EBLUP METHOD OF TIME SERIES AND CROSS-SECTION DATA FOR ESTIMATING EDUCATION INDEX IN DISTRICT PURWAKARTA.

Transcription

1 For Eblp Statstka Method dan Of Koptas e Seres : Indonesan And Cross-Secton Jornal of Statstcs Data ISSN For : Estatng Edcaton Index In Dstrct Prwakarta Vol 0 No7, Oktober 05, p: FSK : Indonesan Jornal aalable of Statstcs onlne at: jornalpbacd/ndexphp/statstka Vol 0 No EBLUP MEHOD OF IME SERIES AND CROSS-SECION DAA FOR ESIMAING EDUCAION INDEX IN DISRIC PURWAKARA Febryan Eka Spratn, Bd Ssetyo, Ksan Sadk, Departent of Statstcs, Bogor Agrcltral Unersy, Indonesa E-al : febryanekas@yahoolcod ABSRAC Snce decentralsaton was pleented n Indonesa, ore detaled nforaton abot the condon of an area becoes ery necessary to know as an ealaton of deelopent that the goernent has done the sccess deelopent of a regon can be seen throgh the Han Deelopent Index (HDI HDI conssts of three basc densons, knowledge as one of that three basc easred by the ndex of edcaton hs ndex s easred by the Adlt Leracy Rate and Mean Years of Schoolng Edcaton s one of the portant factors n prong han deelopent he enhanceent of edcaton ndex reslts n ncreasng the HDI of an area Prwakarta has a son that s ade as a dstrct that excels n edcaton n West Jaa, bt ntl now Prwakarta s edcaton ndex s stll below the West Jaa pronce One step that can be done s to seek nforaton on the edcaton ndex each dstrct n Prwakarta, wh the a to prode the rght polcy n each regon Drect estaton of the coponents forng the HDI for dstrcts s not feasble becase these estates wll generate a great ale of arance, hs s de to the sze of the saple sed s too sall hs stdy proposes a statstcal ethod by perforng the estaton sng sall area estaton hese estates sng nforaton fro srrondng areas that can proe the effecteness of the saple sze and the lower the standard error Soe sreys are condcted reglarly eery year, n condctng ndrect estaton n the srey sch as ths, effcency of estatng edcaton ndex for dstrct leel can be proed by ncldng the rando effect of the area as well as the rando effect of te (Sadk and Notodpro, 006 So n ths stdy wll be sed Eprcal Best Lnear Unbased Predcton (EBLUP by cobnng the te seres and cross-secton data for estatng the edcaton ndex at the leel of dstrcts n Prwakarta he drect estaton of edcaton ndex prodce a larger arance than or ethode, shown by coparng ean sqare error (MSE of drect ethod and ndrect ethod, drect ethod hae the largest MSE Key words : Indrect Estaton, Sall Area Estator, EBLUP, e Seres and Cross-Secton, HDI, Edcaton Index INRODUCION Backgrond Snce the pleentaton of decentralsaton n Indonesa, local goernents are gen the freedo to anage ther respecte regons he need for data or ore detaled nforaton abot the condon of an area becoe ndspensable hat nforaton s sed to deterne as well as an ealaton of deelopent that local goernent has been done Sccessfl deelopent of a regon can be seen throgh the Han Deelopent Index (HDI HDI s based on three basc densons: long and healthy lfe, knowledge and a decent lfe denson (BPS 007 Each denson s easred by an ndex there are lfe expectancy ndex, edcaton ndex and the prchasng power ndexedcaton s an portant and effecte factor for han deelopent Accordng to odaro and Sh (006 n Ilha (04, Edcaton plays an portant role n create han capables of a contry to absorb and create odern technology and to deelop the capacy to create sstanable growth and deelopent Increased of edcaton ndex wll reslt n ncreasng a persons capacy as a reslt of edcaton, by ncreasng a persons capacy s expected to get a better job and gettng a hgher ncoe Hgher ncoe leels wll 34

