svyatk: Atkinson index

In convey: Income Concentration Analysis with Complex Survey Samples

Atkinson index

Description

Estimate the Atkinson index, an inequality measure

Usage

svyatk(formula, design, ...)

## S3 method for class 'survey.design'
svyatk(
  formula,
  design,
  epsilon = 1,
  na.rm = FALSE,
  deff = FALSE,
  linearized = FALSE,
  influence = FALSE,
  ...
)

## S3 method for class 'svyrep.design'
svyatk(
  formula,
  design,
  epsilon = 1,
  na.rm = FALSE,
  deff = FALSE,
  linearized = FALSE,
  return.replicates = FALSE,
  ...
)

## S3 method for class 'DBIsvydesign'
svyatk(formula, design, ...)

Arguments

formula	a formula specifying the income variable
design	a design object of class survey.design or class svyrep.design from the survey library.
...	future expansion
epsilon	a parameter that determines the sensivity towards inequality in the bottom of the distribution. Defaults to epsilon = 1.
na.rm	Should cases with missing values be dropped?
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)
return.replicates	Return the replicate estimates?

Details

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

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.

Author(s)

Guilherme Jacob, Djalma Pessoa and Anthony Damico

References

Matti Langel (2012). Measuring inequality in finite population sampling. PhD thesis: Universite de Neuchatel, URL https://doc.rero.ch/record/29204/files/00002252.pdf.

Martin Biewen and Stephen Jenkins (2002). Estimation of Generalized Entropy and Atkinson Inequality Indices from Complex Survey Data. DIW Discussion Papers, No.345, URL https://www.diw.de/documents/publikationen/73/diw_01.c.40394.de/dp345.pdf.

See Also

svygei

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)


# subset all designs to positive income and non-missing records only
des_eusilc_pos_inc <- subset( des_eusilc , eqincome > 0 )
des_eusilc_rep_pos_inc <- subset( des_eusilc_rep , eqincome > 0 )


# linearized design
svyatk( ~eqincome , des_eusilc_pos_inc, epsilon = .5 )
svyatk( ~eqincome , des_eusilc_pos_inc )
svyatk( ~eqincome , des_eusilc_pos_inc, epsilon = 2 )

# replicate-weighted design
svyatk( ~eqincome , des_eusilc_rep_pos_inc, epsilon = .5 )
svyatk( ~eqincome , des_eusilc_rep_pos_inc )
svyatk( ~eqincome , des_eusilc_rep_pos_inc, epsilon = 2 )


# subsetting
svyatk( ~eqincome , subset(des_eusilc_pos_inc, db040 == "Styria"), epsilon = .5 )
svyatk( ~eqincome , subset(des_eusilc_pos_inc, db040 == "Styria") )
svyatk( ~eqincome , subset(des_eusilc_pos_inc, db040 == "Styria"), epsilon = 2 )

svyatk( ~eqincome , subset(des_eusilc_rep_pos_inc, db040 == "Styria"), epsilon = .5 )
svyatk( ~eqincome , subset(des_eusilc_rep_pos_inc, db040 == "Styria") )
svyatk( ~eqincome , subset(des_eusilc_rep_pos_inc, db040 == "Styria"), epsilon = 2 )

## Not run: 

# linearized design using a variable with missings (but subsetted to remove negatives)
svyatk( ~py010n , subset(des_eusilc, py010n > 0 | is.na(py010n)), epsilon = .5 )
svyatk( ~py010n , subset(des_eusilc, py010n > 0 | is.na(py010n)), epsilon = .5 , na.rm=TRUE )

# replicate-weighted design using a variable with missings (but subsetted to remove negatives)
svyatk( ~py010n , subset(des_eusilc_rep, py010n > 0 | is.na(py010n)), epsilon = .5 )
svyatk( ~py010n , subset(des_eusilc_rep, py010n > 0 | is.na(py010n)), epsilon = .5 , 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 )


# subset all designs to positive income and non-missing records only
dbd_eusilc_pos_inc <- subset( dbd_eusilc , eqincome > 0 )


# database-backed linearized design
svyatk( ~eqincome , dbd_eusilc_pos_inc, epsilon = .5 )
svyatk( ~eqincome , dbd_eusilc_pos_inc )
svyatk( ~eqincome , dbd_eusilc_pos_inc, epsilon = 2 )

svyatk( ~eqincome , subset(dbd_eusilc_pos_inc, db040 == "Styria"), epsilon = .5 )
svyatk( ~eqincome , subset(dbd_eusilc_pos_inc, db040 == "Styria") )
svyatk( ~eqincome , subset(dbd_eusilc_pos_inc, db040 == "Styria"), epsilon = 2 )

# database-backed linearized design using a variable with missings
# (but subsetted to remove negatives)
svyatk( ~py010n , subset(dbd_eusilc, py010n > 0 | is.na(py010n)), epsilon = .5 )
svyatk( ~py010n , subset(dbd_eusilc, py010n > 0 | is.na(py010n)), epsilon = .5 , na.rm=TRUE )


dbRemoveTable( conn , 'eusilc' )

dbDisconnect( conn , shutdown = TRUE )


## End(Not run)

convey documentation built on Oct. 16, 2024, 5:10 p.m.