Package 'vardpoor'

Extra variables for domain estimation

Description

The function computes extra variables for domain estimation. Each unique D row defines a domain. Extra variables are computed for each Y variable.

Usage

domain(Y, D, dataset = NULL, checking = TRUE)

Arguments

Y	Matrix of study variables. Any object convertible to data.table with numeric values, NA values are not allowed. Object convertible to data.table or variable names as character, column numbers.
D	Matrix of domain variables. Any object convertible to data.table. The number of rows of D must match the number of rows of Y. Duplicated names are not allowed. Object convertible to data.table or variable names as character, column numbers.
dataset	Optional survey data object convertible to data.table.
checking	Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

Value

Numeric data.table containing extra variables for domain estimation.

References

Carl-Erik Sarndal, Bengt Swensson, Jan Wretman. Model Assisted Survey Sampling. Springer-Verlag, 1992, p.70.

See Also

vardom, vardomh

Examples

### Example 0
 
domain(Y = 1, D = "A")
 
  
### Example 1

Y1 <- as.matrix(1 : 10)
colnames(Y1) <- "Y1"
D1 <- as.matrix(rep(1, 10))
colnames(D1) <- "D1"
domain(Y = Y1, D = D1)
  
### Example 2
Y <- matrix(1 : 20, 10, 2)
colnames(Y) <- paste0("Y", 1 : 2)
D <- matrix(rep(1 : 2, each = 5), 10, 1)
colnames(D) <- "D"
domain(Y, D)

### Example 3
Y <- matrix(1 : 20, 10, 2)
colnames(Y) <- paste0("Y", 1 : 2)
D <- matrix(rep(1 : 4, each = 5), 10, 2)
colnames(D) <- paste0("D", 1 : 2)
domain(Y, D)
  
### Example 4
Y <- matrix(1 : 20, 10, 2)
colnames(Y) <- paste0("Y", 1 : 2)
D <- matrix(c(rep(1 : 2, each = 5), rep(3, 10)), 10, 2)
colnames(D) <- paste0("D", 1 : 2)
domain(Y, D)

---

Estimation of weighted percentiles

Description

The function computes the estimates of weighted percentiles.

Usage

incPercentile(
  Y,
  weights = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  k = c(20, 80),
  dataset = NULL,
  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.
weights	Optional weight variable. One dimensional object convert 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, the estimates of percentiles are computed 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 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.
k	A vector of values between 0 and 100 specifying the percentiles to be computed (0 gives the minimum, 100 gives the maximum).
dataset	Optional survey data object convertible to data.table.
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 data.table containing the estimates of weighted income percentiles specified by k.

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.

See Also

linarpt, linarpr, linqsr

Examples

library("laeken")
data("eusilc")
incPercentile(Y = "eqIncome", weights = "rb050", Dom = "db040", dataset = eusilc)

---

Linearization of the ratio estimator

Description

Computes linearized variable for the ratio estimator.

Usage

lin.ratio(
  Y,
  Z,
  weight,
  Dom = NULL,
  dataset = NULL,
  percentratio = 1,
  checking = TRUE
)

Arguments

Y	Matrix of numerator variables. Any object convertible to data.table with numeric values, NA values are not allowed.
Z	Matrix of denominator variables. Any object convertible to data.table with numeric values, NA values are not allowed.
weight	Weight variable. One dimensional object convertible to one-column data.table.
Dom	Optional variables used to define population domains. If supplied, the linearized variables are computed for each domain. An object convertible to data.table.
dataset	Optional survey data object convertible to data.table.
percentratio	Positive integer value. All linearized variables are multiplied with percentratio value, by default - 1.
checking	Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

Value

The function returns the data.table of the linearized variables for the ratio estimator.

References

Carl-Erik Sarndal, Bengt Swensson, Jan Wretman. Model Assisted Survey Sampling. Springer-Verlag, 1992, p.178.

See Also

domain, vardom, vardomh, vardcros, vardchanges, vardannual

Examples

library("data.table")
Y <- data.table(Y = rchisq(10, 3))
Z <- data.table(Z = rchisq(10, 3))
weights <- rep(2, 10)
data.table(Y, Z, weights,
           V1 = lin.ratio(Y, Z, weights, percentratio = 1),
           V10 = lin.ratio(Y, Z, weights, percentratio = 10),
           V100 = lin.ratio(Y, Z, weights, percentratio = 100))

---

Linearization of at-risk-of-poverty rate

Description

Estimates the at-risk-of-poverty rate (defined as the proportion of persons with equalized disposable income below at-risk-of-poverty threshold) and computes linearized variable for variance estimation.

Usage

linarpr(
  Y,
  id = NULL,
  weight = NULL,
  Y_thres = NULL,
  wght_thres = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  percentage = 60,
  order_quant = 50,
  var_name = "lin_arpr",
  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 or logical vector).
weight	Optional weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector).
Y_thres	Variable (for example equalized disposable income) used for computation and linearization of poverty threshold. One dimensional object convertible to one-column data.table or variable name as character, column number. Variable specified for inc is used as income_thres if income_thres is not defined.
wght_thres	Weight variable used for computation and linearization of poverty threshold. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector. Variable specified for weight is used as wght_thres if wght_thres is not defined.
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 at-risk-of-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 at-risk-of-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.

Details

The implementation strictly follows the Eurostat definition.

Value

A list with four objects are returned:

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

• threshold - a data.table containing the estimated at-risk-of-poverty threshold.

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

• lin - a data.table containing the linearized variables of the at-risk-of-poverty rate (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, varpoord, vardcrospoor, vardchangespoor

Examples

library("data.table")
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
    
# Full population
d <- linarpr(Y = "eqIncome", id = "IDd",
             weight = "rb050", Dom = NULL,
             dataset = dataset1, percentage = 60,
             order_quant = 50L)
d$value
    
## Not run: 
# By domains
dd <- linarpr(Y = "eqIncome", id = "IDd",
              weight = "rb050", Dom = "db040",
              dataset = dataset1, percentage = 60,
              order_quant = 50L)
dd
## End(Not run)

---

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.

Details

The implementation strictly follows the Eurostat definition.

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).

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

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
## End(Not run)

---

Linearization of the aggregate replacement ratio

Description

Estimates the aggregate replacement ratio (defined as the gross median individual pension income of the population aged 65-74 relative to the gross median individual earnings from work of the population aged 50-59, excluding other social benefits) and computes linearized variable for variance estimation.

Usage

linarr(
  Y,
  Y_den,
  id = NULL,
  age,
  pl085,
  month_at_work,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  order_quant = 50,
  var_name = "lin_arr",
  checking = TRUE
)

Arguments

Y	Numerator variable (for gross pension income). One dimensional object convertible to one-column data.table or variable name as character, column number.
Y_den	Denominator variable (for example gross individual earnings). 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.
age	Age variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
pl085	Retirement variable (Number of months spent in retirement or early retirement). One dimensional object convertible to one-column data.table or variable name as character, column number.
month_at_work	Variable for total number of month at work (sum of the number of months spent at full-time work as employee, number of months spent at part-time work as employee, number of months spent at full-time work as self-employed (including family worker), number of months spent at part-time work as self-employed (including family worker)). 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.
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 at-risk-of-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.

Details

The implementation strictly follows the Eurostat definition.

Value

A list with four objects are returned:

• value - a data.table containing the estimated the aggregate replacement ratio.

• lin - a data.table containing the linearized variables of the aggregate replacement ratio.

