Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Normalizaion vs. denominaion 1 h JRC Annual Training on Comosie ndiaors & Mulirieria Deision Analysis (CON 1) Normalisaion Doroa Weziak-Bialowolska doroa.bialowolska@jr.e.euroa.eu Euroean Commission Join Researh Cenre Eonomeris and Alied Saisis Uni Comosie ndiaors Researh Grou (JRC-CON) To obain omarabiliy aross variables 1. adjus for dferen naure of indiaors (osiive vs. negaive orienaion owards he inde). adjus for dferen unis of measuremen aross indiaors 3. adjus for dferen ranges of variaion To obain omarabiliy aross ounries dividing he raw daa by size of oulaion, land area, gross domesi rodu, or oher denominaor o make daa omarable aross ounries Normalisaion 1 Normalisaion Doroa Weziak-Bialowolska Weziak-Bialowolska, D., & Dijksra, L. (1). Regional Human Povery 1h JRC Annual Training on nde - overy in he regions of he Euroean Union. JRC Siene Comosie and ndiaors and MCDA Poliy Reors, JRC997. doi:1.788/13 Doroa Weziak-Bialowolska Weziak-Bialowolska, D., & Dijksra, L. (1). Regional Human Povery 1h JRC Annual Training on nde - overy in he regions of he Euroean Union. JRC Siene Comosie and ndiaors and MCDA Poliy Reors, JRC997. doi:1.788/13 Purose of normalisaion Purose of normalisaion Adjus for dferen unis of measuremen Adjus for dferen range of variaion Number of years % Normalisaion Dimension-less indiaors nfan moraliy rae is eressed as he number of deahs of hildren less han one year of age er 1, live birhs (ar-er-housand;.1% - 1.%) Long-erm unemloymen rae is he number of eole wih oninuous eriods of unemloymen eending for a year or longer, eressed as a erenage of he oal unemloyed (1% - %) Normalisaion 3 Normalisaion
1 1 1 1 8. 1 1.. 3 7 3 1 1 1.. 3 3.. 1 7 3 1 1 1.. 3 3.. Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Purose of normalisaion () Normalizaion mehods Adjus for dferen range of variaion Linear sale 1 1 1 Raio sale 1 1 Normalizaion 8 8 1 1 1 Dferen mehods of normalizaion Dferen Ranking Normalisaion Normalisaion Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA To sele he aroriae mehod, we should ake ino aoun: Ouliers may beome uninended benhmarks have a srong ima on he orrelaion sruure Linear sale Normalizaion mehods wheher we wan o kee ereme values, i.e. reward for eeional behaviour Raio sale wheher we wan o benhmark agains a referene ounry Z-sores Min-ma wheher he omosie is ime deenden (issue of omarabiliy over ime) wheher we wan o kee sores for he normalized indiaors Normalisaion 7 Normalisaion 8
Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Sandardizaion (Z-sore) Sandardizaion (Z-sore), Original ndiaor (wih ereme values) mean() = 1. sd() = 1. 18 1 Normalized indiaor sandardized mean() =. sd() = 1. moses a sandard normal disribuion 1 1 1 All normalized indiaors have he same variane (=1) bu no neessarily he same range of variaion # of ounries 1 # of ounries 1 8 Sandardized sores whih are below average are negaive imliaions on he use of geomeri average as an aggregaion mehod Ereme values remain, whih is desirable an inenion is o reward eeional behavior 1 3 7 8 9 indiaor value Ereme values are sill here -1 1 3 7 indiaor value Normalisaion 9 Normalisaion 1 Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Sandardizaion (Z-sore), Resaling (Min-Ma) ma, min min For ime-deenden sudies, in order o assess ounry erformane aross years, he average and he sandard deviaion aross ounries are alulaed for a referene year, usually he iniial ime oin. All normalized indiaors have he same range of variaion (,1) bu no neessarily he same variane ( ) ma( ) min( ) Oherwise, we loose info on boh rend and sread. Ereme values remain, whih is desirable an inenion is o reward eeional behavior Normalisaion 11 Normalisaion 1
