vardcros: 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, Dom = NULL,
         Z = NULL, country, periods,
         dataset = NULL, linratio=FALSE,
         percentratio = 1, use.estVar = FALSE,
         household_level_max=TRUE,
         withperiod=TRUE, netchanges=TRUE,
         confidence = .95)

Arguments

Variables of interest. Object convertible to data.table or variable names as character, column numbers.

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.

variable for unit ID codes (for household surveys - secondary unit id number). 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.

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.

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.

periods

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.

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 integer 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

household_level_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 household . If value is FALSE, then the size of sample for variance under simple random sampl

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 b

confidence

Optional positive value for confidence interval. This variable by default is 0.95.

Value

A list with three objects are returned by the function:
data_net_changesA data.table containing aggregation of weighted data by period (if available), country, strata, PSU.
var_gradA data.table containing estimation for Y, the variance, gradient for numerator and denominator by period, country and population domains (if available).
resultsA data.table containing period - survey periods, country - survey countries, 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.

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. 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 http://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.

Examples

Run this code

# Example 1
data(eusilc)
set.seed(1)
data <- data.table(eusilc,
                   year=rep(2010, nrow(eusilc)),
                   country=rep("AT", nrow(eusilc)))
data[, country:=as.character(country)]
data[age<0, age:=0]
PSU <- data[,.N, keyby="db030"]
PSU[, N:=NULL]
PSU[, PSU:=trunc(runif(nrow(PSU), 0, 100))]
data <- merge(data, PSU, by="db030", all=TRUE)
PSU <- eusilc <- 0

data[, strata:="XXXX"]
data[, t_pov:=trunc(runif(nrow(data), 0, 2))]
data[, t_dep:=trunc(runif(nrow(data), 0, 2))]
data[, t_lwi:=trunc(runif(nrow(data), 0, 2))]
data[, exp:= 1]
data[, exp2:= 1 * (age < 60)]

# At-risk-of-poverty (AROP)
data[, pov:= ifelse (t_pov == 1, 1, 0)]

# Severe material deprivation (DEP)
data[, dep:= ifelse (t_dep == 1, 1, 0)]

# Low work intensity (LWI)
data[, lwi:= ifelse (t_lwi == 1 & exp2 == 1, 1, 0)]

# At-risk-of-poverty or social exclusion (AROPE)
data[, arope:= ifelse (pov == 1 | dep == 1 | lwi == 1, 1, 0)]

result11 <- vardcros(Y="arope",
                    H="strata", PSU="PSU", w_final="rb050",
                    id="db030", Dom="rb090", Z=NULL,
                    country="country", periods="year",
                    dataset=data,
                    linratio=FALSE,  
                    withperiod=TRUE,
                    netchanges=TRUE,
                    confidence = .95)

# Example 2
data(eusilc)
set.seed(1)
data <- 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))))
data[age<0, age:=0]
PSU <- data[,.N, keyby="db030"]
PSU[, N:=NULL]
PSU[, PSU:=trunc(runif(nrow(PSU), 0, 100))]
data <- merge(data, PSU, by="db030", all=TRUE)
PSU <- eusilc <- 0
data[, strata:="XXXX"]
data[, strata:=as.character(strata)]
data[, t_pov:=trunc(runif(nrow(data), 0, 2))]
data[, t_dep:=trunc(runif(nrow(data), 0, 2))]
data[, t_lwi:=trunc(runif(nrow(data), 0, 2))]
data[, exp:= 1]
data[, exp2:= 1 * (age < 60)]

# At-risk-of-poverty (AROP)
data[, pov:= ifelse (t_pov == 1, 1, 0)]

# Severe material deprivation (DEP)
data[, dep:= ifelse (t_dep == 1, 1, 0)]

# Low work intensity (LWI)
data[, lwi:= ifelse (t_lwi == 1 & exp2 == 1, 1, 0)]

# At-risk-of-poverty or social exclusion (AROPE)
data[, 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="db030", Dom="rb090", Z=NULL,
                    country="country", period="year",
                    dataset=data,
                    linratio=FALSE, 
                    withperiod=TRUE,
                    netchanges=TRUE,
                    confidence = .95)

data2 <- data[exp2==1]
result12 <- vardcros(Y=c("lwi"),
                    H="strata", PSU="PSU", w_final="rb050",
                    id="db030", Dom="rb090", Z=NULL,
                    country="country", period="year",
                    dataset=data2,
                    linratio=FALSE, 
                    withperiod=TRUE,
                    netchanges=TRUE,
                    confidence = .95)

### Example 3
data(eusilc)
set.seed(1)
year <- 2011
data <- 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))),
                   rb020=c(rep("AT", nrow(eusilc)),
                           rep("AT", nrow(eusilc)),
                           rep("AT", nrow(eusilc)),
                           rep("AT", nrow(eusilc))))
data[, rb020:=as.character(rb020)]

data[, u:=1]
data[age<0, age:=0]
data[, strata:="XXXX"]
PSU <- data[,.N, keyby="db030"]
PSU[, N:=NULL]
PSU[, PSU:=trunc(runif(nrow(PSU), 0, 100))]
data <- merge(data, PSU, by="db030", all=TRUE)
thres <- data.table(rb020=as.character(rep("AT",4)),
                    thres= c(11406, 11931, 12371, 12791),
                    rb010=2008:2011)
setnames(thres, names(thres), tolower(names(thres)))
data <- merge(data, thres, all.x=TRUE, by=c("rb010", "rb020"))
data[is.na(u), u:=0]
data <- data[u==1]
setkeyv(data, c("rb020", "rb030"))

#############
# T3        #
#############

T3 <- data[rb010==year-3]
T3[, strata1:=strata]
T3[, PSU1:=PSU]
T3[, w1:=rb050]
T3[, inc1:=eqIncome]
T3[, rb110_1:=db030]
setnames(T3, "thres", "thres1")
T3[, pov1:=inc1<=thres1]
T3 <- T3[, c("rb020", "rb030", "strata", "PSU", "inc1", "pov1"), with=FALSE]

#############
# T2        #
#############
T2 <- data[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 <- data[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 <- data[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("rb020", "rb030", "strata4", "PSU4", "w4", "inc4", "pov4"), with=FALSE]
apv <- merge(T3, T2, all=TRUE)
apv <- merge(apv, T1, all=TRUE)
apv <- merge(apv, T0, all=TRUE)
apv <- apv[(!is.na(inc1)) & (!is.na(inc2)) & (!is.na(inc3)) & (!is.na(inc4))]
apv[, ppr:=ifelse(((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))),1,0)]

result20 <- vardcros(Y="ppr", H="strata", PSU="PSU",
                    w_final="w4", id="rb030",
                    Dom = NULL, Z=NULL,
                    country="rb020", periods=NULL,
                    dataset=apv,
                    linratio=FALSE, 
                    withperiod=FALSE,
                    netchanges=FALSE,
                    confidence = .95)