Generalized linearization of a smooth function of survey statistics

contrastinf(exprlist, infunlist)

Arguments

exprlist: a call
infunlist: a list of lists, each having two components: value - the estimate value and lin - the linearized variable

Value

a list with two components: values - the estimate value and lin - the linearized variable

Details

The call must use function that deriv knows how to differentiate. It allows to compute the linearized variable of a complex indicator from the linearized variables of simpler component variables, avoiding the formal derivatives calculations.

References

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.

Author

Djalma Pessoa, Guilherme Jacob, and Anthony Damico

Examples

library(survey)
#> Loading required package: grid
#> Loading required package: Matrix
#> Loading required package: survival
#> 
#> Attaching package: ‘survey’
#> The following object is masked from ‘package:graphics’:
#> 
#>     dotchart
library(laeken)
data(eusilc) ; names( eusilc ) <- tolower( names( eusilc ) )

# linearized design
des_eusilc <- svydesign( ids = ~rb030 , strata = ~db040 ,  weights = ~rb050 , data = eusilc )
des_eusilc <- convey_prep(des_eusilc)

w <- weights(des_eusilc)

# ratio linearization
T1 = list(value = sum(w*eusilc$eqincome) , lin = eusilc$eqincome )
T2 = list(value = sum(w), lin = rep (1, nrow(eusilc)) )
list_all <- list( T1 = T1, T2 = T2)
lin_R = contrastinf (quote(T1/T2), list_all)

# estimate of the variable eqincome mean
lin_R$value
#> [1] 19890.81
# se estimate of the variable eqincome mean
SE(svytotal(lin_R$lin, des_eusilc))
#>          [,1]
#> [1,] 86.82948
# to check, use
svymean (~eqincome, des_eusilc)
#>           mean     SE
#> eqincome 19891 86.829

# quintile share ratio (qsr) linearization
S20 <- svyisq(~ eqincome, design = des_eusilc, .20, linearized = TRUE)
S20_val <- coef (S20); attributes (S20_val) <- NULL
S20_lin <- attr(S20 , "linearized" )
S80 <- svyisq(~ eqincome, design = des_eusilc, .80, linearized = TRUE)
S80_val <- coef (S80); attributes (S80_val) <- NULL
S80_lin <- attr(S80 , "linearized" )
SU <- list (value = S80_val, lin = S80_lin )
SI <- list (value = S20_val, lin = S20_lin )
TOT <- list(value = sum( w * eusilc$eqincome) , lin = eusilc$eqincome )
list_all <- list (TOT = TOT, SI = SI, SU = SU )
lin_QSR <- contrastinf( quote((TOT-SU)/SI), list_all)

# estimate of the qsr
lin_QSR$value
#> [1] 3.970004
# se estimate of the qsr:
SE(svytotal(lin_QSR$lin, des_eusilc))
#>            [,1]
#> [1,] 0.04255041
# to check, use
svyqsr(~eqincome, des_eusilc )
#>           qsr     SE
#> eqincome 3.97 0.0426
# proportion of income below the quantile .20
list_all <- list (TOT = TOT, SI = SI )
lin_Lor <- contrastinf( quote(SI/TOT), list_all)
# estimate of the proportion of income below the quantile .20
lin_Lor$value
#> [1] 0.08939032
# se estimate
SE(svytotal(lin_Lor$lin,des_eusilc))
#>              [,1]
#> [1,] 0.0006809416