R/svyrmir.R

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

#' Relative median income ratio
#'
#' Estimate the ratio between the median income of people with age above 65 and the median income of people with age below 65.
#'
#'
#' @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 age formula defining the variable age
#' @param agelim the age cutpoint, the default is 65
#' @param quantiles income quantile, usually .5 (median)
#' @param na.rm Should cases with missing values be dropped?
#' @param med_old return the median income of people older than agelim
#' @param med_young return the median income of people younger than agelim
#' @param ... arguments passed on to `survey::oldsvyquantile`
#'
#' @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 ) )
#'
#' # missing completely at random, missingness rate = .20
#' ind_miss <- rbinom(nrow(eusilc), 1, .20 )
#' eusilc$eqincome_miss <- eusilc$eqincome
#' is.na(eusilc$eqincome_miss)<- ind_miss==1
#'
#' # linearized design
#' des_eusilc <- svydesign( ids = ~rb030 , strata = ~db040 ,  weights = ~rb050 , data = eusilc )
#' des_eusilc <- convey_prep(des_eusilc)
#'
#' svyrmir( ~eqincome , design = des_eusilc , age = ~age, med_old = TRUE )
#'
#' # replicate-weighted design
#' des_eusilc_rep <- as.svrepdesign( des_eusilc , type = "bootstrap" )
#' des_eusilc_rep <- convey_prep(des_eusilc_rep)
#'
#' svyrmir( ~eqincome , design = des_eusilc_rep, age= ~age, med_old = TRUE )
#'
#' \dontrun{
#'
#' # linearized design using a variable with missings
#' svyrmir( ~ eqincome_miss , design = des_eusilc,age= ~age)
#' svyrmir( ~ eqincome_miss , design = des_eusilc , age= ~age, na.rm = TRUE )
#' # replicate-weighted design using a variable with missings
#' svyrmir( ~ eqincome_miss , design = des_eusilc_rep,age= ~age )
#' svyrmir( ~ eqincome_miss , design = des_eusilc_rep ,age= ~age, 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 )
#'
#' svyrmir( ~eqincome , design = dbd_eusilc , age = ~age )
#'
#' dbRemoveTable( conn , 'eusilc' )
#'
#' dbDisconnect( conn , shutdown = TRUE )
#'
#' }
#'
#' @export
svyrmir <-
  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("svyrmir", design)

  }

#' @rdname svyrmir
#' @export
svyrmir.survey.design  <-
  function(formula,
           design,
           age,
           agelim = 65,
           quantiles = 0.5,
           na.rm = FALSE,
           med_old = FALSE,
           med_young = 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."
      )

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

    if (na.rm) {
      nas <- rowSums(is.na(x))
      design <- design[nas == 0, ]

      if (length(nas) > length(design$prob)) {
        incvar <- incvar[nas == 0]
        agevar <- agevar[nas == 0]
      } else{
        incvar[nas > 0] <- 0
        agevar[nas > 0] <- 0
      }
    }
    if (is.null(names(design$prob)))
      names(design$prob) <- as.character(seq(length(design$prob)))
    w <- 1 / design$prob
    N <- sum(w)
    h <- h_fun(incvar, w)
    age.name <- terms.formula(age)[[2]]

    dsub1 <-
      eval(substitute(
        within_function_subset(design , subset = age < agelim) ,
        list(age = age.name, agelim = agelim)
      ))
    if (nrow(dsub1) == 0)
      stop("zero records in the set of non-elderly people")

    if ("DBIsvydesign" %in% class(dsub1)) {
      ind1 <- names(design$prob) %in% which(dsub1$prob != Inf)
    } else{
      ind1 <- names(design$prob) %in% names(dsub1$prob)
    }


    q_alpha1 <-
      survey::oldsvyquantile(
        x = formula,
        design = dsub1,
        quantiles = quantiles,
        method = "constant",
        na.rm = na.rm,
        ...
      )
    q_alpha1 <- as.vector(q_alpha1)

