vardpoor (version 0.20.1)

linarpt: Linearization of at-risk-of-poverty threshold

Description

Estimates the at-risk-of-poverty threshold (defined as percentage (usually 60%) of equalised disposable income after social transfers quantile (usually median)) and computes linearized variable for variance estimation.

Usage

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

Arguments

Y

Study variable (for example equalised disposable income after social transfers). 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 at-risk-of-poverty threshold is done for each domain. An object convertible to data.table or variable names as character vector, column numbers as numeric vector.

period

Optional variable for survey period. If supplied, linearization of at-risk-of-poverty threshold is done for each survey period. Object convertible to data.table or variable names as character, column numbers as numeric vector.

dataset

Optional survey data object convertible to data.table.

percentage

A numeric value in range \(\left[ 0,100 \right]\) for \(p\) in the formula for at-risk-of-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 \(\left[ 0,100 \right]\) for \(\alpha\) in the formula for at-risk-of-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.

Value

A list with three objects are returned:

• quantile - a data.table containing the estimated value of the quantile used for at-risk-of-poverty threshold estimation.

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

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

Details

The implementation strictly follows the Eurostat definition.

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

linarpr, incPercentile, varpoord , vardcrospoor, vardchangespoor

Examples

# NOT RUN {
library("data.table") 
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)

# Full population
d1 <- linarpt(Y = "eqIncome", id = "IDd",
              weight = "rb050", Dom = NULL,
              dataset = dataset1, percentage = 60,
              order_quant = 50L)
d1$value

# }
# NOT RUN {
# By domains
d2 <- linarpt(Y = "eqIncome", id = "IDd",
              weight = "rb050", Dom = "db040",
              dataset = dataset1, percentage = 60,
              order_quant = 50L)
d2$value
# }
# NOT RUN {
 
# }