svylorenz | R Documentation |

Estimate the Lorenz curve, an inequality graph

```
svylorenz(formula, design, ...)
## S3 method for class 'survey.design'
svylorenz(
formula,
design,
quantiles = seq(0, 1, 0.1),
empirical = FALSE,
plot = TRUE,
add = FALSE,
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,
add = FALSE,
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, ...)
```

`formula` |
a formula specifying the income variable |

`design` |
a design object of class |

`...` |
additional arguments passed to |

`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 |

`plot` |
Should the Lorenz curve be plotted? Defaults to |

`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 |

`alpha` |
a number that especifies de confidence level for the graph. |

`na.rm` |
Should cases with missing values be dropped? Defaults to |

`deff` |
Return the design effect (see |

`linearized` |
Should a matrix of linearized variables be returned |

`influence` |
Should a matrix of (weighted) influence functions be returned? (for compatibility with |

`return.replicates` |
Return the replicate estimates? |

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.

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.

Guilherme Jacob, Djalma Pessoa and Anthony Damico

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`

```
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)
```

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