    Fprime1 <-
      densfun(
        formula = formula,
        design = dsub1,
        q_alpha1,
        h = h,
        FUN = "F",
        na.rm = na.rm
      )
    N1 <- sum(w * ind1)
    linquant1 <-
      -(1 / (N1 * Fprime1)) * ind1 * ((incvar <= q_alpha1) - quantiles)


    dsub2 <-
      eval(substitute(
        within_function_subset(design , subset = age >= agelim) ,
        list(age = age.name, agelim = agelim)
      ))

    if (nrow(dsub2) == 0)
      stop("zero records in the set of elderly people")

    if ("DBIsvydesign" %in% class(dsub2)) {
      ind2 <- names(design$prob) %in% which(dsub2$prob != Inf)
    } else{
      ind2 <- names(design$prob) %in% names(dsub2$prob)
    }



    q_alpha2 <-
      survey::oldsvyquantile(
        x = formula,
        design = dsub2,
        quantiles = quantiles,
        method = "constant",
        na.rm = na.rm,
        ...
      )
    q_alpha2 <- as.vector(q_alpha2)

    Fprime2 <-
      densfun(
        formula = formula,
        design = dsub2,
        q_alpha2,
        h = h,
        FUN = "F",
        na.rm = na.rm
      )
    N2 <- sum(w * ind2)

    linquant2 <-
      -(1 / (N2 * Fprime2)) * ind2 * ((incvar <= q_alpha2) - quantiles)
    # linearize ratio of medians

    MED1 <- list(value = q_alpha1 , lin = linquant1)
    MED2 <- list(value = q_alpha2 , lin = linquant2)
    list_all <- list(MED1 = MED1, MED2 = MED2)

    RMED <- contrastinf(quote(MED2 / MED1), list_all)
    rval <- as.vector(RMED$value)
    lin <- RMED$lin

    variance <-
      survey::svyrecvar(
        lin / design$prob,
        design$cluster,
        design$strata,
        design$fpc,
        postStrata = design$postStrata
      )

    colnames(variance) <-
      rownames(variance) <-
      names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]
    class(rval) <- c("cvystat" , "svystat")
    attr(rval , "var") <- variance
    attr(rval, "lin") <- lin
    attr(rval , "statistic") <- "rmir"
    if (med_old)
      attr(rval, "med_old") <- q_alpha2
    if (med_young)
      attr(rval, "med_young") <- q_alpha1

    rval
  }


#' @rdname svyrmir
#' @export
svyrmir.svyrep.design <-
  function(formula,
           design,
           age,
           agelim = 65,
           quantiles = 0.5,
           na.rm = FALSE,
           med_old = FALSE,
           med_young = 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."
      )

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

    if (na.rm) {
      nas <- rowSums(is.na(x))
      design <- design[nas == 0, ]
      df <- model.frame(design)
      incvar <- incvar[nas == 0]
      agevar <- agevar[nas == 0]
    }

    ComputeRmir <-
      function(x, w, quantiles, age, agelim) {
        indb <- age < agelim
        quant_below <- computeQuantiles(x[indb], w[indb], p = quantiles)
        inda <-  age >= agelim
        quant_above <- computeQuantiles(x[inda], w[inda], p = quantiles)
        c(quant_above, quant_below, quant_above / quant_below)
      }

    ws <- weights(design, "sampling")

    Rmir_val <-
      ComputeRmir(
        x = incvar,
        w = ws,
        quantiles = quantiles,
        age = agevar,
        agelim = agelim
      )

    rval <- Rmir_val[3]

    ww <- weights(design, "analysis")
    qq <-
      apply(ww, 2, function(wi)
        ComputeRmir(
          incvar,
          wi,
          quantiles = quantiles,
          age = agevar,
          agelim = agelim
        )[3])
    if (anyNA(qq))
      variance <- NA
    else
      variance <-
      survey::svrVar(qq,
                     design$scale,
                     design$rscales,
                     mse = design$mse,
                     coef = rval)

    variance <- as.matrix(variance)

    colnames(variance) <-
      rownames(variance) <-
      names(rval) <-
      strsplit(as.character(formula)[[2]] , ' \\+ ')[[1]]

    class(rval) <- c("cvystat" , "svrepstat")
    attr(rval , "var") <- variance
    attr(rval, "lin") <- NA
    attr(rval , "statistic") <- "rmir"
    if (med_old)
      attr(rval, "med_old") <- Rmir_val[1]
    if (med_young)
      attr(rval, "med_young") <- Rmir_val[2]

    rval
  }

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

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

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

        getvars(
          age,
          design$db$connection,
          design$db$tablename,
          updates = design$updates,
          subset = design$subset
        )
      )

    NextMethod("svyrmir", design)
  }