fm_construct: Fuzzy monetary poverty estimation
In FuzzyPovertyR: Estimation of Fuzzy Poverty Measures
fm_construct R Documentation
Fuzzy monetary poverty estimation
Description
fm_construct constructs fuzzy monetary poverty estimates.
Usage
fm_construct(
predicate,
weight = NULL,
fm = "verma",
ID = NULL,
HCR,
interval = c(1, 10),
alpha = NULL,
hh.size,
z_min,
z_max,
z1,
z2,
b,
z,
breakdown = NULL,
data = NULL,
verbose = FALSE
)
Arguments
predicate
A numeric vector representing the poverty predicate (i.e. income or expenditure)
weight
A numeric vector of sampling weights of the same length of predicate. 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
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)
data
An optional data frame containing the variables to be used
verbose
Logical. whether to print the proceeding of the procedure
Details
It implements the fuzzy set approach to monetary poverty measurement where
the usual dichotomy poor (1) not-poor(0) is replaced with a continuum score in $(0,1)$
Value
an object of class FuzzyMonetary containing the (fuzzy) membership function for each individual in the sample,
the estimated expected value (estimate) of the function and the parameters of the
membership functions (supplied or calculated). If breakdown is supplied it gives an output for each level.
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.
Examples
#The following examples are based on the dataset eusilc
#included in the package.
#fm = "verma"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma", HCR = 0.154, ID = eusilc$ID)
#fm = "verma1999"
#In this example we set alpha=4.5
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma1999", alpha = 4.5, ID = eusilc$ID)
#fm = "TFR"
#In this example we do not use the sample weights. alpha = 4.5
fm_construct(predicate = eusilc$eq_income,
fm = "TFR", alpha = 4.5)
#fm = "belhadj2015"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=15000, b=2,
fm = "belhadj2015")
#fm = "cerioli"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=10000, fm= "cerioli")
#fm = "belhadj2011"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z_min=1000, z_max=8000, fm= "belhadj2011")
#fm = "chakravarty"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z=8000, fm= "chakravarty")
#fm = "ZBM"
#For this index have to use the household size
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
hh.size=eusilc$ncomp , fm= "ZBM")
#######################
##Including breakdown##
#######################
#fm = "verma"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma", HCR = 0.154, ID = eusilc$ID,
breakdown = eusilc$db040)
#fm = "verma1999"
#In this example we set alpha=4.5
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma1999", alpha = 4.5, ID = eusilc$ID,
breakdown = eusilc$db040)
#fm = "TFR"
#In this example we do not use the sample weights. alpha = 4.5
fm_construct(predicate = eusilc$eq_income,
fm = "TFR", alpha = 4.5,
breakdown = eusilc$db040)
#fm = "belhadj2015"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=15000, b=2,
fm = "belhadj2015", breakdown = eusilc$db040)
#fm = "cerioli"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=10000, fm= "cerioli", breakdown = eusilc$db040)
#fm = "belhadj2011"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z_min=1000, z_max=8000, fm= "belhadj2011",
breakdown = eusilc$db040)
#fm = "chakravarty"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z=8000, fm= "chakravarty", breakdown = eusilc$db040)
#fm = "ZBM"
#For this index we have to use the household size
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
hh.size=eusilc$ncomp , fm= "ZBM",
breakdown = eusilc$db040)
FuzzyPovertyR documentation built on Oct. 3, 2024, 5:06 p.m.
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| fm_construct | R Documentation |
Fuzzy monetary poverty estimation
Description
fm_construct constructs fuzzy monetary poverty estimates.
Usage
fm_construct(
predicate,
weight = NULL,
fm = "verma",
ID = NULL,
HCR,
interval = c(1, 10),
alpha = NULL,
hh.size,
z_min,
z_max,
z1,
z2,
b,
z,
breakdown = NULL,
data = NULL,
verbose = FALSE
)
Arguments
predicate |
A numeric vector representing the poverty predicate (i.e. income or expenditure) |
weight |
A numeric vector of sampling weights of the same length of predicate. 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 |
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) |
data |
An optional data frame containing the variables to be used |
verbose |
Logical. whether to print the proceeding of the procedure |
Details
It implements the fuzzy set approach to monetary poverty measurement where the usual dichotomy poor (1) not-poor(0) is replaced with a continuum score in $(0,1)$
Value
an object of class FuzzyMonetary containing the (fuzzy) membership function for each individual in the sample,
the estimated expected value (estimate) of the function and the parameters of the
membership functions (supplied or calculated). If breakdown is supplied it gives an output for each level.
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.
Examples
#The following examples are based on the dataset eusilc
#included in the package.
#fm = "verma"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma", HCR = 0.154, ID = eusilc$ID)
#fm = "verma1999"
#In this example we set alpha=4.5
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma1999", alpha = 4.5, ID = eusilc$ID)
#fm = "TFR"
#In this example we do not use the sample weights. alpha = 4.5
fm_construct(predicate = eusilc$eq_income,
fm = "TFR", alpha = 4.5)
#fm = "belhadj2015"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=15000, b=2,
fm = "belhadj2015")
#fm = "cerioli"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=10000, fm= "cerioli")
#fm = "belhadj2011"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z_min=1000, z_max=8000, fm= "belhadj2011")
#fm = "chakravarty"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z=8000, fm= "chakravarty")
#fm = "ZBM"
#For this index have to use the household size
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
hh.size=eusilc$ncomp , fm= "ZBM")
#######################
##Including breakdown##
#######################
#fm = "verma"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma", HCR = 0.154, ID = eusilc$ID,
breakdown = eusilc$db040)
#fm = "verma1999"
#In this example we set alpha=4.5
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
fm = "verma1999", alpha = 4.5, ID = eusilc$ID,
breakdown = eusilc$db040)
#fm = "TFR"
#In this example we do not use the sample weights. alpha = 4.5
fm_construct(predicate = eusilc$eq_income,
fm = "TFR", alpha = 4.5,
breakdown = eusilc$db040)
#fm = "belhadj2015"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=15000, b=2,
fm = "belhadj2015", breakdown = eusilc$db040)
#fm = "cerioli"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z1=100, z2=10000, fm= "cerioli", breakdown = eusilc$db040)
#fm = "belhadj2011"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z_min=1000, z_max=8000, fm= "belhadj2011",
breakdown = eusilc$db040)
#fm = "chakravarty"
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
z=8000, fm= "chakravarty", breakdown = eusilc$db040)
#fm = "ZBM"
#For this index we have to use the household size
fm_construct(predicate = eusilc$eq_income, weight = eusilc$DB090,
hh.size=eusilc$ncomp , fm= "ZBM",
breakdown = eusilc$db040)
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