Doroa Weziak-Bialowolska Resaling (Min-Ma) Original ndiaor (wih ereme values) Resaling aroah is easier CON o 1 1h JRC Annual Training on ommuniae Comosie o ndiaors a wider ubli and MCDA beause i normalizes -/9/1, indiaors sra o T an idenial range [, 1], [1, 1], [1, 1], where usually higher sores reresen beer ahievemen Normalized indiaor Min-ma ransformaion Doroa Weziak-Bialowolska Resaling (Min-Ma) The eression ma, min min 1h JRC Annual Training on Comosie ndiaors and MCDA # of ounries 1 1 # of ounries 1 1 is someimes used in ime-deenden sudies. However, :, ma, 1 3 7 8 9 indiaor value Ereme values are sill resen 1.1..3....7.8.9 1 indiaor value he normalized indiaor would be larger han 1 An alernaive mehod for ime deenden indiaors is: Normalisaion 13 Normalisaion 1 Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Resaling (Min-Ma) ma T ma min T min min min where he minimum and maimum for eah indiaor are alulaed aross ounries and ime. The normalized indiaors have values beween and 1. When daa for a new ime oin beome available he global minimum and/or he maimum may be affeed. To mainain omarabiliy beween he eising and he new daa, he omosie indiaor for he eising daa mus be realulaed. T An advanage of min-ma resaling mehod over sandardizaion, is ha re-saling widens he range of an indiaor, whih is imoran for he indiaors wih a small range of values, as i allows dfereniaion beween ounries/objes wih similar levels of erformane. Min-ma resaling mehod is no aroriae in he resene of ereme values or ouliers, whih an disor he normalized indiaor. To onrol for his he neessary reamen should be made o avoid ha ereme values bias he resuls. Normalisaion 1 Normalisaion 1
Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Normalizaion mehods Ranking aross ounries rank(, ) Linear sale 1) All ounries are sored aording o he indiaor of ineres ) Sores are relaed by ranks he highes sores reeives he firs ranking Raio sale osiion (rank 1) Ranks Caegorial sales Uses ordinal informaion only, informaion on level is los all normalized indiaors have he same range of variaion [1,n] (n= nof ounries) and he same variane ereme values disaear Normalisaion 17 Normalisaion 18 Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Caegorial sales Normalizaion mehods 8 1 1 7 9 1 7 9 1 Linear sale Raio sale This normalisaion mehod adjuss for ereme values: i is desirable we wan o disard eeional behavior Disane from he referene ounry Over ime Normalisaion 19 Normalisaion
Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Disane from he referene ounry Disane from he referene ounry A dferen aroah is o onsider he ounry iself as he referene ounry and alulae he disane in erms of he iniial ime oin as: Useful in roblems involving a benhmark ounry The referene ounry an be: he grou leader a hyoheial ounry (arge o be reahed in a given imeframe) or an aggregae (eg., EU8, world) This aroah was used in Conern Abou Environmenal Problems (Parker, 1991) for measuring he onern of he ubli in relaion o erain environmenal roblems in hree ounries (aly, Frane and he UK) and in he Euroean Union., Normalisaion 1 Normalisaion Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Disane from he referene ounry Over ime 1 Normalized indiaors have neiher he same range nor he same variane Feasible only wih longiudinal daa The normalizaion does no adjus for ereme values: i is desirable we wan o reward eeional behavior Normalisaion 3 Normalisaion
Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Summary Table Adjus for measuremen uni Adjus for variane Adjus for range Adjus for ereme values ranking z-sore Minma Disane o referene ounry Caegorial sales Y Y Y Y Y Y Y N N N Y Y N Y N Y Y N N N Y 1 3 Conlusions Dferen normalizaion mehods an be found eligible for use Tes all eligible mehods They will rovide dferen resuls for he omosie indiaor Are hese resuls robus? he greaer he number of indiaors, he less he ima on he final ranking due o he seleion of he mehod Robusness ess mus be arried ou o hek his Normalisaion Normalisaion Doroa Weziak-Bialowolska 1h JRC Annual Training on Comosie ndiaors and MCDA Referenes: Annoni, P., Weziak-Bialowolska, D., & Dijksra, L. (1). Qualiy of Le a he subnaional level: an oeraional eamle for he EU. JRC Sieni and Poliy Reors, EUR 3. doi:1.788/797 Saisana, M., & Weziak-Bialowolska, D. (13). UCN s Environmen and Gender nde. JRC suggesions on how o enhane he saisial oherene of he oneual framework. JRC Sieni and Poliy Reors,. Weziak-Bialowolska, D., & Dijksra, L. (1). Regional Human Povery nde - overy in he regions of he Euroean Union. JRC Siene and Poliy Reors, JRC997. doi:1.788/13 Normalisaion 7