval , "var") <- varest
    attr(rval, "lin") <- NA
    attr(rval , "statistic") <- "rmpg"
    if (thresh)
      attr(rval, "thresh") <- Rmpg_val[1]
    if (poor_median)
      attr(rval, "poor_median") <- Rmpg_val[2]
    rval
  }

#' @rdname svyrmpg
#' @export
svyrmpg.DBIsvydesign <-
  function (formula, design, ...) {
    if (!("logical" %in% class(attr(design, "full_design")))) {
      full_design <- attr(design , "full_design")

      full_design$variables <-
        getvars(
          formula,
          attr(design , "full_design")$db$connection,
          attr(design , "full_design")$db$tablename,
          updates = attr(design , "full_design")$updates,
          subset = attr(design , "full_design")$subset
        )

      attr(design , "full_design") <- full_design

      rm(full_design)

    }

    design$variables <-
      getvars(
        formula,
        design$db$connection,
        design$db$tablename,
        updates = design$updates,
        subset = design$subset
      )

    NextMethod("svyrmpg", design)

  }

ComputeRmpg <-
  function(xf, wf, ind, quantiles, percent , varname = NULL ) {
    thresh <- percent * computeQuantiles(xf, wf, p = quantiles)
    x <- xf[ind]
    w <- wf[ind]
    if ( is.na( thresh ) ) return( NA )
    indpoor <- ( x <= thresh )
    if ( !any( indpoor ) ) {
      if ( !is.null( varname ) ) warning( paste( "zero records in the set of poor people.  determine the poverty threshold by running svyarpt on ~", varname ) )
      return( NA )
    }
    medp <- computeQuantiles(x[indpoor], w[indpoor], p = 0.5)
    c( thresh , medp, 1 - ( medp / thresh ) )
  }