FuzzyPovertyR (version 3.0.2)

fs_construct: 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)

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.

Arguments

steps4_5

The results from fs_equate.

weight

A numeric vector of sampling weights of length nrow(step1). 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.

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)