fs_construct {FuzzyPovertyR}

Fuzzy supplementary poverty estimation (Step 7)

Description

Step 7. Constructs the fuzzy supplementary poverty measure based on Steps1-6.

Usage

fs_construct(steps4_5, weight, alpha, breakdown = NULL)

Arguments

steps4_5

The results from 'fs_equate'.

weight

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

alpha

The value of the exponent in the FM equation. If NULL it is calculated so that it equates the expectation of the membership function to HCR.

breakdown

A Dimension of sub-domains to calculate estimates for (using the same alpha). If numeric will be coerced to a Dimension.

Value

An object of class FuzzySupplementary containing the fuzzy membership function for each unit, the point estimate (i.e. the expected value of the function), and the alpha parameter.

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 FS index is compute without and with breakdown and using an HCR = 0.12
#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

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

#Step 7 the FS index without breakdown

fs_results = fs_construct(steps4_5 = steps4_5,
             weight = eusilc$DB090, alpha = alpha, breakdown = NULL)

#Step 7 the FS index with breakdown

fs_results = fs_construct(steps4_5 = steps4_5,
             weight = eusilc$DB090, alpha = alpha, breakdown = eusilc$db040)