rescaleColumns() - (preprocessing stage) Rescales columns using min-max normalization, z-scoring, or ranking. (.csv export option)
linearAggExc() - Creates composite indicators for multiple years returning scores and ranks for each statistical unit through linear aggregation. Automatically computes alternative scores and ranks for inclusion and exclusion of individual indicators.(.csv export option)
To display uncertainity analysis, the package offers functions:
ranksCount() - Counts the number (percent) of times a statistical unit takes a given rank. (.csv export option)
descStats_scores_ranks() - Provides a table with the initial rank, average and median rank taken accross simulations. Also computes standard deviation and coefficient of variation. (.csv export option)
ranksCount_colCode() - Exports .xlsx tables with the frequencies of each rank color coded for initial, median and modal rank.
rankShift_avg() - Computes the average shift in ranking (total, per year, and per country and year).
boxplotRanks() - Create boxplots of ranks taken in different simulations. (.png export option)
library(devtools)install_github("marinaferent/compIndTools")Some examples are provided below.
rescaleColumns() - Rescales (min -max, z-score, rank) values per column in a dataframe.
library(compIndTools)
dataTest_moreYears[c(1:5,27:32),1:5]## country time fixedTerm fixedTermComp selfEmployment
## 1 Belgium 2001 243.0769 300.42918 485.8757
## 2 Bulgaria 2001 160.0000 145.92275 NA
## 3 Czech Republic 2001 NA NA 146.8927
## 4 Denmark 2001 261.5385 163.09013 242.9379
## 5 Germany 2001 353.8462 55.79399 310.7345
## 27 Sweden 2001 449.2308 167.38197 214.6893
## 28 United Kingdom 2001 175.3846 72.96137 570.6215
## 29 Belgium 2002 206.1538 248.92704 485.8757
## 30 Bulgaria 2002 135.3846 141.63090 NA
## 31 Czech Republic 2002 NA NA 146.8927
## 32 Denmark 2002 243.0769 154.50644 242.9379
rescaleColumns(dataTest_moreYears)[c(1:5,27:32),1:5]## country time fixedTerm fixedTermComp selfEmployment
## [1,] "Belgium" "2001" "25.16" "29.44" "48.59"
## [2,] "Bulgaria" "2001" "16.56" "13.85" NA
## [3,] "Czech Republic" "2001" NA NA "14.69"
## [4,] "Denmark" "2001" "27.07" "15.58" "24.29"
## [5,] "Germany" "2001" "36.62" "4.76" "31.07"
## [6,] "Sweden" "2001" "46.5" "16.02" "21.47"
## [7,] "United Kingdom" "2001" "18.15" "6.49" "57.06"
## [8,] "Belgium" "2002" "21.34" "24.24" "48.59"
## [9,] "Bulgaria" "2002" "14.01" "13.42" NA
## [10,] "Czech Republic" "2002" NA NA "14.69"
## [11,] "Denmark" "2002" "25.16" "14.72" "24.29"
rescaleColumns(dataTest_moreYears, method="z-score", decim=3)[1:5,1:5]## country time fixedTerm fixedTermComp selfEmployment
## [1,] "Belgium" "2001" "-0.258" "0.373" "0.373"
## [2,] "Bulgaria" "2001" "-0.679" "-0.388" NA
## [3,] "Czech Republic" "2001" NA NA "-0.976"
## [4,] "Denmark" "2001" "-0.164" "-0.303" "-0.593"
## [5,] "Germany" "2001" "0.304" "-0.831" "-0.324"
linearAggExc()- Computes index scores and ranks using linear aggregation for one or multiple time periods. Automatically computes alternative scores and ranks for inclusion and exclusion of individual indicators.
