# contrastinf: Generalized linearization of a smooth function of survey... In convey: Income Concentration Analysis with Complex Survey Samples

 contrastinf R Documentation

## Generalized linearization of a smooth function of survey statistics

### Description

Generalized linearization of a smooth function of survey statistics

### Usage

```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

### 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.

### Value

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

### Author(s)

Djalma Pessoa and Anthony Damico

### 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.

`svyqsr`

### Examples

```library(survey)
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
# se estimate of the variable eqincome mean
SE(svytotal(lin_R\$lin, des_eusilc))
# to check, use
svymean (~eqincome, des_eusilc)

# quintile share ratio (qsr) linearization
S20 <- svyisq(~ eqincome, design = des_eusilc, .20)
S20_val <- coef (S20); attributes (S20_val) <- NULL
S20_lin <- attr(S20 , "lin" )
S80 <- svyisq(~ eqincome, design = des_eusilc, .80)
S80_val <- coef (S80); attributes (S80_val) <- NULL
S80_lin <- attr(S80 , "lin" )
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
# se estimate of the qsr:
SE(svytotal(lin_QSR\$lin, des_eusilc))
# to check, use
svyqsr(~eqincome, des_eusilc )
# 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
# se estimate
SE(svytotal(lin_Lor\$lin,des_eusilc))

```

convey documentation built on April 28, 2022, 1:06 a.m.