Description
Calculate Alkire-Foster Multidimensional Poverty Measures.
Description
Estimate Multidimensional Poverty Indices disaggregated by population subgroups based on the Alkire and Foster method (2011) <doi:10.1016/j.jpubeco.2010.11.006>. This includes the calculation of standard errors and confidence intervals. Other partial indices such as incidence, intensity and indicator-specific measures as well as intertemporal changes analysis can also be estimated. The standard errors and confidence intervals are calculated considering the complex survey design.
README.md
mpitbR: A Toolbox for Calculating Multidimensional Poverty Indices in R
Here it is provided a package for estimating multidimensional poverty measures based on the Alkire-Foster method which mirrors the estimation procedures of the original mpitb Stata package.
Installation
You can install the development version of mpitbR from GitHub or installing it from CRAN.
# If the package is not available in CRAN you can install it from GitHub!
# From CRAN
if (!require("mpitbR", character.only = TRUE)) {
install.packages("mpitbR")
}
#> Loading required package: mpitbR
# From Github
if (!require("mpitbR", character.only = TRUE)) {
devtools::install_github("girelaignacio/mpitbR")
}
This process may take time the first time.
A short example
# Here we use the same synthetic household survey-like dataset from the Stata package example
data <- subset(syn_cdta)
data <- na.omit(data)
# Define the survey structure
svydata <- survey::svydesign(id=~psu, weights = ~weight, strata = ~stratum, data = data)
# mpitb set command
# First we define the indicators with their dimensions names (d1,d2,d3) as a list
indicators <- list(d1 = c("d_nutr","d_cm"),
d2 = c("d_satt","d_educ"),
d3 = c("d_elct","d_sani","d_wtr","d_hsg","d_ckfl","d_asst"))
# Set the multidimensional poverty measurement project
set <- mpitb.set(svydata, indicators = indicators, name = "myname", desc = "pref. desc")
# mpitb est command
# Estimate!
system.time(
est <- mpitb.est(set, c(20, 33), over = c("area","region"),
tvar = "t", cotyear = "year")
)
#> ****** SPECIFICATION ******
#> Call:
#> mpitb.est.mpitb_set(set = set, klist = c(20, 33), over = c("area",
#> "region"), cotyear = "year", tvar = "t")
#> Name: myname
#> Weighting scheme: equal
#> Description: pref. desc
#> ___________________
#>
#> Dimension 1: d1 0.333 (d_nutr, d_cm)
#> Dimension 2: d2 0.333 (d_satt, d_educ)
#> Dimension 3: d3 0.333 (d_elct, d_sani, d_wtr, d_hsg, d_ckfl, d_asst)
#> ___________________
#>
#> Indicator 1: d_nutr 0.1667
#> Indicator 2: d_cm 0.1667
#> Indicator 3: d_satt 0.1667
#> Indicator 4: d_educ 0.1667
#> Indicator 5: d_elct 0.0556
#> Indicator 6: d_sani 0.0556
#> Indicator 7: d_wtr 0.0556
#> Indicator 8: d_hsg 0.0556
#> Indicator 9: d_ckfl 0.0556
#> Indicator 10: d_asst 0.0556
#>
#> ****** ESTIMATION ******
#> ___________________
#> Partial AF measures: ' M0 H A ' under estimation... DONE
#>
#> ___________________
#> Indicator-specific measures: ' hd hdk actb pctb ' under estimation... DONE
#>
#> ___________________
#> Estimate changes over time over ' M0 H A hd hdk ' measures... DONE
#>
#> ****** RESULTS ******
#> ___________________
#> Parameters
#> Number of time periods: 2
#> Subgroups: 3
#> Poverty cut-offs (k): 2
#>
#> *Notes:
#> Confidence level: 95 %
#> Parallel estimations: FALSE
#> user system elapsed
#> 45.06 1.00 97.00
Some comparisons with the original Stata package
The equivalent command of the previous example in the mpitb Stata package is the following:
mpitb est, name(trial01) measures(all) /// indmeasures(all) aux(all) /// klist(20 33) weight(equal) /// lframe(myresults, replace) /// svy over(area region) /// cotmeasures(all) cotframe(mycot, replace) tvar(t) cotyear(year)
Here below, we compare the results from the Stata package and this version in R. We merged both data frames with the results (point estimate, standard errors, and confidence intervals). We calculate the L1 distance between the estimates ($|\theta_{R}-\theta_{Stata}|$) by measure in the case of the “lframe” results and by ctype and annualized measure in the case of the “cotframe” results.
The following output shows the summary of the distribution of this comparisons (suffix “.x” refers to the estimates of the R package and “.y” to the Stata version).