dataTest_oneYear[1:5,1:5]## country time fixedTerm fixedTermComp selfEmployment
## 1 Belgium 2002 206.1538 248.9270 485.8757
## 2 Bulgaria 2002 135.3846 141.6309 NA
## 3 Czech Republic 2002 NA NA 146.8927
## 4 Denmark 2002 243.0769 154.5064 242.9379
## 5 Germany 2002 341.5385 47.2103 310.7345
direction=c(1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1)
weight=c(1/18, 1/18, 1/18, 1/18, 1/18, 1/18, 1/15, 1/15, 1/15, 1/75, 1/75, 1/75, 1/75, 1/75, 1/15, 1/6, 1/6)
a=linearAggExc(dataTest_oneYear, direction, weight)
#to also store the scores and ranks into 2 .csv files:
#a=linearAggExc(dataTest, direction, weight, path="E:/Sample folder")
a$scores[1:5,1:5]## Statistical unit Time S0 S1 S2
## 1 Belgium 2002 -30.582826 -42.035818 -16.753546
## 2 Bulgaria 2002 9.376503 1.855135 17.244886
## 3 Czech Republic 2002 16.800431 16.800431 16.800431
## 4 Denmark 2002 -90.919783 -104.424056 -82.336092
## 5 Germany 2002 3.791631 -15.182728 6.414426
a$ranks[1:5,1:5]## Statistical unit Time S0 S1 S2
## 1 Belgium 2002 14 14 14
## 2 Bulgaria 2002 9 8 7
## 3 Czech Republic 2002 6 5 8
## 4 Denmark 2002 25 25 24
## 5 Germany 2002 11 11 12
#for multiple years data: for each year one scores and one ranks matrix will be stored as a .csv file in the path folder:
#linearAggExc(x=dataTest_moreYears, direction=direction, weight=weight, path="E:/Sample folder", year1=2001, yearT=2003)ranksCount() - Computes number and percent of times that each rank is taken by each statistical unit.
ranks2001[1:5,]## Statistical.unit Time S0 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17
## 1 Belgium 2001 14 15 14 18 16 16 10 19 14 14 14 14 14 14 14 12 10 19
## 2 Bulgaria 2001 8 7 8 6 10 6 13 8 9 6 8 8 7 7 8 6 20 15
## 3 Czech Republic 2001 5 4 6 5 5 5 6 5 6 8 6 6 5 6 5 8 17 10
## 4 Denmark 2001 25 25 25 25 25 23 24 25 25 25 25 25 25 24 24 26 27 3
## 5 Germany 2001 13 11 12 12 8 12 7 13 12 11 12 13 12 13 11 19 2 13
a=ranksCount(ranks2001)
a$rankNb[1:5,]## Statistical unit Time R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28
## 1 Belgium 2001 0 0 0 0 0 0 0 0 0 2 0 1 0 9 1 2 0 1 2 0 0 0 0 0 0 0 0 0
## 2 Bulgaria 2001 0 0 0 0 0 4 3 6 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
## 3 Czech Republic 2001 0 0 0 1 7 6 0 2 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## 4 Denmark 2001 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 11 1 1 0
## 5 Germany 2001 0 1 0 0 0 0 1 1 0 0 3 6 5 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
a$rankPc[1:5,]## Statistical unit Time R1 R2 R3 R4 R5 R6 R7 R8 R9
## 1 Belgium 2001 0% 0% 0% 0% 0% 0% 0% 0% 0%
## 2 Bulgaria 2001 0% 0% 0% 0% 0% 22.22% 16.67% 33.33% 5.56%
## 3 Czech Republic 2001 0% 0% 0% 5.56% 38.89% 33.33% 0% 11.11% 0%
## 4 Denmark 2001 0% 0% 5.56% 0% 0% 0% 0% 0% 0%
## 5 Germany 2001 0% 5.56% 0% 0% 0% 0% 5.56% 5.56% 0%
## R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22
## 1 11.11% 0% 5.56% 0% 50% 5.56% 11.11% 0% 5.56% 11.11% 0% 0% 0%
## 2 5.56% 0% 0% 5.56% 0% 5.56% 0% 0% 0% 0% 5.56% 0% 0%
## 3 5.56% 0% 0% 0% 0% 0% 0% 5.56% 0% 0% 0% 0% 0%
## 4 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%
## 5 0% 16.67% 33.33% 27.78% 0% 0% 0% 0% 0% 5.56% 0% 0% 0%
## R23 R24 R25 R26 R27 R28
## 1 0% 0% 0% 0% 0% 0%
## 2 0% 0% 0% 0% 0% 0%
## 3 0% 0% 0% 0% 0% 0%
## 4 5.56% 16.67% 61.11% 5.56% 5.56% 0%
## 5 0% 0% 0% 0% 0% 0%
###to automatically store the two .csv files in the desired folder, use path:
#ranksCount(ranks2001, decim=0, path="E:/Sample folder")descStats_scores_ranks() - Computes average, median, stdev, and coefficient of variation for ranks or scores from multiple simulations. Returns master file with initial rank (score), followed by average and median one for each statistical unit and each period.