2 Eblp Method Of e Seres And Cross-Secton Data For Estatng Edcaton Index In Dstrct Prwakarta FSK : Indonesan Jornal of Statstcs Vol 0 No ncrease prchasng power Index, on the other hand soeone wh a hgh leel of ncoe can get better health care so that the ndex lfe expectancy ncreased too Prwakarta s one of the dstrcts n West Jaa who pay bg attenton to edcaton, wh the son s akes Prwakarta as dstrcts that excel n edcaton n West Jaa, bt ntl now Prwakarta s edcaton ndex was stll below West Jaa Pronce Based on data fro BPS Prwakarta s edcaton ndex n 03 aonted to 08, whle the pronce of West Jaa 083 herefore, to realze ths son, the goernent prwakarta shold ge specal attenton n the feld of edcatonone step that can be done s to look for the aont of nforaton on the edcaton ndex each dstrct n Prwakarta hs was done wh the a to prode the rght polcy for each sb-dstrct Edcaton ndex calclaton s done sng data fro the Natonal Socoeconoc Srey (Ssenas Drect estaton of Edcaton ndex for dstrcts s not feasble becase these estates wll generate a large standard error de to sall saples sze (Datta and Lahr, 000 o sole these probles, statstcal ethods by perforng the sall area estaton (SAE can be sed hs estaton are based on odels (plc or explc whch prode a lnk to related sall area throgh sppleentary data sch as adnstratf record and recent censs conts (rao-y 994 the whole of sppleentary data shold hae releance or corelaton to the paraeters obsered (Rao, 003 Models for sall area estaton s lnear xed odels One of technqe copleton lnear xed odel s Eprcal best lnear predcton Unbased (EBLUP that was deeloped by Harlle (977 In the srey condcted perodcally as SUSENAS, effcency of edcaton ndex estaton for the dstrct leel can be ncreased by ncldng rando effect of the area as well as the rando effect of te (Sadk and Notodpro, 006 objecte of ths stdy s estatng the edcaton ndex at the dstrct leel n Prwakarta sng Eprcal Best Lnear Unbased Predcton (EBLUP by cobnng the te seres data and crosssecton LIERAURE REVIEW Edcaton ndex n HDI denson n HDI s easred by edcaton ndex, the ndex s coposed by two basc coponents, naely leracy rate and ean years school he letter leracy rate s the acheeent of basc edcaton to the poplaton, n ths way the poplaton s expected to apply n eeryday lfe, so as to deelop the socal and econoc condon he leracy rate s the percentage of the poplaton aged 5 years and aboe who can read and wre Latn letters or other characters Mean years school ndcatng hgher school edcaton acheed by the people n an area he hgher the ean years school eans hgher leels of edcaton were ndertaken he ean years school descrbes the nber of years sed by the poplaton aged 5 years and aboe n ndergong foral edcaton EBLUP Rao-Y (e Seres and Cross- Sectonal Model Soe sreys are often condcted repeatedly by replacng soe eleents of s saples whch s SUSENAS Rao and Y (99, 994 extend Fay-Herot odels to oercoe te seres and cross-secton data Asse that Where y e,,, and t,, ( x ( Cobnng ( and ( ay be wrten as y x e (3 follow AR ( process for each,, y, t s drect estator fro srey for h sall area at te t, gy ( s eans fncton of sall area, whle e s saplng error, s assed norally dstrbted wh zero ean and block dagonal coarance atrx blockdag (,, x s ector of fxed coarate for h sall area at te t Here N(0,, N(0,,and, are ndependent Based on ( show that assed 35

3 Eblp Method Of e Seres And Cross-Secton Data For Estatng Edcaton Index In Dstrct Prwakarta FSK : Indonesan Jornal of Statstcs Vol 0 No depend on rando sall area effect ( and rando area by te spesfc effect ( Arrangng data as y ( y,, y ; y,, y ; y,, y ( y,, y, eqaton persaaan (3 can rewre as atrx for y X Z e (4 Wh X ( X,, X ; X ( x,, x Z I (,, ; (,, e ( e,, e (,,, e ( e,, e Where t s t-ektor of and I s denty atrx wh order frther E ( 0, co( I E ( 0, co( I R Ee ( 0, e co( blockdag (,, s a x atrx wh eleents j / ( and co( y V R ZZ blockdag ( R J, wh J Rao-Y (994 analogze odel (3 as a General Lnear Mxed Model (GLMM de to a cobnaton of fxed and rando effects In GLMM perfored estate of the lnear cobnaton of paraeters, whle eqaton ( s specal case of lner l l l wh cobnaton l x, l s -ector wh n the h poson and 0 elsewhere, and l s ( ector wh n the th and 0 elsewhere here are aros ethods of paraeter estaton n General Lnear Mxed Models, whch s the Best Lnear Unbased Predcton (BLUP and EBLUP BLUP sed to estate rando and xtre effects of a sall area odels and has the sallest Mean Sqare Error (MSE of all the nbased and lnear estators (Rahan 008 Assng that,, are known, the BLUP of s l ( l Z l R V ( y X And can rewre as for t(,,, y x J y X where ( t ( ( ( X V X X V y s Generalze Least Sqare estator fro, t s h row of In practce paraeters,, are nknown, therefore eprcal BLUP s obtaned by replacng those paraeters wh ther consstent estator he paraeters estator ( ˆ, ˆ, ˆ are obtaned by sng Max Lkelhood (ML and Restrcted Max Lkelhood (REML ethod (see Dallo 04,ths stdy sng ML ethod to estate the paraeters and MSE MEHODOLOGY Data exploraton Varable respone ( y of ths stdy s edcaton ndex whch easred by SUSENAS s data fro 009 ntl 03 and axlary arables are obtaned fro cencs PODES 008 and 0 here are 9 arables : x : otal Poplaton x : Nber of Farng Faly x 3 : Nber of far workers Faly x 4 : Nber of non Electrcy Faly x 5 : Male/Feale x 6 : Nber of eleenter school x 7 : Nber of Jnor Hgh school x 8 : Nber of Senor Hgh school x 9 : Nber of Letter of proerty Data exploraton condcted on all axlary arables and edcaton ndces n each sb-dstrct n the dstrct of Prwakarta Exploraton reslts data can be seen n able whch shows that oerall axlary arables hae a dfferent ales of range s necessary to standardze the data Standardzaton of data s done nto noral standard for Where : th Data : Mean Data 36