# "lframe" COMPARISONS
aggregate(abs(b.x - b.y)~ measure, merged, summary)
#> measure abs(b.x - b.y).Min. abs(b.x - b.y).1st Qu. abs(b.x - b.y).Median
#> 1 A 2.537193e-10 2.496580e-09 6.505966e-09
#> 2 actb 2.573115e-14 6.975318e-11 1.892713e-10
#> 3 H 1.972034e-13 3.192835e-09 9.451868e-09
#> 4 hd 5.355799e-12 1.776457e-09 4.280438e-09
#> 5 hdk 2.442491e-15 1.071102e-09 2.483521e-09
#> 6 M0 1.436365e-11 1.280760e-09 2.683751e-09
#> 7 pctb 2.979159e-12 7.875736e-10 1.820007e-09
#> abs(b.x - b.y).Mean abs(b.x - b.y).3rd Qu. abs(b.x - b.y).Max.
#> 1 8.427761e-09 1.304837e-08 2.210272e-08
#> 2 4.151699e-10 4.673255e-10 3.131624e-09
#> 3 1.100592e-08 1.678608e-08 2.963083e-08
#> 4 5.174864e-09 7.316088e-09 1.486417e-08
#> 5 3.248355e-09 4.859661e-09 1.471275e-08
#> 6 3.275439e-09 4.787983e-09 1.169818e-08
#> 7 3.267782e-09 3.926226e-09 2.626389e-08
aggregate(abs(se.x - se.y)~ measure, merged, summary)
#> measure abs(se.x - se.y).Min. abs(se.x - se.y).1st Qu.
#> 1 A 5.416848e-13 5.584464e-11
#> 2 H 1.160892e-11 1.849522e-10
#> 3 hd 6.822338e-13 1.575026e-10
#> 4 hdk 5.614433e-15 1.316371e-10
#> 5 M0 1.465078e-13 6.681607e-11
#> abs(se.x - se.y).Median abs(se.x - se.y).Mean abs(se.x - se.y).3rd Qu.
#> 1 1.480838e-10 1.902079e-10 2.567154e-10
#> 2 4.395547e-10 4.371655e-10 6.625546e-10
#> 3 3.627557e-10 4.065640e-10 6.459523e-10
#> 4 2.777703e-10 3.432593e-10 4.983902e-10
#> 5 1.752028e-10 2.275738e-10 3.695835e-10
#> abs(se.x - se.y).Max.
#> 1 6.804142e-10
#> 2 1.160708e-09
#> 3 1.563327e-09
#> 4 1.832390e-09
#> 5 6.184998e-10
aggregate(abs(ll.x - ll.y)~ measure, merged, summary)
#> measure abs(ll.x - ll.y).Min. abs(ll.x - ll.y).1st Qu.
#> 1 A 2.891913e-10 4.516447e-09
#> 2 H 3.786096e-11 3.067251e-09
#> 3 hd 2.317469e-12 1.400088e-09
#> 4 hdk 2.370888e-12 8.662990e-10
#> 5 M0 3.895412e-12 1.577318e-09
#> abs(ll.x - ll.y).Median abs(ll.x - ll.y).Mean abs(ll.x - ll.y).3rd Qu.
#> 1 7.651098e-09 9.340626e-09 1.471136e-08
#> 2 7.146682e-09 9.442070e-09 1.297974e-08
#> 3 3.383367e-09 4.334191e-09 6.363083e-09
#> 4 1.933710e-09 2.616787e-09 3.715519e-09
#> 5 2.832272e-09 3.768499e-09 5.334923e-09
#> abs(ll.x - ll.y).Max.
#> 1 2.192765e-08
#> 2 2.958044e-08
#> 3 1.482086e-08
#> 4 1.457998e-08
#> 5 1.119702e-08
aggregate(abs(ul.x - ul.y)~ measure, merged, summary)
#> measure abs(ul.x - ul.y).Min. abs(ul.x - ul.y).1st Qu.
#> 1 A 1.068123e-10 3.338948e-09
#> 2 H 2.997895e-10 3.667333e-09
#> 3 hd 1.238520e-11 2.432907e-09
#> 4 hdk 2.556844e-12 1.451214e-09
#> 5 M0 4.180370e-11 1.734692e-09
#> abs(ul.x - ul.y).Median abs(ul.x - ul.y).Mean abs(ul.x - ul.y).3rd Qu.
#> 1 9.316736e-09 1.024661e-08 1.643490e-08
#> 2 7.834429e-09 9.890734e-09 1.367126e-08
#> 3 5.388588e-09 6.273871e-09 9.840444e-09
#> 4 3.231405e-09 4.022657e-09 5.815440e-09
#> 5 2.776975e-09 3.904529e-09 5.206159e-09
#> abs(ul.x - ul.y).Max.