References

Working group on Statistics on Income and Living Conditions (2015) Task 5 - Improvement and optimization of calculation of net change. LC- 139/15/EN, Eurostat.
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

varpoord, vardcrospoor, vardchangespoor

Examples

library("data.table")
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
dataset1$pl085 <- 12 * trunc(runif(nrow(dataset1), 0, 2))
dataset1$month_at_work <- 12 * trunc(runif(nrow(dataset1), 0, 2))
    
# Full population
d <- linarr(Y = "eqIncome", Y_den = "eqIncome",
            id = "IDd", age = "age",  
            pl085 = "pl085", month_at_work = "month_at_work",
            weight = "rb050",  Dom = NULL,
            dataset = dataset1, order_quant = 50L)
d$value
    
## Not run: 
# By domains
dd <- linarr(Y = "eqIncome", Y_den = "eqIncome",
             id = "IDd", age = "age",  
             pl085 = "pl085", month_at_work = "month_at_work",
             weight = "rb050",  Dom = "db040",
             dataset = dataset1, order_quant = 50L)
 dd
## End(Not run)

---

Linearization of the Gini coefficient I

Description

Estimate the Gini coefficient, which is a measure for inequality, and its linearization.

Usage

lingini(
  Y,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  var_name = "lin_gini",
  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 Gini 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 Gini 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.
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 Gini coefficients (in percentage) by G. Osier and Eurostat. lin - a data.table containing the linearized variables of the Gini coefficients (in percentage) by G. Osier.

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

lingini2, linqsr, varpoord, vardcrospoor, vardchangespoor

Examples

library("laeken")
library("data.table")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)[1 : 3,]
 
# Full population
dat1 <- lingini(Y = "eqIncome", id = "IDd",
                weight = "rb050", dataset = dataset1)
dat1$value
  
## Not run: 
# By domains
dat2 <- lingini(Y = "eqIncome", id = "IDd", weight = "rb050",
                Dom = c("db040"), dataset = dataset1)
dat2$value
## End(Not run)

---

Linearization of the Gini coefficient II

Description

Estimate the Gini coefficient, which is a measure for inequality, and its linearization.

Usage

lingini2(
  Y,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  var_name = "lin_gini2",
  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 Gini 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 Gini 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.
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 two objects are returned by the function:

• value - a data.table containing the estimated Gini coefficients (in percentage) by Langel and Tille (2012) and Eurostat.

• lin - a data.table containing the linearized variables of the Gini coefficients (in percentage) by Langel and Tille (2012).

References

Eric Graf, Yves Tille, Variance Estimation Using Linearization for Poverty and Social Exclusion Indicators, Survey Methodology, June 2014 61 Vol. 40, No. 1, pp. 61-79, Statistics Canada, Catalogue no. 12-001-X, URL https://www150.statcan.gc.ca/n1/pub/12-001-x/12-001-x2014001-eng.pdf
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.
Matti Langel, Yves Tille, Corrado Gini, a pioneer in balanced sampling and inequality theory. Metron - International Journal of Statistics, 2011, vol. LXIX, n. 1, pp. 45-65, URL doi:10.1007/BF03263549.
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.

See Also

lingini, linqsr, varpoord, vardcrospoor, vardchangespoor

Examples

library("data.table")
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
    
# Full population
dat1 <- lingini2(Y = "eqIncome", id = "IDd",
                 weight = "rb050",  dataset = dataset1)
dat1$value
    
## Not run: 
# By domains
dat2 <- lingini2(Y = "eqIncome", id = "IDd",
                 weight = "rb050", Dom = c("db040"),
                 dataset = dataset1)
dat2$value
## End(Not run)

---

Linearization of the gender pay (wage) gap.

Description

Estimation of gender pay (wage) gap and computation of linearized variables for variance estimation.

Usage

lingpg(
  Y,
  gender = NULL,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  var_name = "lin_gpg",
  checking = TRUE
)

Arguments

Y	Study variable (for example the gross hourly earning). One dimensional object convertible to one-column data.table or variable name as character, column number.
gender	Numerical variable for gender, where 1 is for males, but 2 is for females. 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, estimation and linearization of gender pay (wage) 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, estimation and linearization of gender pay (wage) 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.
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 two objects are returned:

• value - a data.table containing the estimated gender pay (wage) gap (in percentage).

• lin - a data.table containing the linearized variables of the gender pay (wage) gap (in percentage) for variance estimation.

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

linqsr, lingini, varpoord , vardcrospoor, vardchangespoor

Examples

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

dataset1[, IDnum := .I]

setnames(dataset1, "sex", "sexf")
dataset1[sexf == "male", sex:= 1]
dataset1[sexf == "female", sex:= 2]
  
# Full population
gpgs1 <- lingpg(Y = "earningsHour", gender = "sex",
                id = "IDnum", weight = "weights",
                dataset = dataset1)
gpgs1$value
  
## Not run: 
# Domains by education
gpgs2 <- lingpg(Y = "earningsHour", gender = "sex",
                id = "IDnum", weight = "weights",
                Dom = "education", dataset = dataset1)
gpgs2$value
    
# Sort variable
gpgs3 <- lingpg(Y = "earningsHour", gender = "sex",
                id = "IDnum", weight = "weights",
                sort = "IDnum", Dom = "education",
                dataset = dataset1)
gpgs3$value
    
# Two survey periods
dataset1[, year := 2010]
dataset2 <- copy(dataset1)
dataset2[, year := 2011]
dataset1 <- rbind(dataset1, dataset2)

gpgs4 <- lingpg(Y = "earningsHour", gender = "sex",
                id = "IDnum", weight = "weights", 
                sort = "IDnum", Dom = "education",
                period = "year", dataset = dataset1)
gpgs4$value
names(gpgs4$lin)
## End(Not run)

---

Linearization of the median income of individuals below the At Risk of Poverty Threshold

Description

Estimation of the median income of individuals below At Risk of Poverty Threshold and computation of linearized variable for variance estimation. The At Risk of Poverty Threshold is estimated for the whole population always. The median income is estimated for the whole population or for each domain.

Usage

linpoormed(
  Y,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  percentage = 60,
  order_quant = 50,
  var_name = "lin_poormed",
  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 median income of persons below a poverty threshold 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 median income of persons below a poverty threshold 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.

Value

A list with two objects are returned by the function:

• value - a data.table containing the estimated median income of individuals below the At Risk of Poverty Threshold.

• lin - a data.table containing the linearized variables of the median income below the At Risk of Poverty Threshold.

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, linrmpg, varpoord, vardcrospoor, vardchangespoor

Examples

library("laeken")
library("data.table")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
 
# Full population
d <- linpoormed(Y = "eqIncome", id = "IDd",
                weight = "rb050", Dom = NULL,
                dataset = dataset1, percentage = 60,
                order_quant = 50L)
  
## Not run: 
# Domains by location of houshold
dd <- linpoormed(Y = "eqIncome", id = "IDd",
                 weight = "rb050", Dom = "db040",
                 dataset = dataset1, percentage = 60,
                 order_quant = 50L)
dd
## End(Not run)

---

Linearization of the Quintile Share Ratio

Description

Estimate the Quintile Share Ratio, which is defined as the ratio of the sum of equalized disposable income received by the top 20% to the sum of equalized disposable income received by the bottom 20%, and its linearization.

Usage

linqsr(
  Y,
  id = NULL,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  alpha = 20,
  var_name = "lin_qsr",
  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 income quantile share ratio 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 income quantile share ratio 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.
alpha	a numeric value in range $[0,100]$ for the order of the Quintile Share Ratio.
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 two objects are returned by the function:

• value - a data.table containing the estimated Quintile Share Ratio by G. Osier and Eurostat papers.

• lin - a data.table containing the linearized variables of the Quintile Share Ratio by G. Osier paper.

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

incPercentile, varpoord, vardcrospoor, vardchangespoor

Examples

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

# Full population
dd <- linqsr(Y = "eqIncome", id = "IDd",
             weight = "rb050", Dom = NULL,
             dataset = dataset1, alpha = 20)
dd$value
 
## Not run: 
# By domains
dd <- linqsr(Y = "eqIncome", id = "IDd",
             weight = "rb050", Dom = "db040",
             dataset = dataset1, alpha = 20)
dd$value
## End(Not run)

---

Linearization of the relative median income ratio

Description

Estimates the relative median income ratio (defined as the ratio of the median equivalised disposable income of people aged above age to the median equivalised disposable income of those aged below 65) and computes linearized variable for variance estimation.

