convey (version 1.0.1)

svyfgt: FGT measure of poverty

Description

Estimate the FGT measure.

Usage

svyfgt(formula, design, ...)
# S3 method for survey.design
svyfgt(
  formula,
  design,
  g,
  type_thresh = "abs",
  abs_thresh = NULL,
  percent = 0.6,
  quantiles = 0.5,
  na.rm = FALSE,
  thresh = FALSE,
  deff = FALSE,
  linearized = FALSE,
  influence = FALSE,
  ...
)
# S3 method for svyrep.design
svyfgt(
  formula,
  design,
  g,
  type_thresh = "abs",
  abs_thresh = NULL,
  percent = 0.6,
  quantiles = 0.5,
  na.rm = FALSE,
  thresh = FALSE,
  deff = FALSE,
  linearized = FALSE,
  return.replicates = FALSE,
  ...
)
# S3 method for DBIsvydesign
svyfgt(formula, design, ...)

Value

Object of class "cvystat", which are vectors with a "var" attribute giving the variance and a "statistic" attribute giving the name of the statistic.

Arguments

formula

a formula specifying the income variable

design

a design object of class survey.design or class svyrep.design from the survey library.

...

passed to svyarpr and svyarpt

g

If g=0 estimates the headcount ratio; If g=1 estimates the average normalised poverty gap, and if g=2 estimates the average squared normalised poverty gap

type_thresh

type of poverty threshold. If "abs" the threshold is fixed and given the value of abs_thresh; if "relq" it is given by percent times the quantile; if "relm" it is percent times the mean.

abs_thresh

poverty threshold value if type_thresh is "abs"

percent

the multiple of the the quantile or mean used in the poverty threshold definition

quantiles

the quantile used used in the poverty threshold definition

na.rm

Should cases with missing values be dropped?

thresh

return the poverty threshold value

deff

Return the design effect (see survey::svymean)

linearized

Should a matrix of linearized variables be returned?

influence

Should a matrix of (weighted) influence functions be returned? (for compatibility with svyby). Not implemented yet for linearized designs.

return.replicates

Return the replicate estimates?

Author

Djalma Pessoa, Anthony Damico, and Guilherme Jacob

Details

you must run the convey_prep function on your survey design object immediately after creating it with the svydesign or svrepdesign function.

The FGT poverty measures have three special cases. When g = 0, the FGT measure is the headcount poverty rate, assigning the same "poverty-weight" to all persons below the poverty line. When g = 1, it becomes the poverty gap ratio, a measure which accounts for the intensity of income shortfall among the poor. When g = 2. it becomes the squared poverty gap ratio, a measure that also accounts for inequality of poverty intesity across the poor. The g is a poverty sensitivity parameter, adding more weight to people with greater income shortfalls as it increases.

References

James Foster, Joel Greer and Erik Thorbecke (1984). A class of decomposable poverty measures. Econometrica, Vol.52, No.3, pp. 761-766.

Y.G. Berger and C. J. Skinner (2003), Variance estimation for a low income proportion. Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 52, No. 4, pp. 457-468. DOI tools:::Rd_expr_doi("10.1111/1467-9876.00417")

Buhong Zheng (2001). Statistical inference for poverty measures with relative poverty lines. Journal of Econometrics, Vol. 101, pp. 337-356.

Guillaume Osier (2009). Variance estimation for complex indicators of poverty and inequality. Journal of the European Survey Research Association, Vol.3, No.3, pp. 167-195, ISSN 1864-3361, 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 https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X19990024882.

See Also

svyarpt

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 )

# replicate-weighted design
des_eusilc_rep <- as.svrepdesign( des_eusilc , type = "bootstrap" )
des_eusilc_rep <- convey_prep( des_eusilc_rep )

# headcount ratio, poverty threshold fixed
svyfgt(~eqincome, des_eusilc, g=0,  abs_thresh=10000)
# poverty gap index, poverty threshold fixed
svyfgt(~eqincome, des_eusilc, g=1,  abs_thresh=10000)
# headcount ratio, poverty threshold equal to arpt
svyfgt(~eqincome, des_eusilc, g=0, type_thresh= "relq" , thresh = TRUE)
# poverty gap index, poverty threshold equal to arpt
svyfgt(~eqincome, des_eusilc, g=1, type_thresh= "relq", thresh = TRUE)
# headcount ratio, poverty threshold equal to .6 times the mean
svyfgt(~eqincome, des_eusilc, g=0, type_thresh= "relm", thresh = TRUE)
# poverty gap index, poverty threshold equal to 0.6 times the mean
svyfgt(~eqincome, des_eusilc, g=1, type_thresh= "relm" , thresh = TRUE)

#  using svrep.design:
# headcount ratio, poverty threshold fixed
svyfgt(~eqincome, des_eusilc_rep, g=0,  abs_thresh=10000)
# poverty gap index, poverty threshold fixed
svyfgt(~eqincome, des_eusilc, g=1,  abs_thresh=10000)
# headcount ratio, poverty threshold equal to arpt
svyfgt(~eqincome, des_eusilc_rep, g=0, type_thresh= "relq" , thresh = TRUE)
# poverty gap index, poverty threshold equal to arpt
svyfgt(~eqincome, des_eusilc, g=1, type_thresh= "relq", thresh = TRUE)
# headcount ratio, poverty threshold equal to .6 times the mean
svyfgt(~eqincome, des_eusilc_rep, g=0, type_thresh= "relm" , thresh = TRUE)
# poverty gap index, poverty threshold equal to 0.6 times the mean
svyfgt(~eqincome, des_eusilc_rep, g=1, type_thresh= "relm", thresh = TRUE)

if (FALSE) {

# 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 )

# headcount ratio, poverty threshold fixed
svyfgt(~eqincome, dbd_eusilc, g=0, abs_thresh=10000)
# poverty gap index, poverty threshold fixed
svyfgt(~eqincome, dbd_eusilc, g=1, abs_thresh=10000)
# headcount ratio, poverty threshold equal to arpt
svyfgt(~eqincome, dbd_eusilc, g=0, type_thresh= "relq", thresh = TRUE)
# poverty gap index, poverty threshold equal to arpt
svyfgt(~eqincome, dbd_eusilc, g=1, type_thresh= "relq")
# headcount ratio, poverty threshold equal to .6 times the mean
svyfgt(~eqincome, dbd_eusilc, g=0, type_thresh= "relm")
# poverty gap index, poverty threshold equal to 0.6 times the mean
svyfgt(~eqincome, dbd_eusilc, g=1, type_thresh= "relm")

dbRemoveTable( conn , 'eusilc' )

dbDisconnect( conn , shutdown = TRUE )

}