# svylorenz: Lorenz curve In convey: Income Concentration Analysis with Complex Survey Samples

 svylorenz R Documentation

## Lorenz curve

### Description

Estimate the Lorenz curve, an inequality graph

### Usage

``````svylorenz(formula, design, ...)

## S3 method for class 'survey.design'
svylorenz(
formula,
design,
quantiles = seq(0, 1, 0.1),
empirical = FALSE,
plot = TRUE,
curve.col = "red",
ci = TRUE,
alpha = 0.05,
na.rm = FALSE,
deff = FALSE,
linearized = FALSE,
influence = FALSE,
...
)

## S3 method for class 'svyrep.design'
svylorenz(
formula,
design,
quantiles = seq(0, 1, 0.1),
empirical = FALSE,
plot = TRUE,
curve.col = "red",
ci = TRUE,
alpha = 0.05,
na.rm = FALSE,
deff = FALSE,
linearized = FALSE,
return.replicates = FALSE,
...
)

## S3 method for class 'DBIsvydesign'
svylorenz(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. `...` additional arguments passed to `plot` methods `quantiles` a sequence of probabilities that defines the quantiles sum to be calculated `empirical` Should an empirical Lorenz curve be estimated as well? Defaults to `FALSE`. `plot` Should the Lorenz curve be plotted? Defaults to `TRUE`. `add` Should a new curve be plotted on the current graph? `curve.col` a string defining the color of the curve. `ci` Should the confidence interval be plotted? Defaults to `TRUE`. `alpha` a number that especifies de confidence level for the graph. `na.rm` Should cases with missing values be dropped? Defaults to `FALSE`. `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.

Notice that the 'empirical' curve is observation-based and is the one actually used to calculate the Gini index. On the other hand, the quantile-based curve is used to estimate the shares, SEs and confidence intervals.

This way, as the number of quantiles of the quantile-based function increases, the quantile-based curve approacches the observation-based curve.

### Value

Object of class "`oldsvyquantile`", which are vectors with a "`quantiles`" attribute giving the proportion of income below that quantile, and a "`SE`" attribute giving the standard errors of the estimates.

### Author(s)

Guilherme Jacob, Djalma Pessoa and Anthony Damico

### References

Milorad Kovacevic and David Binder (1997). Variance Estimation for Measures of Income Inequality and Polarization - The Estimating Equations Approach. Journal of Official Statistics, Vol.13, No.1, 1997. pp. 41 58. URL https://www.scb.se/contentassets/ca21efb41fee47d293bbee5bf7be7fb3/variance-estimation-for-measures-of-income-inequality-and-polarizationâ€”the-estimating-equations-approach.pdf.

Shlomo Yitzhaki and Robert Lerman (1989). Improving the accuracy of estimates of Gini coefficients. Journal of Econometrics, Vol.42(1), pp. 43-47, September.

Matti Langel (2012). Measuring inequality in finite population sampling. PhD thesis. URL http://doc.rero.ch/record/29204.

`oldsvyquantile`

### 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 )
svylorenz( ~eqincome , des_eusilc, seq(0,1,.05), alpha = .01 )

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

svylorenz( ~eqincome , des_eusilc_rep, seq(0,1,.05), alpha = .01 )

## Not run:

# linearized design using a variable with missings
svylorenz( ~py010n , des_eusilc, seq(0,1,.05), alpha = .01 )
svylorenz( ~py010n , des_eusilc, seq(0,1,.05), alpha = .01, na.rm = TRUE )
# demonstration of `curve.col=` and `add=` parameters
svylorenz( ~eqincome , des_eusilc, seq(0,1,.05), alpha = .05 , add = TRUE , curve.col = 'green' )
# replicate-weighted design using a variable with missings
svylorenz( ~py010n , des_eusilc_rep, seq(0,1,.05), alpha = .01 )
svylorenz( ~py010n , des_eusilc_rep, seq(0,1,.05), alpha = .01, 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 )

svylorenz( ~eqincome , dbd_eusilc, seq(0,1,.05), alpha = .01 )

# highlithing the difference between the quantile-based curve and the empirical version:
svylorenz( ~eqincome , dbd_eusilc, seq(0,1,.5), empirical = TRUE, ci = FALSE, curve.col = "green" )
svylorenz( ~eqincome , dbd_eusilc, seq(0,1,.5), alpha = .01, add = TRUE )
legend( "topleft", c("Quantile-based", "Empirical"), lwd = c(1,1), col = c("red", "green"))
# as the number of quantiles increases, the difference between the curves gets smaller
svylorenz( ~eqincome , dbd_eusilc, seq(0,1,.01), empirical = TRUE, ci = FALSE, curve.col = "green" )
svylorenz( ~eqincome , dbd_eusilc, seq(0,1,.01), alpha = .01, add = TRUE )
legend( "topleft", c("Quantile-based", "Empirical"), lwd = c(1,1), col = c("red", "green"))

dbRemoveTable( conn , 'eusilc' )

dbDisconnect( conn , shutdown = TRUE )

## End(Not run)

``````

convey documentation built on May 29, 2024, 4:18 a.m.