| fm_var {FuzzyPovertyR} | R Documentation |
Fuzzy monetary poverty estimation
Description
This function estimates the variance of the fuzzy monetary poverty index
Usage
fm_var(
predicate,
weight,
fm,
ID = NULL,
type = "bootstrap",
R = 100,
M = NULL,
stratum,
psu,
f = 0.01,
verbose = FALSE,
HCR,
interval = c(1, 10),
alpha = NULL,
hh.size,
z_min,
z_max,
z1,
z2,
b,
z,
breakdown = NULL,
data = NULL
)
Arguments
predicate |
A numeric vector representing the poverty predicate (i.e. income or expenditure) |
weight |
A numeric vector of sampling weights. if NULL weights will set equal to n (n = sample size) |
fm |
The membership function (default is "verma". Other options are "ZBM", "belhadj2015", "belhadj2011", "chakravarty", "cerioli", "verma1999" and "TFR". See Betti et. al., 2023) |
ID |
A numeric or character vector of IDs. if NULL (the default) it is set as the row sequence |
type |
The variance estimation method chosen. One between 'bootstrap' (default) or 'jackknife' |
R |
The number of bootstrap replicates. Default is 500 |
M |
The size of bootstrap samples. Default is 'nrow(data)' |
stratum |
The vector identifying the stratum (if 'jackknife' is chosen as variance estimation technique) |
psu |
The vector identifying the psu (if 'jackknife' is chosen as variance estimation technique) |
f |
The finite population correction fraction (if 'jackknife' is chosen as variance estimation technique) |
verbose |
Logical. whether to print the proceeding of the variance estimation procedure |
HCR |
If fm="verma" or fm="verma1999" or fm="TFR" . The value of the head count ratio used to compute alpha so that the membership function equals the HCR |
interval |
If fm="verma" or fm="verma1999" or fm="TFR". A numeric vector of length two to look for the value of alpha (if not supplied) |
alpha |
The value of the exponent in equations of "verma", "verma1999" and "TFR". If NULL it is calculated so that it equates the expectation of the membership function to HCR. |
hh.size |
If fm="ZBM". A numeric vector of household size |
z_min |
A parameter of the membership function if fm="belhadj2011", i.e. the z_min: $mu=1 for 0 <y_i<z_min$ (see: See Betti et. al, 2023) |
z_max |
A parameter of the membership function if fm="belhadj2011", i.e. the z_max: $mu=0 for y_i>z_max$ (see: See Betti et. al, 2023) |
z1 |
A parameter of the membership function if fm="belhadj2015" or fm="cerioli". For "belhadj2015" z1: $mu=1 for y_i<z1$ while for "cerioli" $mu=1 for 0 <y_i<z1$ (see: See Betti et. al, 2023) |
z2 |
A parameter of the membership function if fm="belhadj2015" or fm="cerioli". For "belhadj2015" z2: $mu=0 for y_i>z2$ while for "cerioli" the z1: $mu=0 for y_i>z2$ (see: See Betti et. al, 2023) |
b |
A parameter of the membership function if fm="belhadj2015". The shape parameter (if b=1 the mf is linear between z1 and z2) |
z |
A parameter of the membership function if fm="chakravarty", i.e. $mu=0 for y_i>=z$ (see: See Betti et. al, 2023) |
breakdown |
A factor of sub-domains to calculate estimates for (using the same alpha). If numeric will be coerced to a factor. |
data |
an optional data frame containing the variables to be used |
Value
An object of class FuzzyMonetary containing the estimate of variance with the method selected. if breakdown is not NULL, the variance is estimated for each sub-domain.
References
Belhadj, B. (2011). A new fuzzy unidimensional poverty index from an information theory perspective. Empirical Economics, 40(1):687–704.
Belhadj, B. (2015). Employment measure in developing countries via minimum wage and poverty new fuzzy approach. Opsearch, 52(1):329–339.
Betti, G., Cheli, B., Lemmi, A., and Verma, V. (2006). Multidimensional and longitudinal poverty: an integrated fuzzy approach. In Betti, G. and Lemmi, A., editors, Fuzzy set approach to multidimensional poverty measurement, pages 115–137. Springer, Boston, USA.
Betti, G., D’Agostino, A., Lemmi, A., & Neri, L. (2023). The fuzzy approach to poverty measurement. In Research Handbook on Measuring Poverty and Deprivation Edited by Silber, J. (pp. 489-500). Edward Elgar Publishing.
Betti, G. and Verma, V. (1999). Measuring the degree of poverty in a dynamic and comparative context: a multi-dimensional approach using fuzzy set theory. In Proceedings, iccs-vi, volume 11, pages 289–300.
Cerioli, A. and Zani, S. (1990). A fuzzy approach to the measurement of poverty. In Income and Wealth Distribution, Inequality and Poverty: Proceedings of the Second International Conference on Income Distribution by Size: Generation, Distribution, Measurement and Applications., 272–284. Springer, Boston, USA.
Chakravarty, S. R. (2006). An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets. Fuzzy Set Approach to Multidimensional Poverty Measurement, 49-72.
Cheli, B. and Lemmi, A. (1995). A ’totally’ fuzzy and relative approach to the multidimensional analysis of poverty. 24(1):115–134.
Zedini, A. and Belhadj, B. (2015). A new approach to unidimensional poverty analysis: Application to the Tunisian case. Review of Income and Wealth, 61(3):465–476.
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
#The following examples are based on the dataset eusilc
#included in the package.
#Example 1 using bootstrap and breakdown
#fm = "verma"
fm_var(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma", breakdown = eusilc$db040, type = "bootstrap",
alpha = 4)
#fm = "belhadj2015"
fm_var(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "belhadj2015", breakdown = eusilc$db040, type = "bootstrap",
z1 = 100, z2 = 15000, b = 2)
#Example 2 using jackknife without breakdown
#fm = "verma1999"
fm_var(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma1999", type = "jackknife",
stratum = eusilc$stratum , psu = eusilc$psu,
alpha = 4)
#fm = "cerioli"
fm_var(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "cerioli", type = "jackknife",
stratum = eusilc$stratum , psu = eusilc$psu,
z1 = 1000, z2 = 12000)