# svyrich: Richness measures (EXPERIMENTAL) In convey: Income Concentration Analysis with Complex Survey Samples

 svyrich R Documentation

## Richness measures (EXPERIMENTAL)

### Description

Estimate Peichl, Schaefer and Scheicher (2010) richness measures.

### Usage

```svyrich(formula, design, ...)

## S3 method for class 'survey.design'
svyrich(
formula,
design,
type_measure,
g,
type_thresh = "abs",
abs_thresh = NULL,
times = 1,
quantiles = 0.5,
na.rm = FALSE,
thresh = FALSE,
...
)

## S3 method for class 'svyrep.design'
svyrich(
formula,
design,
type_measure,
g,
type_thresh = "abs",
abs_thresh = NULL,
times = 1,
quantiles = 0.5,
na.rm = FALSE,
thresh = FALSE,
...
)

## S3 method for class 'DBIsvydesign'
svyrich(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. `...` passed to `svyarpt` `type_measure` A string "Cha", "FGTT1" or "FGTT2" defining the richness measure. `g` Richness preference parameter. `type_thresh` type of richness threshold. If "abs" the threshold is fixed and given the value of abs_thresh; if "relq" it is given by `times` times the quantile; if "relm" it is `times` times the mean. `abs_thresh` richness threshold value if type_thresh is "abs" `times` the multiple of the quantile or mean used in the richness threshold definition `quantiles` the quantile used used in the richness threshold definition `na.rm` Should cases with missing values be dropped? `thresh` return the richness threshold value

### 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.

### Note

This function is experimental and is subject to change in later versions.

### Author(s)

Guilherme Jacob, Djalma Pessoa and Anthony Damico

### References

Michal Brzezinski (2014). Statistical Inference for Richness Measures. Applied Economics, Vol. 46, No. 14, pp. 1599-1608, <doi:10.1080/00036846.2014.880106>

Andreas Peichl, Thilo Schaefer, and Christoph Scheicher (2010). Measuring richness and poverty: A micro data application to Europe and Germany. Review of Income and Wealth, Vol. 56, No.3, pp. 597-619.

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.

`svyfgt`

### 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 )

# concave FGT-like richness measure
# headcount ratio, richness threshold fixed
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=0,  abs_thresh=30000)
# richness gap index, richness threshold fixed
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=1,  abs_thresh=30000)
# headcount ratio, richness threshold equal to the median
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=0, type_thresh= "relq" )
# richness gap index, richness threshold equal to the median
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=1, type_thresh= "relq" )
# headcount ratio, richness threshold equal to the mean
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=0, type_thresh= "relm" )
# richness gap index, richness threshold equal to the mean
svyrich(~eqincome, des_eusilc, type_measure = "FGTT1" , g=1, type_thresh= "relm" )

#  using svrep.design:
# headcount ratio, richness threshold fixed
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=0, abs_thresh=30000 )
# richness gap index, richness threshold fixed
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=1, abs_thresh=30000 )
# headcount ratio, richness threshold equal to the median
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=0, type_thresh= "relq" )
# richness gap index, richness threshold equal to the median
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=1, type_thresh= "relq" )
# headcount ratio, richness threshold equal to the mean
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=0, type_thresh= "relm" )
# richness gap index, richness threshold equal to the mean
svyrich(~eqincome, des_eusilc_rep, type_measure = "FGTT1" , g=1, type_thresh= "relm" )

## Not run:

# 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, richness threshold fixed
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=0, abs_thresh=30000 )
# richness gap index, richness threshold fixed
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=1, abs_thresh=30000 )
# headcount ratio, richness threshold equal to the median
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=0, type_thresh= "relq" )
# richness gap index, richness threshold equal to the median
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=1, type_thresh= "relq" )
# headcount ratio, richness threshold equal to the mean
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=0, type_thresh= "relm" )
# richness gap index, richness threshold equal to the mean
svyrich(~eqincome, dbd_eusilc, type_measure = "FGTT1" , g=1, type_thresh= "relm" )

dbRemoveTable( conn , 'eusilc' )

dbDisconnect( conn , shutdown = TRUE )

## End(Not run)

```

convey documentation built on April 28, 2022, 1:06 a.m.