4 Eblp Method Of e Seres And Cross-Secton Data For Estatng Edcaton Index In Dstrct Prwakarta FSK : Indonesan Jornal of Statstcs Vol 0 No : Standar Deaton able Reslt of Data Eksploraton N Mn Max Mean Std Deaton x x x x x x x x x Once the data are standardzed, then perfored a correlaton analyss to fnd arables that had a sgnfcant correlaton to the response arable (edcaton ndex Correlaton analyss reslts can be seen n able able Correlaton analyss reslts Pearson Sg (- Correlaton taled Indeks Penddkan 80 Zscore (x 309 ** Zscore (x Zscore (x3-3 * Zscore (x Zscore (x Zscore (x6 34 ** Zscore (x Zscore (x8 96 ** Zscore (x ** Correlaton s sgnfcant at the 00 leel (-taled * Correlaton s sgnfcant at the 005 leel (-taled Fro the table show that after standardzaton, there are for arables that correlated sgnfcantly wh Edcaton Index, whch Zscore arables x (zx, Zscore x3 (ZX3, Zscore x6 (ZX6 and Zscore x8 (zx8 RESUL AND DISCUSSION Prwakarta dstrct conssts of 7 sbdstrcts here s a dstrct that does not se as saple, the aerage nber of poplaton N n each sb-dstrct fro years s nhabants (Podes, 008 and 0 and jst 08% are sed as saple, the nber of ths saple ery sall for each dstrct hs sall sze of saples ake the drect estators generated ch greater MSE than proposed sall area odel It can be seen n Fgre 000E E E E E+00 Fgre MSE of Edcaton Index he resltng eqaton odel fro EBLUP Rao- Y s Edcaton _ Index 0,870 0, x 0, x 3+0,000973x x 8 Wh ˆ , ˆ dan ˆ 0056 Edcaton ndex estaton reslts for each sb-dstrct sng the EBLUP Rao- Y ethod shown n table 3 able 3 Edcaton Index estaton reslt Sb- Dstrc Drect Estaton EBLUP Rao-Y "ML" Year

5 Eblp Method Of e Seres And Cross-Secton Data For Estatng Edcaton Index In Dstrct Prwakarta FSK : Indonesan Jornal of Statstcs Vol 0 No Based on the reslts estaton by sng a odel-y Rao, the aerage of edcaton ndex drng the each sb-dstrct can be seen n fgre Fgre Aerage of Edcaton Index Fro Fgre shows that there are three sb-dstrcts that hae an aerage edcaton ndex s aboe aerage edcaton ndex dstrcts prwakarta naely the dstrcts 0,00 and (Jatlhr, Prwakarta and Bngrsar dstrcts 00 (dstrcts Prwakarta s a dstrct that has the ost hgh aerage edcaton ndex drng the perod It s ery reasonable becase Prwakarta s the cy center so ery easy access to edcatonal facles n sbdstrc Prwakarta Sb-dstrcts 30 (dstrcts egal War has the lowest aerage edcaton ndex, ths cold hae been de to the locaton of the dstrct that s qe far fro the dstrct prwakarta It akes nadeqate edcatonal facles CONCLUSION edcaton Index Estaton of Edcaton Index n Prwakarta dstrct sng a odel of sall area Rao -Y s ch better than the drect estaton, shown by the MSE, drect estaton prodces a ch larger MSE than odel of sall area Rao Y he sall area estaton odel s estaton reslts wold be better f nclded a rando effect of area and te (odel-y Rao REFERENCES [BPS] Badan Psat Statstk 007 Pblkas Indeks Pebangnan Mansa Jakarta (ID:Badan Psat Statstk Dallo MS 04 Sall Area Estaton Under Skew-Noral Nested Error Models [dsertas] [Canada]: Carleton Unersy Ilha S 04 Analss Pengarh Anggaran Penddkan terhadap Indeks Pebangnan Mansa d Indonesa [ess] ID[Bogor]: Instt Pertanan Bogor Rahan A 008 A Reew of Sall Area Estaton Probles and Methodologcal Deelopents Astrala: Unersy of Canberra Rao JNK 003 Sall Area Estaton New Jersey (US: John Wley & Sons, Inc 003 Soe New Deelopents n Sall Area Estaton Jornal of Iranan Statstcal Socety ( : Rao JNK dan Y M 994 Sall Area Estaton by Cobnng e Seres And Cross-Sectonal Data Proceedng of the Secton on srey Research Method Aercan Statstcal Assocaton 994 Sall Area Estaton By Cobnng e Seres and Cross-Sectonal Data he Canadan jornal of statstcs (4: 5-58 Sadk K dan Notodpro KA 006 Model E- BLUP dala Sall Area Estaton ntk Model yang Mengandng Rando Walk Jrnal For Statstka dan Koptas(: