R/svyisq.R

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

#' Linearization of the total below a quantile
#'
#' Computes the linearized variable of the total in the lower tail of
#' the distribution of a variable.
#'
#' @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 alpha the order of the quantile
#' @param upper return the total in the total in the upper tail. Defaults to \code{FALSE}.
#' @param quantile return the upper bound of the lower tail
#' @param na.rm Should cases with missing values be dropped?
#' @param deff Return the design effect (see \code{survey::svymean})
#' @param linearized Should a matrix of linearized variables be returned
#' @param influence Should a matrix of (weighted) influence functions be returned? (for compatibility with \code{\link[survey]{svyby}})
#' @param return.replicates Return the replicate estimates?
#' @param ... future expansion. not used.
#' @param ... arguments passed on to `survey::oldsvyquantile`
#'
#' @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.
#'
#' @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.
#'
#' @author Djalma Pessoa, Guilherme Jacob, and Anthony Damico
#'
#' @seealso \code{\link{svyarpr}}
#'
#' @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(laeken)
#' data(eusilc) ; names( eusilc ) <- tolower( names( eusilc ) )
#' library(survey)
#' des_eusilc <- svydesign(ids = ~rb030, strata =~db040,  weights = ~rb050, data = eusilc)
#' des_eusilc <- convey_prep(des_eusilc)
#' svyisq(~eqincome, design=des_eusilc,.20 , quantile = TRUE)
#'
#' # replicate-weighted design
#' des_eusilc_rep <- as.svrepdesign( des_eusilc , type = "bootstrap" )
#' des_eusilc_rep <- convey_prep(des_eusilc_rep)
#'
#' svyisq( ~eqincome , design = des_eusilc_rep, .20 , quantile = TRUE )
#'
#' \dontrun{
#'
#' # linearized design using a variable with missings
#' svyisq( ~ py010n , design = des_eusilc, .20 )
#' svyisq( ~ py010n , design = des_eusilc , .20, na.rm = TRUE )
#' # replicate-weighted design using a variable with missings
#' svyisq( ~ py010n , design = des_eusilc_rep, .20 )
#' svyisq( ~ py010n , design = des_eusilc_rep , .20,  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 )
#'
#' svyisq( ~ eqincome , design = dbd_eusilc, .20 )
#'
#' dbRemoveTable( conn , 'eusilc' )
#'
#' dbDisconnect( conn , shutdown = TRUE )
#'
#' }
#'
#' @export
svyisq <-
  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("svyisq", design)

  }

#' @rdname svyisq
#' @export
svyisq.survey.design <-
  function(formula,
           design,
           alpha,
           quantile = FALSE,
           upper = FALSE ,
           na.rm = FALSE,
           deff = FALSE ,
           linearized = FALSE ,
           influence = FALSE ,
           ...) {
    # test for convey_prep
    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."
      )

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

    # treat missing values
    if (na.rm) {
      nas <- is.na(incvar)
      design <- design[!nas,]
      if (length(nas) > length(design$prob))
        incvar <- incvar[!nas]
      else
        incvar[nas] <- 0
    }

    # collect weights
    w <- 1 / design$prob

    # store quantile
    # q_alpha <- survey::svyquantile(x = formula, design = design, quantiles = alpha, method = "constant", na.rm = na.rm,...)
    q_alpha <- computeQuantiles(incvar , w , alpha)

    # compute value
    estimate <- CalcISQ(incvar , w , alpha)
    if (upper)
      estimate <- sum(w * incvar) - estimate

    # compute linearized functions
    h <- h_fun(incvar, w)
    Fprime0 <-
      densfun(
        formula = formula,
        design = design,
        q_alpha[[1]] ,
        FUN = "F",
        na.rm = na.rm
      )
    Fprime1 <-
      densfun(
        formula = formula,
        design = design,
        q_alpha[[1]] ,
        FUN = "big_s",
        na.rm = na.rm
      )
    lin <- CalcISQ_IF(incvar , w, alpha , Fprime0 , Fprime1)
    if (upper) lin <- ifelse( w > 0 , incvar - lin , 0 )

    # ensure length
    if (length(lin) != length(design$prob)) {
      tmplin <- rep(0 , nrow(design$variables))
      tmplin[w > 0] <- lin
      lin <- tmplin
      rm(tmplin)
      names(lin) <- rownames(design$variables)
    }

    # compute variance
    variance <-
      survey::svyrecvar(
        lin / design$prob,
        design$cluster,
        design$strata,
        design$fpc,
        postStrata = design$postStrata
      )
    variance[which(is.nan(variance))] <- NA
    colnames(variance) <-
      rownames(variance) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]

    # compute deff
    if (is.character(deff) || deff) {
      nobs <- sum(weights(design , "sampling") > 0)
      npop <- sum(weights(design , "sampling"))
      if (deff == "replace")
        vsrs <- survey::svyvar(lin , design, na.rm = na.rm) * npop ^ 2 / nobs
      else
        vsrs <-
        survey::svyvar(lin , design , na.rm = na.rm) * npop ^ 2 * (npop - nobs) /
        (npop * nobs)
      deff.estimate <- variance / vsrs
    }

    # coerce to matrix
    lin <-
      matrix(lin ,
             nrow = length(lin) ,
             dimnames = list(names(lin) , strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]))

    # build result object
    rval <- estimate
    names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]
    class(rval) <- c("cvystat" , "svystat")
    attr(rval, "var") <- variance
    attr(rval, "statistic") <- "isq"
    if (quantile)
      attr(rval, "quantile") <- q_alpha
    if (linearized)
      attr(rval, "linearized") <- lin
    if (influence)
      attr(rval , "influence")  <-
      sweep(lin , 1 , design$prob , "/")
    if (linearized |
        influence)
      attr(rval , "index") <- as.numeric(rownames(lin))
    if (is.character(deff) ||
        deff)
      attr(rval, "deff") <- deff.estimate
    rval

  }

#' @rdname svyisq
#' @export
svyisq.svyrep.design <-
  function(formula,
           design,
           alpha,
           quantile = FALSE,
           upper = FALSE ,
           na.rm = FALSE,
           deff = FALSE ,
           linearized = FALSE ,
           return.replicates = FALSE ,
           ...) {
    # check for convey_prep
    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."
      )

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

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

    # collect sampling weights
    ws <- weights(design, "sampling")

    # compute point estimate
    q_alpha <- computeQuantiles(incvar , ws, alpha)
    estimate <- CalcISQ(incvar , ws, alpha)
    if (upper)
      estimate <- sum(ws * incvar) - estimate

    # store quantile
    # if (quantile) q_alpha <- survey::oldsvyquantile(x = formula, design = design, quantiles = alpha, method = "constant", na.rm = na.rm,...)

    # collect analysis weights
    ww <- weights(design, "analysis")

    # compute replicates
    qq <- apply(ww, 2 , function(wi) {
      if (upper)
        sum(wi * incvar) - CalcISQ(incvar , wi , alpha)
      else
        CalcISQ(incvar , wi , alpha)
    })

    # compute variance
    if (any(is.na(qq)))
      variance <- as.matrix(NA)
    else {
      variance <-
        survey::svrVar(qq ,
                       design$scale ,
                       design$rscales ,
                       mse = design$mse ,
                       coef = estimate)
      this.mean <- attr(variance , "means")
      variance <- as.matrix(variance)
      attr(variance , "means") <- this.mean
    }
    colnames(variance) <-
      rownames(variance) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]

    # compute deff
    if (is.character(deff) || deff || linearized) {
      # compute linearized functions
      h <- h_fun(incvar, ws)

      N <- sum(ws)
      u <- (q_alpha[[1]] - incvar) / h
      vectf <- exp(-(u ^ 2) / 2) / sqrt(2 * pi)
      v <- ws * incvar
      Fprime0 <- sum(vectf * ws) / (N * h)
      Fprime1 <- sum(vectf * v) / h

      lin <- CalcISQ_IF(incvar , ws, alpha , Fprime0 , Fprime1)
      if (upper)
        lin <- incvar[ws > 0] - lin

      # compute deff
      nobs <- length(design$pweights)
      npop <- sum(design$pweights)
      vsrs <-
        unclass(
          survey::svyvar(
            lin ,
            design,
            na.rm = na.rm,
            return.replicates = FALSE,
            estimate.only = TRUE
          )
        ) * npop ^ 2 / nobs
      if (deff != "replace")
        vsrs <- vsrs * (npop - nobs) / npop
      deff.estimate <- variance / vsrs

      # filter observation
      names(lin) <- rownames(design$variables)

      # coerce to matrix
      lin <-
        matrix(lin ,
               nrow = length(lin) ,
               dimnames = list(names(lin) , strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]))

    }

    # build result object
    rval <- estimate
    names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]
    class(rval) <- c("cvystat" , "svrepstat")
    attr(rval, "var") <- variance
    attr(rval, "statistic") <- "isq"
    if (quantile)
      attr(rval, "quantile") <- q_alpha
    if (linearized)
      attr(rval, "linearized") <- lin
    if (linearized)
      attr(rval , "index") <- as.numeric(rownames(lin))

    # keep replicates
    if (return.replicates) {
      attr(qq , "scale") <- design$scale
      attr(qq , "rscales") <- design$rscales
      attr(qq , "mse") <- design$mse
      rval <- list(mean = rval , replicates = qq)
      class(rval) <- c("cvystat" , "svrepstat")
    }

    # add design effect estimate
    if (is.character(deff) ||
        deff)
      attr(rval , "deff") <- deff.estimate

    # return object
    rval

  }

#' @rdname svyisq
#' @export
svyisq.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("svyisq", design)
  }


# function for point estimates
CalcISQ <- function(x , pw , alpha) {
  # filter observations
  x <- x [pw > 0]
  pw <- pw [pw > 0]

  # compute quantile
  q_alpha <- computeQuantiles(x , pw , alpha)

  # compute total below quantile
  sum(x * (x <= q_alpha) * pw)

}

# function for linearized functions
CalcISQ_IF <- function(x , pw , alpha , Fprime0 , Fprime1) {

  # population size
  N <- sum(pw)

  # compute quantile
  q_alpha <- computeQuantiles(x , pw , alpha)

  # linearization
  h <- h_fun(x, pw)
  # Fprime0 <- CalcDensFun( x , pw , q_alpha , h=h , FUN = "F" )
  # Fprime1 <- CalcDensFun( x , pw , q_alpha , FUN = "big_s" )
  iq <- -(1 / (N * Fprime0)) * ((x <= q_alpha) - alpha)
  isqalpha1 <- x * (x <= q_alpha)
  isqalpha <- isqalpha1 + Fprime1 * iq

  # add indices
  names(isqalpha) <- names(pw)

  # return estimate
  ifelse( pw != 0 , isqalpha , 0 )

}

# function for density estimation
CalcDensFun <- function(x ,
                        pw ,
                        q_alpha ,
                        h = NULL ,
                        FUN = "F") {
  # filter observations
  x <- x[pw > 0]
  pw <- pw[pw > 0]

  # intermediate estimates
  N <- sum(pw)
  if (is.null(h))
    h <- h_fun(x, pw)

  # calculation
  u <- (x - x) / h
  vectf <- exp(-(u ^ 2) / 2) / sqrt(2 * pi)
  if (FUN == "F") {
    res <- sum(vectf * pw) / (N * h)
  } else {
    v <- pw * x
    res <- sum(vectf * v) / h
  }

  # final estimate
  res

}