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#' 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 ) )
}
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