Usage

linrmir(
  Y,
  id = NULL,
  age,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  order_quant = 50,
  var_name = "lin_rmir",
  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.
age	Age variable. 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.
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 the relative median income ratio 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.

Details

The implementation strictly follows the Eurostat definition.

Value

A list with four objects are returned:

• value - a data.table containing the estimated relative median income ratio.

• lin - a data.table containing the linearized variables of the relative median income ratio.

References

Working group on Statistics on Income and Living Conditions (2015) Task 5 - Improvement and optimization of calculation of net change. LC- 139/15/EN, Eurostat.
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

varpoord, vardcrospoor, vardchangespoor

Examples

library("laeken")
library("data.table")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
 
# Full population
d <- linrmir(Y = "eqIncome", id = "IDd",  age = "age",
             weight = "rb050", Dom = NULL,  
             dataset = dataset1, order_quant = 50L)
 
## Not run: 
 # By domains
 dd <- linrmir(Y = "eqIncome", id = "IDd", age = "age",
               weight = "rb050", Dom = "db040",
               dataset = dataset1, order_quant = 50L)
 dd
## End(Not run)

---

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)

---

Residual estimation of calibration

Description

Computes the estimation residuals of calibration.

Usage

residual_est(Y, X, weight, q, dataset = NULL, checking = TRUE)

Arguments

Y	Matrix of the variable of interest.
X	Matrix of the auxiliary variables for the calibration estimator. This is the matrix of the sample calibration variables.
weight	Weight variable. One dimensional object convertible to one-column data.frame.
q	Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column data.frame.
dataset	Optional survey data object convertible to data.table.
checking	Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

Details

The function implements the following estimator:

$e_k=Y_k-X_k^{'}B$

where

$\hat{B} = \left(\sum_{s} weight_k q_k X_k X^{'}_{k} \right)^{-1} \left(\sum_{s} weight_k q_k X_k Y_k \right)$

.

Value

A list with objects are returned by the function:

• residuals - a numeric data.table containing the estimated residuals of calibration.

• betas - a numeric data.table containing the estimated coefficients of calibration.

References

Sixten Lundstrom and Carl-Erik Sarndal. Estimation in the presence of Nonresponse and Frame Imperfections. Statistics Sweden, 2001, p. 43-44.

See Also

domain, lin.ratio, linarpr, linarpt, lingini, lingini2, lingpg, linpoormed, linqsr, linrmpg, vardom, vardomh, varpoord, variance_est, variance_othstr

Examples

Y <- matrix(rchisq(10, 3), 10, 1)
X <- matrix(rchisq(20, 3), 10, 2)
w <- rep(2, 10)
q <- rep(1, 10)
residual_est(Y, X, w, q)

### Test2
Y <- matrix(rchisq(10, 3), 10, 1)
X <- matrix(c(rchisq(10, 2), rchisq(10, 2) + 10), 10, 2)
w <- rep(2, 10)
q <- rep(1, 10)
residual_est(Y, X, w, q)
as.matrix(lm(Y ~ X - 1, weights = w * q)$residuals)

---

The estimation of the simple random sampling.

Description

Computes the estimation of the simple random sampling.

Usage

var_srs(Y, w = rep(1, length(Y)))

Arguments

Y	The variables of interest.
w	Weight variable. One dimensional object convertible to one-column data.frame.

Value

A list with objects are returned by the function:

• S2p - a data.table containing the values of the variance estimation of the population.

• varsrs - a data.table containing the values of the variance estimation of the simple random sampling.

References

Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en

See Also

vardom, vardomh, varpoord

Examples

Ys <- matrix(rchisq(10, 3), 10, 1)
ws <- c(rep(2, 5), rep(3, 5))
var_srs(Ys, ws)

---

Variance estimation for measures of annual net change or annual for single and multistage stage cluster sampling designs

Description

Computes the variance estimation for measures of annual net change or annual for single and multistage stage cluster sampling designs.

Usage

vardannual(
  Y,
  H,
  PSU,
  w_final,
  ID_level1,
  ID_level2,
  Dom = NULL,
  Z = NULL,
  gender = NULL,
  country = NULL,
  years,
  subperiods,
  dataset = NULL,
  year1 = NULL,
  year2 = NULL,
  X = NULL,
  countryX = NULL,
  yearsX = NULL,
  subperiodsX = NULL,
  X_ID_level1 = NULL,
  ind_gr = NULL,
  g = NULL,
  q = NULL,
  datasetX = NULL,
  frate = 0,
  percentratio = 1,
  use.estVar = FALSE,
  use.gender = FALSE,
  confidence = 0.95,
  method = "cros"
)

Arguments

Y	Variables of interest. Object convertible to data.table or variable names as character, column numbers.
H	The unit stratum variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
PSU	Primary sampling unit variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
w_final	Weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level1	Variable for level1 ID codes. 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, variables are calculated for each domain. An object convertible to data.table or variable names as character vector, column numbers.
Z	Optional variables of denominator for ratio estimation. If supplied, the ratio estimation is computed. Object convertible to data.table or variable names as character, column numbers. This variable is NULL by default.
gender	Numerical variable for gender, where 1 is for males, but 2 is for females. One dimensional object convertible to one-column data.table or variable name as character, column number.
country	Variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
years	Variable for the all survey years. The values for each year are computed independently. Object convertible to data.table or variable names as character, column numbers.
subperiods	Variable for the all survey sub-periods. The values for each sub-period are computed independently. Object convertible to data.table or variable names as character, column numbers.
year1	The vector of years from variable years describes the first year for measures of annual net change.
year2	The vector of years from variable periods describes the second year for measures of annual net change.
X	Optional matrix of the auxiliary variables for the calibration estimator. Object convertible to data.table or variable names as character, column numbers.
countryX	Optional variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
yearsX	Variable of the all survey years. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to data.table or variable names as character, column numbers.
subperiodsX	Variable for the all survey sub-periods. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to data.table or variable names as character, column numbers.
X_ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ind_gr	Optional variable by which divided independently X matrix of the auxiliary variables for the calibration. One dimensional object convertible to one-column data.table or variable name as character, column number.
g	Optional variable of the g weights. One dimensional object convertible to one-column data.table or variable name as character, column number.
q	Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column data.table or variable name as character, column number.
datasetX	Optional survey data object in household level convertible to data.table.
frate	Positive numeric value. Sampling rate in percentage, by default - 0.
percentratio	Positive numeric value. All linearized variables are multiplied with percentratio value, by default - 1.
use.estVar	Logical value. If value is TRUE, then R function estVar is used for the estimation of covariance matrix of the residuals. If value is FALSE, then R function estVar is not used for the estimation of covariance matrix of the residuals.
use.gender	Logical value. If value is TRUE, then subperiods is defined together with gender.
confidence	optional; either a positive value for confidence interval. This variable by default is 0.95.
method	character value; value 'cros' is for measures of annual or value 'netchanges' is for measures of annual net change. This variable by default is netchanges.
ID_level2	Optional

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

dataset

Optional

survey data object convertible to data.table.

Value

A list with objects are returned by the function:

• crossectional_results - a data.table containing:

  • year - survey years,

  • subperiods - survey sub-periods,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • sample_size - the sample size (in numbers of individuals),

  • pop_size - the population size (in numbers of individuals),

  • total - the estimated totals,

  • variance - the estimated variance of cross-sectional or longitudinal measures,

  • sd_w - the estimated weighted variance of simple random sample,

  • sd_nw - the estimated variance estimation of simple random sample,

  • pop - the population size (in numbers of households),

  • sampl_siz - the sample size (in numbers of households),

  • stderr_w - the estimated weighted standard error of simple random sample,

  • stderr_nw - the estimated standard error of simple random sample,

  • se - the estimated standard error of cross-sectional or longitudinal,

  • rse - the estimated relative standard error (coefficient of variation),

  • cv - the estimated relative standard error (coefficient of variation) in percentage,

  • absolute_margin_of_error - the estimated absolute margin of error,

  • relative_margin_of_error - the estimated relative margin of error,

  • CI_lower - the estimated confidence interval lower bound,

  • CI_upper - the estimated confidence interval upper bound,

  • confidence_level - the positive value for confidence interval.