Example 1: one-year data
ranks2001[1:5,1:5]## Statistical.unit Time S0 S1 S2
## 1 Belgium 2001 14 15 14
## 2 Bulgaria 2001 8 7 8
## 3 Czech Republic 2001 5 4 6
## 4 Denmark 2001 25 25 25
## 5 Germany 2001 13 11 12
dataTestList=list(ranks2001)
a=descStats_scores_ranks(dataTestList,
#path="E:/Sample folder"
)
a$masterFile## 0
## Belgium "14 (Avg=14.5; Me=14)"
## Bulgaria "8 (Avg=8.89; Me=8)"
## Czech Republic "5 (Avg=6.56; Me=6)"
## Denmark "25 (Avg=23.67; Me=25)"
## Germany "13 (Avg=11.44; Me=12)"
## Estonia "7 (Avg=7.78; Me=7)"
## Ireland "12 (Avg=11.39; Me=12)"
## Greece "22 (Avg=21.72; Me=22)"
## Spain "6 (Avg=7.22; Me=6)"
## France "11 (Avg=10.83; Me=11)"
## Croatia "28 (Avg=28; Me=28)"
## Italy "16 (Avg=16.06; Me=16)"
## Cyprus "18 (Avg=17.39; Me=17.5)"
## Latvia "21 (Avg=20.17; Me=21)"
## Lithuania "23 (Avg=23.06; Me=23)"
## Luxembourg "15 (Avg=15.78; Me=15.5)"
## Hungary "26 (Avg=25.83; Me=26)"
## Malta "9 (Avg=9.44; Me=9.5)"
## Netherlands "20 (Avg=19.06; Me=20)"
## Austria "10 (Avg=10.11; Me=10)"
## Poland "17 (Avg=17.33; Me=17)"
## Portugal "3 (Avg=3.33; Me=3)"
## Romania "1 (Avg=1.06; Me=1)"
## Slovenia "19 (Avg=18.39; Me=19)"
## Slovakia "24 (Avg=23.94; Me=24)"
## Finland "4 (Avg=4.39; Me=4)"
## Sweden "27 (Avg=26.39; Me=27)"
## United Kingdom "2 (Avg=2.28; Me=2)"
Example 2: multiple years data
names(ranks2001_2003)## [1] "ranks2001" "ranks2002" "ranks2003"
a=descStats_scores_ranks(ranks2001_2003, time=c(2001, 2002, 2003), decim=4)
a$masterFile[1:5,]## 2001 2002
## Belgium "14 (Avg=14.5; Me=14)" "14 (Avg=14.1111; Me=14)"
## Bulgaria "8 (Avg=8.8889; Me=8)" "9 (Avg=9.3889; Me=8)"
## Czech Republic "5 (Avg=6.5556; Me=6)" "6 (Avg=7.6111; Me=6.5)"
## Denmark "25 (Avg=23.6667; Me=25)" "25 (Avg=23.7222; Me=25)"
## Germany "13 (Avg=11.4444; Me=12)" "11 (Avg=10.4444; Me=11)"
## 2003
## Belgium "14 (Avg=14.1667; Me=14)"
## Bulgaria "9 (Avg=9.7222; Me=8)"
## Czech Republic "6 (Avg=6.9444; Me=6)"
## Denmark "24 (Avg=22.6667; Me=24)"
## Germany "12 (Avg=11.3889; Me=12)"
a$x_stdev[1:5,]## 2001 2002 2003
## Belgium "2.5029" "2.2981" "2.0934"
## Bulgaria "3.6604" "3.9279" "3.7386"
## Czech Republic "2.9748" "3.0705" "3.0577"
## Denmark "5.2244" "4.9918" "4.9705"
## Germany "3.3646" "2.8947" "2.9732"
ranksCount_colCode() - Returns a color coded table with frequency of each rank. Initial, median and modal rank frequency cells are color-coded.
