# Variance estimation for measures of change for sample surveys for indicators on social exclusion and poverty Computes the variance estimation for measures of change for indicators on social exclusion and poverty. ```r 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: $$ \frac{p}{100} \cdot Z_{\frac{\alpha}{100}}.p/100 * Z(\alpha/100). $$ 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: $$ \frac{p}{100} \cdot Z_{\frac{\alpha}{100}}.p/100 * Z(\alpha/100). $$ 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. ## Returns 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. ## Examples ```r ### 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 ``` ## 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 [http://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF](http://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 [http://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF](http://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](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`

vardchangespoor function