• crossectional_var_grad - a data.table containing:

  • year - survey years,

  • subperiods - survey sub-periods,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • grad - the estimated gradient,

  • var - the estimated a design-based variance.

• vardchanges_grad_var - a data.table containing:

  • year_1 - survey years of years1,

  • subperiods_1 - survey sub-periods of years1,

  • year_2 - survey years of years2,

  • subperiods_2 - survey sub-periods of years2,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • nams - gradient names, numerator (num) and denominator (den), for each year,

  • grad - the estimated gradient,

  • cros_var - the estimated a design-based variance.

• vardchanges_rho - a data.table containing:

  • year - survey years of years for cross-sectional estimates,

  • subperiods - survey sub-periods of years for cross-sectional estimates,

  • year_1 - survey years of years1,

  • subperiods_1 - survey sub-periods of years1,

  • year_2 - survey years of years2,

  • subperiods_2 - survey sub-periods of years2,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • nams - gradient names, numerator (num) and denominator (den), for each year,

  • rho - the estimated correlation matrix.

• vardchanges_var_tau - a data.table containing:

  • year_1 - survey years of years1,

  • subperiods_1 - survey sub-periods of years1,

  • year_2 - survey years of years2,

  • subperiods_2 - survey sub-periods of years2,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • nams - gradient names, numerator (num) and denominator (den), for each year,

  • var_tau - the estimated covariance matrix.

• vardchanges_results - a data.table containing:

  • year - survey years of years for measures of annual,

  • subperiods - survey sub-periods of years for measures of annual,

  • year_1 - survey years of years1 for measures of annual net change,

  • subperiods_1 - survey sub-periods of years1 for measures of annual net change,

  • year_2 - survey years of years2 for measures of annual net change,

  • subperiods_2 - survey sub-periods of years2 for measures of annual net change,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • estim_1 - the estimated value for period1,

  • estim_2 - the estimated value for period2,

  • estim - the estimated value,

  • var - the estimated variance,

  • se - the estimated standard error,

  • CI_lower - the estimated confidence interval lower bound,

  • CI_upper - the estimated confidence interval upper bound,

  • confidence_level - the positive value for confidence interval,

  • significant - is the the difference significant

• X_annual - a data.table containing:

  • year - survey years of years for measures of annual,

  • year_1 - survey years of years1 for measures of annual net change,

  • year_2 - survey years of years2 for measures of annual net change,

  • period - period1 and period2 together,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • cros_se - the estimated cross-sectional standard error.

• A_matrix - a data.table containing:

  • year - survey years of years1 for measures of annual,

  • year_1 - survey years of years1 for measures of annual net change,

  • year_2 - survey years of years2 for measures of annual net change,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • cols - the estimated matrix_A columns,

  • matrix_A - the estimated matrix A.

• annual_sum - a data.table containing:

  • year - survey years,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • totalY - the estimated value of variables of interest for period1,

  • totalZ - optional the estimated value of denominator for period2,

  • estim - the estimated value for year.

• annual_results - a data.table containing:

  • year - survey years of years for measures of annual,

  • year_1 - survey years of years1 for measures of annual net change,

  • year_2 - survey years of years2 for measures of annual net change,

  • country - survey countries,

  • Dom - optional variable of the population domains,

  • namesY - variable with names of variables of interest,

  • namesZ - optional variable with names of denominator for ratio estimation,

  • estim_1 - the estimated value for period1 for measures of annual net change,

  • estim_2 - the estimated value for period2 for measures of annual net change,

  • estim - the estimated value,

  • var - the estimated variance,

  • se - the estimated standard error,

  • rse - the estimated relative standard error (coefficient of variation),

  • cv - the estimated relative standard error (coefficient of variation) in percentage,

  • absolute_margin_of_error - the estimated absolute margin of error for period1 for measures of annual,

  • relative_margin_of_error - the estimated relative margin of error in percentage for measures of annual,

  • CI_lower - the estimated confidence interval lower bound,

  • CI_upper - the estimated confidence interval upper bound,

  • confidence_level - the positive value for confidence interval,

  • significant - is the the difference significant

References

• Guillaume Osier, Virginie Raymond, (2015), Development of methodology for the estimate of variance of annual net changes for LFS-based indicators. Deliverable 1 - Short document with derivation of the methodology.

• Guillaume Osier, Yves Berger, Tim Goedeme, (2013), Standard error estimation for the EU-SILC indicators of poverty and social exclusion, Eurostat Methodologies and Working papers, URL https://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF.

• Eurostat Methodologies and Working papers, Handbook on precision requirements and variance estimation for ESS household surveys, 2013, URL https://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.

• Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en.

See Also

domain, vardcros, vardchanges

Examples

### Example
library("data.table")
data("eusilc", package = "laeken")

set.seed(1)
eusilc1 <- eusilc[1:20, ]

dataset1 <- data.table(rbind(eusilc1, eusilc1),
                       year = c(rep(2010, nrow(eusilc1)),
                                rep(2011, nrow(eusilc1))))

dataset1[, country := "AT"]
dataset1[, half := .I - 2 * trunc((.I - 1) / 2)]
dataset1[, quarter := .I - 4 * trunc((.I - 1) / 4)]
dataset1[age < 0, age := 0]

PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(.N, 0, 5))]

dataset1 <- merge(dataset1, PSU, all = TRUE, by = "db030")

dataset1[, strata := "XXXX"]
dataset1[, employed := trunc(runif(.N, 0, 2))]
dataset1[, unemployed := trunc(runif(.N, 0, 2))]
dataset1[, labour_force := employed + unemployed]
dataset1[, id_lv2 := paste0("V", .I)]

vardannual(Y = "employed", H = "strata",
           PSU = "PSU", w_final = "rb050",
           ID_level1 = "db030", ID_level2 = "id_lv2",
           Dom = NULL, Z = NULL, years = "year",
           subperiods = "half", dataset = dataset1,
           percentratio = 100, confidence = 0.95,
           method = "cros")
  
vardannual(Y = "employed", H = "strata",
           PSU = "PSU", w_final = "rb050",
           ID_level1 = "db030", ID_level2 = "id_lv2",
           Dom = NULL, Z = NULL, country = "country",
           years = "year", subperiods = "quarter",
           dataset = dataset1, year1 = 2010, year2 = 2011,
           percentratio = 100, confidence = 0.95,
           method = "netchanges")
    
vardannual(Y = "unemployed", H = "strata",
           PSU = "PSU", w_final = "rb050",
           ID_level1 = "db030", ID_level2 = "id_lv2", 
           Dom = NULL, Z = "labour_force",
           country = "country", years = "year",
           subperiods = "quarter", dataset = dataset1,
           year1 = 2010, year2 = 2011,
           percentratio = 100, confidence = 0.95,
           method = "netchanges")

---

Variance estimation for measures of change for single and multistage stage cluster sampling designs

Description

Computes the variance estimation for measures of change for single and multistage stage cluster sampling designs.

