R/svygpg.R

In convey: Income Concentration Analysis with Complex Survey Samples

#' Linearization of the gender pay (wage) gap
#'
#' Estimate the difference between the average gross hourly earnings of men and women expressed as a percentage of the average gross hourly earnings of men.
#'
#'
#' @param formula a formula specifying the gross hourly earnings variable
#' @param design a design object of class \code{survey.design} or class \code{svyrep.design} from the \code{survey} library.
#' @param sex formula with a factor with labels 'male' and 'female'
#' @param na.rm Should cases with missing values be dropped?
#' @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(laeken)
#' library(survey)
#' data(ses)
#' names( ses ) <- gsub( "size" , "size_" , tolower( names( ses ) ) )
#' des_ses <- svydesign(id=~1, weights=~weights, data=ses)
#' des_ses <- convey_prep(des_ses)
#'
#' # linearized design
#' svygpg(~earningshour, des_ses, ~sex)
#' # replicate-weighted design
#' des_ses_rep <-  as.svrepdesign( des_ses , type = "bootstrap" )
#' des_ses_rep <- convey_prep(des_ses_rep)
#'
#' svygpg(~earningshour, des_ses_rep, ~sex)
#'
#' \dontrun{
#'
#' # database-backed design
#' library(RSQLite)
#' library(DBI)
#' dbfile <- tempfile()
#' conn <- dbConnect( RSQLite::SQLite() , dbfile )
#' dbWriteTable( conn , 'ses' , ses )
#'
#' dbd_ses <- svydesign(id=~1, weights=~weights, data="ses", dbname=dbfile, dbtype="SQLite")
#' dbd_ses <- convey_prep( dbd_ses )
#'
#' svygpg(formula=~earningshour, design=dbd_ses, sex= ~sex)
#'
#' dbRemoveTable( conn , 'ses' )
#'
#' }
#'
#' @export
svygpg <-
	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("svygpg", design)

	}

#' @rdname svygpg
#' @export
svygpg.survey.design <-
	function(formula, design, sex,  na.rm=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.")

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

		# sex factor
		mf <- model.frame(sex, design$variables, na.action = na.pass)

		xx <- lapply(attr(terms(sex), "variables")[-1], function(tt) model.matrix(eval(bquote(~0 + .(tt))), mf))

		cols <- sapply(xx, NCOL)

		sex <- matrix(nrow = NROW(xx[[1]]), ncol = sum(cols))

		scols <- c(0, cumsum(cols))

		for (i in 1:length(xx))sex[, scols[i] + 1:cols[i]] <- xx[[i]]


		colnames(sex) <- do.call("c", lapply(xx, colnames))

		sex <- as.matrix(sex)

		x <- cbind(wagevar,sex)

		if(na.rm){

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

			if (length(nas) > length(design$prob)){
				wagevar <- wagevar[nas == 0]
				sex <- sex[nas==0,]
			} else{
				wagevar[nas > 0] <- 0
				sex[nas > 0,] <- 0
			}

		}

		w <- 1 / design$prob
		ind <- names(design$prob)


		if(na.rm){
			if (length(nas) > length(design$prob)) sex <- sex[!nas,] else sex[nas] <- 0
		}

		col_female <- grep("female", colnames(sex))
		col_male <- setdiff(1:2, col_female)

		# create linearization objects of totals
		INDM <- list(value = sum(sex[, col_male]*w), lin=sex[, col_male])
		INDF <- list(value = sum(sex[, col_female]*w), lin=sex[, col_female])
		TM <- list(value = sum(wagevar*sex[, col_male]*w), lin=wagevar*sex[, col_male])
		TF <- list(value = sum(wagevar*sex[, col_female]*w), lin=wagevar*sex[, col_female])
		list_all_tot <- list(INDM=INDM,INDF=INDF,TM=TM,TF=TF)
		IGPG <- contrastinf( quote( ( TM / INDM - TF / INDF ) / ( TM / INDM ) ) , list_all_tot )
		infun <- IGPG$lin

		rval <- IGPG$value
		variance <- survey::svyrecvar(infun/design$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") <- infun
		attr( rval , "statistic" ) <- "gpg"

		rval
	}


#' @rdname svygpg
#' @export
svygpg.svyrep.design <-
	function(formula, design, sex,na.rm=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.")

		wage <- terms.formula(formula)[[2]]
		df <- model.frame(design)
		wage <- df[[as.character(wage)]]

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

		ws <- weights(design, "sampling")
		design <- update(design, one = rep(1, length(wage)))

		# sex factor
		mf <- model.frame(sex, design$variables, na.action = na.pass)

		xx <- lapply(attr(terms(sex), "variables")[-1], function(tt) model.matrix(eval(bquote(~0 + .(tt))), mf))

		cols <- sapply(xx, NCOL)

		sex <- matrix(nrow = NROW(xx[[1]]), ncol = sum(cols))

		scols <- c(0, cumsum(cols))

		for (i in 1:length(xx)) sex[, scols[i] + 1:cols[i]] <- xx[[i]]

		colnames(sex) <- do.call("c", lapply(xx, colnames))

		sex <- as.matrix(sex)

		ComputeGpg <-
			function(earn_hour, w, sex) {
				col_female <- grep("female", colnames(sex))
				col_male <- setdiff(1:2, col_female)
				ind_men <- sex[, col_male]
				ind_fem <- sex[, col_female]
				med_men <- sum(ind_men * earn_hour * w)/sum(ind_men * w)
				med_fem <- sum(ind_fem * earn_hour * w)/sum(ind_fem * w)
				gpg <- (med_men - med_fem)/med_men
				gpg
			}

		rval <- ComputeGpg(earn_hour = wage, w = ws, sex = sex)

		ww <- weights(design, "analysis")

		qq <- apply(ww, 2, function(wi) ComputeGpg(wage, wi, sex = sex))
		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, "statistic") <- "gpg"

		rval
	}

#' @rdname svygpg
#' @export
svygpg.DBIsvydesign <-
	function (formula, design, sex, ...){

		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(sex, 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(sex, design$db$connection, design$db$tablename,updates = design$updates, subset = design$subset)
			)

		NextMethod("svygpg", design)
	}