#> 1 2.196234e-08
#> 2 2.897404e-08
#> 3 2.735358e-08
#> 4 1.487718e-08
#> 5 1.141741e-08
# "cotframe" COMPARISONS
aggregate(abs(b.x - b.y)~ ctype+ann, cot.merged, summary)
#> ctype ann abs(b.x - b.y).Min. abs(b.x - b.y).1st Qu. abs(b.x - b.y).Median
#> 1 abs 0 1.870067e-12 3.408458e-10 8.934434e-10
#> 2 rel 0 0.000000e+00 1.760384e-07 4.433030e-07
#> 3 abs 1 1.213274e-13 3.914198e-11 1.023916e-10
#> 4 rel 1 6.494183e-11 2.521504e-08 5.924641e-08
#> abs(b.x - b.y).Mean abs(b.x - b.y).3rd Qu. abs(b.x - b.y).Max.
#> 1 1.223757e-09 1.741895e-09 7.372153e-09
#> 2 5.706635e-07 8.288004e-07 3.124419e-06
#> 3 1.409919e-10 1.976471e-10 9.089043e-10
#> 4 8.606367e-08 1.148786e-07 4.512245e-07
aggregate(abs(se.x - se.y)~ ctype+ann, cot.merged, summary)
#> ctype ann abs(se.x - se.y).Min. abs(se.x - se.y).1st Qu.
#> 1 abs 0 1.005595e-12 1.705410e-10
#> 2 rel 0 1.336629e-10 7.556717e-08
#> 3 abs 1 5.540273e-14 1.943348e-11
#> 4 rel 1 6.217767e-03 2.685340e-01
#> abs(se.x - se.y).Median abs(se.x - se.y).Mean abs(se.x - se.y).3rd Qu.
#> 1 3.957626e-10 4.869718e-10 7.045401e-10
#> 2 1.794390e-07 2.308181e-07 3.476520e-07
#> 3 4.806957e-11 5.777346e-11 8.246320e-11
#> 4 5.255512e-01 6.358943e-01 8.650374e-01
#> abs(se.x - se.y).Max.
#> 1 1.854281e-09
#> 2 1.575077e-06
#> 3 2.303284e-10
#> 4 2.765468e+00
aggregate(abs(ll.x - ll.y)~ ctype+ann, cot.merged, summary)
#> ctype ann abs(ll.x - ll.y).Min. abs(ll.x - ll.y).1st Qu.
#> 1 abs 0 8.942084e-06 5.865915e-05
#> 2 rel 0 9.729035e-10 4.001384e-07
#> 3 abs 1 1.052010e-06 6.901110e-06
#> 4 rel 1 1.218661e-02 5.263171e-01
#> abs(ll.x - ll.y).Median abs(ll.x - ll.y).Mean abs(ll.x - ll.y).3rd Qu.
#> 1 9.840598e-05 9.207851e-05 1.216658e-04
#> 2 8.386673e-07 1.015672e-06 1.476080e-06
#> 3 1.157778e-05 1.083278e-05 1.431329e-05
#> 4 1.030061e+00 1.246330e+00 1.695442e+00
#> abs(ll.x - ll.y).Max.
#> 1 2.013519e-04
#> 2 3.728481e-06
#> 3 2.368856e-05
#> 4 5.420217e+00
aggregate(abs(ul.x - ul.y)~ ctype+ann, cot.merged, summary)
#> ctype ann abs(ul.x - ul.y).Min. abs(ul.x - ul.y).1st Qu.
#> 1 abs 0 8.941498e-06 5.865930e-05
#> 2 rel 0 3.731699e-10 8.543615e-08
#> 3 abs 1 1.051955e-06 6.901133e-06
#> 4 rel 1 1.218664e-02 5.263170e-01
#> abs(ul.x - ul.y).Median abs(ul.x - ul.y).Mean abs(ul.x - ul.y).3rd Qu.
#> 1 9.840926e-05 9.207839e-05 1.216645e-04
#> 2 2.286018e-07 3.617387e-07 4.645883e-07
#> 3 1.157759e-05 1.083275e-05 1.431344e-05
#> 4 1.030061e+00 1.246330e+00 1.695442e+00
#> abs(ul.x - ul.y).Max.
#> 1 2.013484e-04
#> 2 3.679716e-06
#> 3 2.368807e-05
#> 4 5.420217e+00
All the results are very close with some exceptions found in few estimates of the standard errors of the relative changes over time measures. Since the point estimates (“b”) are close and Delta method is used for calculating the standard errors, here there may be some differences between the “survey” library in R and Stata.