fs_equate {FuzzyPovertyR}

Fuzzy supplementary poverty estimation, finding the alpha parameter (step 6)

Description

Step 6. This function solves $E(mu)^(alpha-1) = HCR$ for alpha.

Usage

fs_equate(steps4_5, weight, HCR, interval = c(1, 10), verbose = TRUE)

Arguments

steps4_5

The results obtained from 'fs_weight'.

weight

A numeric vector of sampling weights. if NULL weights will set equal to n (n = sample size)

HCR

The value of the head count ratio used to compute alpha so that the membership function equals the HCR

interval

The range to look for the value of alpha.

verbose

Logical. whether to print the proceeding of the procedure.

Value

The alpha parameter that solves the non-linear equation $E(mu) = HCR$

References

Betti, G., Gagliardi, F., Lemmi, A., & Verma, V. (2015). Comparative measures of multidimensional deprivation in the European Union. Empirical Economics, 49(3), 1071-1100.

Betti, G., Gagliardi, F., & Verma, V. (2018). Simplified Jackknife variance estimates for fuzzy measures of multidimensional poverty. International Statistical Review, 86(1), 68-86.

Examples

#This example is based on the dataset eusilc included in the package
#The Step 6 of the FS index is computed 
#The step 2-5 are the following (step 1 is the eusilc dataset)
#For more on each step see the ad hoc function included in the package

#Step 2 

step2 = fs_transform(eusilc[,4:23], weight = eusilc$DB090, ID = eusilc$ID)

#Step 3 is the definition of the dimension.
#For more about the step see Betti et al. (2018)

dimensions = c(1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5)

#Step 4-5 finding weights 

steps4_5 = fs_weight(dimensions, step2 = step2, rho = NULL)

#Step 6 computation of alpha parameter

fs_equate(steps4_5 = steps4_5,
          weight = eusilc$DB090, 
          HCR = 0.12, interval = c(1,10))