Usage

vardchanges(
  Y,
  H,
  PSU,
  w_final,
  ID_level1,
  ID_level2,
  Dom = NULL,
  Z = NULL,
  gender = NULL,
  country = NULL,
  period,
  dataset = NULL,
  period1,
  period2,
  X = NULL,
  countryX = NULL,
  periodX = NULL,
  X_ID_level1 = NULL,
  ind_gr = NULL,
  g = NULL,
  q = NULL,
  datasetX = NULL,
  linratio = FALSE,
  percentratio = 1,
  use.estVar = FALSE,
  outp_res = FALSE,
  confidence = 0.95,
  change_type = "absolute",
  checking = TRUE
)

Arguments

Y	Variables of interest. Object convertible to data.table or variable names as character, column numbers.
H	The unit stratum variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
PSU	Primary sampling unit variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
w_final	Weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level2	Optional variable for unit ID codes. 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, variables are calculated for each domain. An object convertible to data.table or variable names as character vector, column numbers.
Z	Optional variables of denominator for ratio estimation. If supplied, the ratio estimation is computed. Object convertible to data.table or variable names as character, column numbers. This variable is NULL by default.
gender	Numerical variable for gender, where 1 is for males, but 2 is for females. One dimensional object convertible to one-column data.table or variable name as character, column number.
country	Variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
period	Variable for the all survey periods. The values for each period are computed independently. Object convertible to data.table or variable names as character, column numbers.
dataset	Optional survey data object convertible to data.table.
period1	The vector of periods from variable periods describes the first period.
period2	The vector of periods from variable periods describes the second period.
X	Optional matrix of the auxiliary variables for the calibration estimator. Object convertible to data.table or variable names as character, column numbers.
countryX	Optional variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
periodX	Optional variable of the all survey periods. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to data.table or variable names as character, column numbers.
X_ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ind_gr	Optional variable by which divided independently X matrix of the auxiliary variables for the calibration. One dimensional object convertible to one-column data.table or variable name as character, column number.
g	Optional variable of the g weights. One dimensional object convertible to one-column data.table or variable name as character, column number.
q	Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column data.table or variable name as character, column number.
datasetX	Optional survey data object in household level convertible to data.table.
linratio	Logical value. If value is TRUE, then the linearized variables for the ratio estimator is used for variance estimation. If value is FALSE, then the gradients is used for variance estimation.
percentratio	Positive numeric value. All linearized variables are multiplied with percentratio value, by default - 1.
use.estVar	Logical value. If value is TRUE, then R function estVar is used for the estimation of covariance matrix of the residuals. If value is FALSE, then R function estVar is not used for the estimation of covariance matrix of the residuals.
outp_res	Logical value. If TRUE estimated residuals of calibration will be printed out.
confidence	optional; either a positive value for confidence interval. This variable by default is 0.95 .
change_type	character value net changes type - absolute or relative.
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 objects are returned by the function:

• res_out - a data.table containing the estimated residuals of calibration with ID_level1 and PSU by periods and countries (if available). #'

• crossectional_results - a data.table containing:
  period - survey periods,
  country - survey countries,
  Dom - optional variable of the population domains,
  namesY - variable with names of variables of interest,
  namesZ - optional variable with names of denominator for ratio estimation,
  sample_size - the sample size (in numbers of individuals),
  pop_size - the population size (in numbers of individuals),
  total - the estimated totals,
  variance - the estimated variance of cross-sectional or longitudinal measures,
  sd_w - the estimated weighted variance of simple random sample,
  sd_nw - the estimated variance estimation of simple random sample,
  pop - the population size (in numbers of households),
  sampl_siz - the sample size (in numbers of households),
  stderr_w - the estimated weighted standard error of simple random sample,
  stderr_nw - the estimated standard error of simple random sample,
  se - the estimated standard error of cross-sectional or longitudinal,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage,
  absolute_margin_of_error - the estimated absolute margin of error,
  relative_margin_of_error - the estimated relative margin of error,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound. #'

• crossectional_var_grad - a data.table containing:
  periods - survey periods,
  country - survey countries,
  Dom - optional variable of the population domains,
  namesY - variable with names of variables of interest,
  namesZ - optional variable with names of denominator for ratio estimation,
  grad - the estimated gradient,
  var - the estimated a design-based variance.

• rho - a data.table containing:
  periods_1 - survey periods of periods1,
  periods_2 - survey periods of periods2,
  country - survey countries,
  Dom - optional variable of the population domains,
  namesY - variable with names of variables of interest,
  namesZ - optional variable with names of denominator for ratio estimation,
  nams - the variable names in correlation matrix,
  rho - the estimated correlation matrix.

• var_tau - a data.table containing:
  periods_1 - survey periods of periods1,
  periods_2 - survey periods of periods2,
  country - survey countries,
  Dom - optional variable of the population domains,
  namesY - variable with names of variables of interest,
  namesZ - optional variable with names of denominator for ratio estimation,
  nams - the variable names in correlation matrix,
  var_tau - the estimated covariance matrix.

• changes_results - a data.table containing:
  periods_1 - survey periods of periods1,
  periods_2 - survey periods of periods2,
  country - survey countries,
  Dom - optional variable of the population domains,
  namesY - variable with names of variables of interest,
  namesZ - optional variable with names of denominator for ratio estimation,
  estim_1 - the estimated value for period1,
  estim_2 - the estimated value for period2,
  estim - the estimated value,
  var - the estimated variance,
  se - the estimated standard error,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound.
  significant - is the the difference significant.

References

Guillaume Osier, Yves Berger, Tim Goedeme, (2013), Standard error estimation for the EU-SILC indicators of poverty and social exclusion, Eurostat Methodologies and Working papers, URL https://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF.
Eurostat Methodologies and Working papers, Handbook on precision requirements and variance estimation for ESS household surveys, 2013, URL https://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.
Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en

See Also

domain, vardcros, vardchangespoor

Examples

### Example 
library("data.table")
library("laeken")
data("eusilc")
set.seed(1)
eusilc1 <- eusilc[1:40,]
set.seed(1)
dataset1 <- data.table(rbind(eusilc1, eusilc1),
                       year = c(rep(2010, nrow(eusilc1)),
                                rep(2011, nrow(eusilc1))))
dataset1[age < 0, age := 0]
PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 5))]
dataset1 <- merge(dataset1, PSU, all = TRUE, by = "db030")
PSU <- eusilc <- NULL
dataset1[, strata := c("XXXX")]

dataset1[, t_pov := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, exp := 1]

# At-risk-of-poverty (AROP)
dataset1[, pov := ifelse (t_pov == 1, 1, 0)]
dataset1[, id_lev2 := paste0("V", .I)]


result <- vardchanges(Y = "pov", H = "strata", 
                      PSU = "PSU", w_final = "rb050",
                      ID_level1 = "db030", ID_level2 = "id_lev2",
                      Dom = NULL, Z = NULL, period = "year",
                      dataset = dataset1, period1 = 2010,
                      period2 = 2011, change_type = "absolute")
result

## Not run: 
data("eusilc")
dataset1 <- data.table(rbind(eusilc, eusilc),
                       year = c(rep(2010, nrow(eusilc)),
                                rep(2011, nrow(eusilc))))
dataset1[age < 0, age := 0]
PSU <- dataset1[,.N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 100))]
dataset1 <- merge(dataset1, PSU, all = TRUE, by = "db030")
PSU <- eusilc <- NULL
dataset1[, strata := "XXXX"]
  
dataset1[, t_pov := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_dep := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_lwi := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, exp := 1]
dataset1[, exp2 := 1 * (age < 60)]
  
# At-risk-of-poverty (AROP)
dataset1[, pov := ifelse (t_pov == 1, 1, 0)]
  
# Severe material deprivation (DEP)
dataset1[, dep := ifelse (t_dep == 1, 1, 0)]
  
# Low work intensity (LWI)
dataset1[, lwi := ifelse (t_lwi == 1 & exp2 == 1, 1, 0)]
  
# At-risk-of-poverty or social exclusion (AROPE)
dataset1[, arope := ifelse (pov == 1 | dep == 1 | lwi == 1, 1, 0)]
dataset1[, dom := 1]
dataset1[, id_lev2 := .I]
  
result <- vardchanges(Y = c("pov", "dep", "lwi", "arope"),
                      H = "strata", PSU = "PSU", w_final = "rb050",
                      ID_level1 = "db030", ID_level2 = "id_lev2",
                      Dom = "rb090", Z = NULL, period = "year",
                      dataset = dataset1, period1 = 2010, 
                      period2 = 2011, change_type = "absolute")
result
## End(Not run)

---

Variance estimation for measures of change for sample surveys for indicators on social exclusion and poverty

Description

Computes the variance estimation for measures of change for indicators on social exclusion and poverty.