ranks2001[1:5,1:5]## Statistical.unit Time S0 S1 S2
## 1 Belgium 2001 14 15 14
## 2 Bulgaria 2001 8 7 8
## 3 Czech Republic 2001 5 4 6
## 4 Denmark 2001 25 25 25
## 5 Germany 2001 13 11 12
#' #ranksCount_colCode(ranks2001, decim=4, path="E:/Sample folder", year="2001")
a=ranksCount_colCode(ranks2001,decim=0)rankShift_avg() - Computes the average shift in ranking. The novelty of the function is that it extends the 1 period formula to encompass multiple time periods. It returns three types of average shift in ranking - total, per year, and per country and year.
ranksInitial2001_2003[1:5,]## Country X2001 X2002 X2003
## 1 Belgium 14 14 14
## 2 Bulgaria 8 9 9
## 3 Czech Republic 5 6 6
## 4 Denmark 25 25 24
## 5 Germany 13 11 12
names(ranksNb2001_2003)## [1] "ranksNb2001" "ranksNb2002" "ranksNb2003"
a=rankShift_avg(ranksInitial2001_2003, ranksNb2001_2003)
a$RsTotal## [1] 0.01544084
a$RsYear## [1] 0.01553103 0.01531117 0.01548031
round(a$RsCountry[[1]],4)## [1] 0.0203 0.0208 0.0228 0.0188 0.0168 0.0198 0.0134 0.0114 0.0218 0.0134
## [11] 0.0089 0.0154 0.0154 0.0163 0.0114 0.0248 0.0094 0.0198 0.0213 0.0139
## [21] 0.0139 0.0119 0.0094 0.0173 0.0104 0.0124 0.0124 0.0114
boxplotRanks() - Creates a boxplot of ranks from simulations.
names(ranks2001_2003)## [1] "ranks2001" "ranks2002" "ranks2003"
boxplotRanks(ranks2001_2003)
If we want to use country codes instead, we could:
countryFullName=c("Belgium", "Bulgaria", "Czech Republic", "Denmark", "Germany", "Estonia", "Ireland", "Greece",
"Spain", "France", "Croatia", "Italy", "Cyprus", "Latvia", "Lithuania", "Luxembourg", "Hungary",
"Malta", "Netherlands", "Austria", "Poland", "Portugal", "Romania", "Slovenia", "Slovakia",
"Finland", "Sweden", "United Kingdom")
countryID=c("BE", "BG", "CZ", "DK", "DE", "EE", "IE", "GR", "ES", "FR", "HR", "IT", "CY", "LV", "LT", "LU", "HU",
"MT", "NL", "AT", "PL", "PT", "RO", "SI", "SK", "FI", "SE", "UK")
boxplotRanks(ranks2001_2003, statUnitsFullName=countryFullName, statUnitsIDs=countryID)
Below we create 3 boxplots and store them in the path folder: (2001.png, 2002.png, and 2003.png)
#boxplotRanks(ranks2001_2003, path="E:/Sample folder", statUnitsFullName=countryFullName, statUnitsIDs=countryID)For theoretical explanation on steps in constructing a composite indicator, please refer to the books and articles listed below. To be mentioned, the references only refer to one-year composite indicators. Present package took the liberty to extend the knowledge to multiple years.
— Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffmann, A., & Giovannini, E. (2008). Handbook on constructing composite indicators: methodology and user guide. OECD Publishing. Retrieved from https://www.oecd.org/els/soc/handbookonconstructingcompositeindicatorsmethodologyanduserguide.htm
— Saisana, M., & Saltelli, A. (2006). Sensitive Issues in the Development of Composite Indicators for PolicyMaking. Conference: Simulation in Industry and Services. Brussels, Belgium.
— Saisana, M., Saltelli, A., & Stefano , T. (2005). Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators. Journal of the Royal Statistical Society: Series A (Statistics in Society), 168(2), 307-323.
— Manca, A. R., Governatori, M., & Mascherini, M. (2010). Towards a set of composite indicators on flexicurity: A comprehensive approach. Luxembourg: Publications Office of the European Union. Retrieved from https://publications.jrc.ec.europa.eu/repository/handle/JRC58069