linrmpg {vardpoor}

Linearization of the relative median at-risk-of-poverty gap

Description

Estimate the relative median at-risk-of-poverty gap, which is defined as the relative difference between the median equalized disposable income of persons below the At Risk of Poverty Threshold and the At Risk of Poverty Threshold itself (expressed as a percentage of the at-risk-of-poverty threshold) and its linearization.

Usage

linrmpg(
  Y,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  percentage = 60,
  order_quant = 50,
  var_name = "lin_rmpg",
  checking = TRUE
)

Arguments

Y

Study variable (for example equalized disposable income). One dimensional object convertible to one-column data.table or variable name as character, column number.

id

Optional variable for unit ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.

weight

Optional weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number.

sort

Optional variable to be used as tie-breaker for sorting. One dimensional object convertible to one-column data.table or variable name as character, column number.

Dom

Optional variables used to define population domains. If supplied, linearization of the relative median at-risk-of-poverty gap is done for each domain. An object convertible to data.table or variable names as character vector, column numbers.

period

Optional variable for survey period. If supplied, linearization of the relative median at-risk-of-poverty gap is done for each time period. Object convertible to data.table or variable names as character, column numbers.

dataset

Optional survey data object convertible to data.table.

percentage

A numeric value in range [0,100] for p in the formula for poverty threshold computation:

\frac{p}{100} \cdot Z_{\frac{\alpha}{100}}.

For example, to compute poverty threshold equal to 60% of some income quantile, p should be set equal to 60.

order_quant

A numeric value in range [0,100] for \alpha in the formula for poverty threshold computation:

\frac{p}{100} \cdot Z_{\frac{\alpha}{100}}.

For example, to compute poverty threshold equal to some percentage of median income, \alpha should be set equal to 50.

var_name

A character specifying the name of the linearized variable.

checking

Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

return A list with two objects are returned by the function:

• value - a data.table containing the estimated relative median at-risk-of-poverty gap (in percentage).

• lin - a data.table containing the linearized variables of the relative median at-risk-of-poverty gap (in percentage).

References

Working group on Statistics on Income and Living Conditions (2004) Common cross-sectional EU indicators based on EU-SILC; the gender pay gap. EU-SILC 131-rev/04, Eurostat.
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/pub/12-001-x/1999002/article/4882-eng.pdf.

See Also

linarpt, linarpr, linpoormed, varpoord, vardcrospoor, vardchangespoor

Examples

library("data.table")
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)

# Full population
d <- linrmpg(Y = "eqIncome", id = "IDd",
             weight = "rb050", Dom = NULL,
             dataset = dataset1, percentage = 60,
             order_quant = 50L)
d$value
d$threshold
  
## Not run: 
# By domains
dd <- linrmpg(Y = "eqIncome", id = "IDd",
              weight = "rb050", Dom = "db040",
              dataset = dataset1, percentage = 60,
              order_quant = 50L)
dd$value
## End(Not run)