Usage

vardchangespoor(
  Y,
  age = NULL,
  pl085 = NULL,
  month_at_work = NULL,
  Y_den = NULL,
  Y_thres = NULL,
  wght_thres = NULL,
  H,
  PSU,
  w_final,
  ID_level1,
  ID_level2,
  Dom = NULL,
  country = NULL,
  period,
  sort = NULL,
  period1,
  period2,
  gender = NULL,
  dataset = NULL,
  X = NULL,
  countryX = NULL,
  periodX = NULL,
  X_ID_level1 = NULL,
  ind_gr = NULL,
  g = NULL,
  q = NULL,
  datasetX = NULL,
  percentage = 60,
  order_quant = 50,
  alpha = 20,
  use.estVar = FALSE,
  confidence = 0.95,
  outp_lin = FALSE,
  outp_res = FALSE,
  type = "linrmpg",
  change_type = "absolute"
)

Arguments

Y	Study variable (for example equalized disposable income or gross pension income). One dimensional object convertible to one-column data.table or variable name as character, column number.
age	Age variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
pl085	Retirement variable (Number of months spent in retirement or early retirement). One dimensional object convertible to one-column data.table or variable name as character, column number.
month_at_work	Variable for total number of month at work (sum of the number of months spent at full-time work as employee, number of months spent at part-time work as employee, number of months spent at full-time work as self-employed (including family worker), number of months spent at part-time work as self-employed (including family worker)). One dimensional object convertible to one-column data.table or variable name as character, column number.
Y_den	Denominator variable (for example gross individual earnings). One dimensional object convertible to one-column data.table or variable name as character, column number.
Y_thres	Variable (for example equalized disposable income) used for computation and linearization of poverty threshold. One dimensional object convertible to one-column data.table or variable name as character, column number. Variable specified for inc is used as income_thres if income_thres is not defined.
wght_thres	Weight variable used for computation and linearization of poverty threshold. One dimensional object convertible to one-column data.table or variable name as character, column number. Variable specified for weight is used as wght_thres if wght_thres is not defined.
H	The unit stratum variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
PSU	Primary sampling unit variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
w_final	Weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector with only one TRUE value (length of the vector has to be the same as the column count of dataset).
ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level2	Optional variable for unit ID codes. 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, variables are calculated for each domain. An object convertible to data.table or variable names as character vector, column numbers.
country	Variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
period	Variable for the all survey periods. The values for each period are computed independently. Object convertible to data.table or variable names as character, column numbers.
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.
period1	The vector from variable period describes the first period.
period2	The vector from variable period describes the second period.
gender	Numerical variable for gender, where 1 is for males, but 2 is for females. One dimensional object convertible to one-column data.table or variable name as character, column number.
dataset	Optional survey data object convertible to data.frame.
X	Optional matrix of the auxiliary variables for the calibration estimator. Object convertible to data.table or variable names as character, column numbers.
countryX	Optional variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
periodX	Optional variable of the survey periods and countries. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to data.table or variable names as character, column numbers.
X_ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ind_gr	Optional variable by which divided independently X matrix of the auxiliary variables for the calibration. One dimensional object convertible to one-column data.table or variable name as character, column number.
g	Optional variable of the g weights. One dimensional object convertible to one-column data.table or variable name as character, column number.
q	Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column data.table or variable name as character, column number.
datasetX	Optional survey data object in household level 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.
alpha	a numeric value in range $[0,100]$ for the order of the income quantile share ratio (in percentage).
use.estVar	Logical value. If value is TRUE, then R function estVar is used for the estimation of covariance matrix of the residuals. If value is FALSE, then R function estVar is not used for the estimation of covariance matrix of the residuals.
confidence	optional; either a positive value for confidence interval. This variable by default is 0.95.
outp_lin	Logical value. If TRUE linearized values of the ratio estimator will be printed out.
outp_res	Logical value. If TRUE estimated residuals of calibration will be printed out.
type	a character vector (of length one unless several.ok is TRUE), example "linarpr","linarpt", "lingpg", "linpoormed", "linrmpg", "lingini", "lingini2", "linqsr", "linarr", "linrmir", "all_choices".
change_type	character value net changes type - absolute or relative.

Value

A list with objects are returned by the function:

• cros_lin_out - a data.table containing the linearized values of the ratio estimator with ID_level2 and PSU by periods and countries (if available).

• cros_res_out - a data.table containing the estimated residuals of calibration with ID_level1 and PSU by periods and countries (if available).

• crossectional_results - a data.table containing:
  period - survey periods,
  country - survey countries,
  Dom - optional variable of the population domains,
  type - type variable,
  count_respondents - the count of respondents,
  pop_size - the population size (in numbers of individuals),
  estim - the estimated value,
  se - the estimated standard error,
  var - the estimated variance,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage.

• changes_results - a data.table containing:
  period - survey periods,
  country - survey countries,
  Dom - optional variable of the population domains,
  type - type variable,
  estim_1 - the estimated value for period1,
  estim_2 - the estimated value for period2,
  estim - the estimated value,
  se - the estimated standard error,
  var - the estimated variance,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage.

References

Guillaume Osier, Yves Berger, Tim Goedeme, (2013), Standard error estimation for the EU-SILC indicators of poverty and social exclusion, Eurostat Methodologies and Working papers, URL https://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF.
Eurostat Methodologies and Working papers, Handbook on precision requirements and variance estimation for ESS household surveys, 2013, URL https://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.
Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en

See Also

domain, vardchanges, vardcros, vardcrospoor

Examples

### Example 
library("laeken")  
library("data.table")
data(eusilc)
set.seed(1)
dataset1 <- data.table(rbind(eusilc, eusilc),
                       year = c(rep(2010, nrow(eusilc)),
                                rep(2011, nrow(eusilc))),
                       country = c(rep("AT", nrow(eusilc)),
                                   rep("AT", nrow(eusilc))))
dataset1[age < 0, age := 0]
PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 100))]
PSU$inc <- runif(nrow(PSU), 20, 100000)
dataset1 <- merge(dataset1, PSU, all = TRUE, by = "db030")
PSU <- eusilc <- NULL
dataset1[, strata := c("XXXX")]
dataset1$pl085 <- 12 * trunc(runif(nrow(dataset1), 0, 2))
dataset1$month_at_work <- 12 * trunc(runif(nrow(dataset1), 0, 2))
dataset1[, id_l2 := paste0("V", .I)]
result <- vardchangespoor(Y = "inc", age = "age",
                          pl085 = "pl085", month_at_work = "month_at_work",
                          Y_den = "inc", Y_thres = "inc",
                          wght_thres = "rb050",  H = "strata", 
                          PSU = "PSU", w_final="rb050",
                          ID_level1 = "db030",  ID_level2 = "id_l2",
                          Dom = c("rb090"), country = "country",
                          period = "year", sort = NULL,  
                          period1 = c(2010, 2011),
                          period2 = c(2011, 2010),
                          gender = NULL, dataset = dataset1,
                          percentage = 60, order_quant = 50L,
                          alpha = 20, confidence = 0.95,
                          type = "linrmpg")
result

---

Variance estimation for measures of annual net change or annual for single stratified sampling designs

Description

Computes the variance estimation for measures of annual net change or annual for single stratified sampling designs.

Usage

vardchangstrs(
  Y,
  H,
  PSU,
  w_final,
  Dom = NULL,
  periods = NULL,
  dataset,
  periods1,
  periods2,
  in_sample,
  in_frame,
  confidence = 0.95,
  percentratio = 1,
  correction = FALSE
)

Arguments

Y	Variables of interest. Object convertible to data.table or variable names as character, column numbers.
H	The unit stratum variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
PSU	Primary sampling unit variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
w_final	Weight variable. 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, variables are calculated for each domain. An object convertible to data.table or variable names as character vector, column numbers.
periods	Variable for the all survey periods. The values for each period are computed independently. Object convertible to data.table or variable names as character, column numbers.
dataset	Optional survey data object convertible to data.table.
periods1	The vector of periods from variable periods describes the first period for measures of change.
periods2	The vector of periods from variable periods describes the second period for measures of change.
in_sample	Sample variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
in_frame	Frame variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
confidence	optional; either a positive value for confidence interval. This variable by default is 0.95.
percentratio	Positive numeric value. All linearized variables are multiplied with percentratio value, by default - 1.
correction	Logical value. If TRUE calculate variance without covariance (negative variance correction).

Value

A list with objects are returned by the function:

• crossectional_results - a data.table containing:
  year - survey years,
  subperiods - survey sub-periods,
  variable - names of variables of interest,
  Dom - optional variable of the population domains,
  estim - the estimated value,
  var - the estimated variance of cross-sectional and longitudinal measures,
  sd_w - the estimated weighted variance of simple random sample,
  se - the estimated standard error of cross-sectional or longitudinal,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage,
  absolute_margin_of_error - the estimated absolute margin of error,
  relative_margin_of_error - the estimated relative margin of error,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound,
  confidence_level - the positive value for confidence interval.

• annual_results - a data.table containing: year_1 - survey years of years1 for measures of annual net change,
  year_2 - survey years of years2 for measures of annual net change,
  Dom - optional variable of the population domains,
  variable - names of variables of interest,
  estim_2 - the estimated value for period2 for measures of annual net change,
  estim_1 - the estimated value for period1 for measures of annual net change,
  estim - the estimated value,
  var - the estimated variance,
  se - the estimated standard error,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage,
  absolute_margin_of_error - the estimated absolute margin of error for period1 for measures of annual,
  relative_margin_of_error - the estimated relative margin of error in percentage for measures of annual,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound,
  confidence_level - the positive value for confidence interval,
  significant - is the the difference significant.

• annual_results_correction - a data.table of corrected variables (if correction TRUE) containing: year_1 - survey years of years1 for measures of annual net change,
  year_2 - survey years of years2 for measures of annual net change,
  Dom - optional variable of the population domains,
  variable - names of variables of interest,
  estim_2 - the estimated value for period2 for measures of annual net change,
  estim_1 - the estimated value for period1 for measures of annual net change,
  estim - the estimated value,
  var - the estimated variance,
  se - the estimated standard error,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage,
  absolute_margin_of_error - the estimated absolute margin of error for period1 for measures of annual,
  relative_margin_of_error - the estimated relative margin of error in percentage for measures of annual,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound,
  confidence_level - the positive value for confidence interval,
  significant - is the the difference significant.

References

Guillaume OSIER, Virginie RAYMOND, (2015), Development of methodology for the estimate of variance of annual net changes for LFS-based indicators. Deliverable 1 - Short document with derivation of the methodology.

See Also

vardchanges, vardannual

---

Variance estimation for cross-sectional, longitudinal measures for single and multistage stage cluster sampling designs

Description

Computes the variance estimation for cross-sectional and longitudinal measures for any stage cluster sampling designs.

Usage

vardcros(
  Y,
  H,
  PSU,
  w_final,
  ID_level1,
  ID_level2,
  Dom = NULL,
  Z = NULL,
  gender = NULL,
  country = NULL,
  period,
  dataset = NULL,
  X = NULL,
  countryX = NULL,
  periodX = NULL,
  X_ID_level1 = NULL,
  ind_gr = NULL,
  g = NULL,
  q = NULL,
  datasetX = NULL,
  linratio = FALSE,
  percentratio = 1,
  use.estVar = FALSE,
  ID_level1_max = TRUE,
  outp_res = FALSE,
  withperiod = TRUE,
  netchanges = TRUE,
  confidence = 0.95,
  checking = TRUE
)

Arguments

Y	Variables of interest. Object convertible to data.table or variable names as character, column numbers.
H	The unit stratum variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
PSU	Primary sampling unit variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
w_final	Weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ID_level2	Optional variable for unit ID codes. 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, variables are calculated for each domain. An object convertible to data.table or variable names as character vector, column numbers.
Z	Optional variables of denominator for ratio estimation. If supplied, the ratio estimation is computed. Object convertible to data.table or variable names as character, column numbers. This variable is NULL by default.
gender	Numerical variable for gender, where 1 is for males, but 2 is for females. One dimensional object convertible to one-column data.table or variable name as character, column number.
country	Variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
period	Variable for the survey periods. The values for each period are computed independently. Object convertible to data.table or variable names as character, column numbers.
dataset	Optional survey data object convertible to data.table.
X	Optional matrix of the auxiliary variables for the calibration estimator. Object convertible to data.table or variable names as character, column numbers.
countryX	Optional variable for the survey countries. The values for each country are computed independently. Object convertible to data.table or variable names as character, column numbers.
periodX	Optional variable of the survey periods and countries. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to data.table or variable names as character, column numbers.
X_ID_level1	Variable for level1 ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.
ind_gr	Optional variable by which divided independently X matrix of the auxiliary variables for the calibration. One dimensional object convertible to one-column data.table or variable name as character, column number.
g	Optional variable of the g weights. One dimensional object convertible to one-column data.table or variable name as character, column number.
q	Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column data.table or variable name as character, column number.
datasetX	Optional survey data object in household level convertible to data.table.
linratio	Logical value. If value is TRUE, then the linearized variables for the ratio estimator is used for variance estimation. If value is FALSE, then the gradients is used for variance estimation.
percentratio	Positive numeric value. All linearized variables are multiplied with percentratio value, by default - 1.
use.estVar	Logical value. If value is TRUE, then R function estVar is used for the estimation of covariance matrix of the residuals. If value is FALSE, then R function estVar is not used for the estimation of covariance matrix of the residuals.
ID_level1_max	Logical value. If value is TRUE, then the size of sample for variance under simple random sampling is taken as maximum value of size in ID_level1 . If value is FALSE, then the size of sample for variance under simple random sampling is taken as count of ID_level2 in ID_level1.
outp_res	Logical value. If TRUE estimated residuals of calibration will be printed out.
withperiod	Logical value. If TRUE is value, the results is with period, if FALSE, without period.
netchanges	Logical value. If value is TRUE, then produce two objects: the first object is aggregation of weighted data by period (if available), country, strata and PSU, the second object is an estimation for Y, the variance, gradient for numerator and denominator by country and period (if available). If value is FALSE, then both objects containing NULL.
confidence	Optional positive value for confidence interval. This variable by default is 0.95.
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 four objects are returned by the function:

• res_out - a data.table containing the estimated residuals of calibration with ID_level1 and PSU.

• data_net_changes - a data.table containing aggregation of weighted data by period (if available) and countries (if available), country, strata, PSU.

• var_grad - a data.table containing estimation for Y, the variance, gradient for numerator and denominator by period, country (if available) and population domains (if available).

• results A data.table containing:
  period - survey periods,
  country - survey countries (if available),
  Dom - optional variable of the population domains,
  namesY - names of variables of interest,
  namesZ - optional variable for names of denominator for ratio estimation,
  sample_size - the sample size (in numbers of individuals),
  pop_size - the population size (in numbers of individuals),
  total - the estimated totals,
  variance - the estimated variance of cross-sectional or longitudinal measures,
  sd_w - the estimated weighted variance of simple random sample,
  sd_nw - the estimated variance estimation of simple random sample,
  pop - the population size (in numbers of households),
  sampl_siz - the sample size (in numbers of households),
  stderr_w - the estimated weighted standard error of simple random sample,
  stderr_nw - the estimated standard error of simple random sample,
  se - the estimated standard error of cross-sectional or longitudinal,
  rse - the estimated relative standard error (coefficient of variation),
  cv - the estimated relative standard error (coefficient of variation) in percentage,
  absolute_margin_of_error - the estimated absolute margin of error,
  relative_margin_of_error - the estimated relative margin of error,
  CI_lower - the estimated confidence interval lower bound,
  CI_upper - the estimated confidence interval upper bound,
  confidence_level - the positive value for confidence interval.

References

Guillaume Osier, Yves Berger, Tim Goedeme, (2013), Standard error estimation for the EU-SILC indicators of poverty and social exclusion, Eurostat Methodologies and Working papers, URL https://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF.
Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en
Eurostat Methodologies and Working papers, Handbook on precision requirements and variance estimation for ESS household surveys, 2013, URL https://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.

See Also

domain, lin.ratio

Examples

library("data.table")
library("laeken")
library("foreach")

# Example 1
data(eusilc)
set.seed(1)
dataset1 <- data.table(eusilc)
dataset1[, year := 2010]
dataset1[, country := "AT"]
dataset1[age < 0, age := 0]
PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 100))]
dataset1 <- merge(dataset1, PSU, by = "db030", all = TRUE)
PSU <- eusilc <- NULL
  
dataset1[, strata := "XXXX"]
dataset1[, t_pov := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_dep := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_lwi := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, exp := 1]
dataset1[, exp2 := 1 * (age < 60)]
  
# At-risk-of-poverty (AROP)
dataset1[, pov := ifelse(t_pov == 1, 1, 0)]
  
# Severe material deprivation (DEP)
dataset1[, dep := ifelse(t_dep == 1, 1, 0)]
  
# Low work intensity (LWI)
dataset1[, lwi := ifelse(t_lwi == 1 & exp2 == 1, 1, 0)]
  
# At-risk-of-poverty or social exclusion (AROPE)
dataset1[, arope := ifelse(pov == 1 | dep == 1 | lwi == 1, 1, 0)]

result11 <- vardcros(Y="arope", H = "strata",
                     PSU = "PSU", w_final = "rb050",
                     ID_level1 = "db030", ID_level2 = "rb030",
                     Dom = "rb090", Z = NULL, country = "country",
                     period = "year", dataset = dataset1,
                     linratio = FALSE, withperiod = TRUE,
                     netchanges = TRUE, confidence = .95)
   
# Example 2
data(eusilc)
set.seed(1)
dataset1 <- data.table(rbind(eusilc, eusilc),
                       year = c(rep(2010, nrow(eusilc)),
                                rep(2011, nrow(eusilc))))
dataset1[, country := "AT"]
dataset1[age < 0, age := 0]
PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 100))]
dataset1 <- merge(dataset1, PSU, by = "db030", all = TRUE)
PSU <- eusilc <- NULL
dataset1[, strata := "XXXX"]
dataset1[, strata := as.character(strata)]
dataset1[, t_pov := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_dep := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, t_lwi := trunc(runif(nrow(dataset1), 0, 2))]
dataset1[, exp := 1]
dataset1[, exp2 := 1 * (age < 60)]
    
# At-risk-of-poverty (AROP)
dataset1[, pov := ifelse(t_pov == 1, 1, 0)]
    
# Severe material deprivation (DEP)
dataset1[, dep := ifelse(t_dep == 1, 1, 0)]
    
# Low work intensity (LWI)
dataset1[, lwi := ifelse(t_lwi == 1 & exp2 == 1, 1, 0)]
    
# At-risk-of-poverty or social exclusion (AROPE)
dataset1[, arope := ifelse(pov == 1 | dep == 1 | lwi == 1, 1, 0)]
    
result11 <- vardcros(Y = c("pov", "dep", "arope"),
                     H = "strata", PSU = "PSU", w_final = "rb050",
                     ID_level1 = "db030", ID_level2 = "rb030",
                     Dom = "rb090", Z = NULL, country = "country",
                     period = "year", dataset = dataset1,
                     linratio = FALSE, withperiod = TRUE,
                     netchanges = TRUE, confidence = .95)
    
dataset2 <- dataset1[exp2 == 1]
result12 <- vardcros(Y = c("lwi"), H = "strata",
                     PSU = "PSU", w_final = "rb050",
                     ID_level1 = "db030", ID_level2 = "rb030",
                     Dom = "rb090", Z = NULL,
                     country = "country", period = "year",
                     dataset = dataset2, linratio = FALSE, 
                     withperiod = TRUE, netchanges = TRUE,
                     confidence = .95)
    
### Example 3
data(eusilc)
set.seed(1)
year <- 2011
dataset1 <- data.table(rbind(eusilc, eusilc, eusilc, eusilc),
                       rb010 = c(rep(2008, nrow(eusilc)),
                                 rep(2009, nrow(eusilc)),
                                 rep(2010, nrow(eusilc)),
                                 rep(2011, nrow(eusilc))))
dataset1[, rb020 := "AT"]
        
dataset1[, u := 1]
dataset1[age < 0, age := 0]
dataset1[, strata := "XXXX"]
PSU <- dataset1[, .N, keyby = "db030"][, N := NULL]
PSU[, PSU := trunc(runif(nrow(PSU), 0, 100))]
dataset1 <- merge(dataset1, PSU, by = "db030", all = TRUE)
thres <- data.table(rb020 = as.character(rep("AT", 4)),
                   thres = c(11406, 11931, 12371, 12791),
                   rb010 = 2008:2011)
dataset1 <- merge(dataset1, thres, all.x = TRUE, by = c("rb010", "rb020"))
dataset1[is.na(u), u := 0]
dataset1 <- dataset1[u == 1]
    
#############
# T3        #
#############
    
T3 <- dataset1[rb010 == year - 3]
T3[, strata1 := strata]
T3[, PSU1 := PSU]
T3[, w1 := rb050]
T3[, inc1 := eqIncome]
T3[, rb110_1 := db030]
T3[, pov1 := inc1 <= thres]
T3 <- T3[, c("rb020", "rb030", "strata", "PSU", "inc1", "pov1"),
           with = FALSE]
    
#############
# T2        #
#############

T2 <- dataset1[rb010 == year - 2]
T2[, strata2 := strata]
T2[, PSU2 := PSU]
T2[, w2 := rb050]
T2[, inc2 := eqIncome]
T2[, rb110_2 := db030]
setnames(T2, "thres", "thres2")
T2[, pov2 := inc2 <= thres2]
T2 <- T2[, c("rb020", "rb030", "strata2", "PSU2", "inc2", "pov2"),
           with = FALSE]
    
#############
# T1        #
#############

T1 <- dataset1[rb010 == year - 1]
T1[, strata3 := strata]
T1[, PSU3 := PSU]
T1[, w3 := rb050]
T1[, inc3 := eqIncome]
T1[, rb110_3 := db030]
setnames(T1, "thres", "thres3")
T1[, pov3 := inc3 <= thres3]
T1 <- T1[, c("rb020", "rb030", "strata3", "PSU3", "inc3", "pov3"),
           with = FALSE]
    
#############
# T0        #
#############

T0 <- dataset1[rb010 == year]
T0[, PSU4 := PSU]
T0[, strata4 := strata]
T0[, w4 := rb050]
T0[, inc4 := eqIncome]
T0[, rb110_4 := db030]
setnames(T0, "thres", "thres4")
T0[, pov4 := inc4 <= thres4]
T0 <- T0[, c("rb010", "rb020", "rb030", "strata4", "PSU4",
             "w4", "inc4", "pov4"), with = FALSE]
apv <- merge(T3, T2, all = TRUE, by = c("rb020", "rb030"))
apv <- merge(apv, T1, all = TRUE, by = c("rb020", "rb030"))
apv <- merge(apv, T0, all = TRUE, by = c("rb020", "rb030"))
apv <- apv[(!is.na(inc1)) & (!is.na(inc2)) & (!is.na(inc3)) & (!is.na(inc4))]
apv[, ppr := as.integer(((pov4 == 1) & ((pov1 == 1 & pov2 == 1 & pov3 == 1) 
                           | (pov1 == 1 & pov2 == 1 & pov3 == 0)
                           | (pov1 == 1 & pov2 == 0 & pov3 == 1)
                           | (pov1 == 0 & pov2 ==1 & pov3 == 1))))]
                                  
result20 <- vardcros(Y = "ppr", H = "strata", PSU = "PSU",
                     w_final = "w4", ID_level1 = "rb030",
                     ID_level2 = "rb030", Dom = NULL,
                     Z = NULL, country = "rb020",
                     period = "rb010", dataset = apv,
                     linratio = FALSE, 
                     withperiod = TRUE,
                     netchanges = FALSE,
                     confidence = .95)
result20

---