Calibration of Expansion Factors in a Multilevel Sampling survey. Abstract

Transcription

1 Calbraton of Epanon Factor n a Multlevel Samplng urvey María Angélca Ferrand 1, Nora Daruch 2, Sabrna Balb 3, Julana Merello 4 1 Inter-Amercan Open Unverty, Roaro, Argentna maferrand@gmal.com 2 Provncal Inttute of Stattc and Survey of Santa Fe, Roaro, Argentna ndaruch@hotmal.com 3 Provncal Inttute of Stattc and Survey of Santa Fe Roaro, Argentna balbabr@yahoo.com.ar 4 Provncal Inttute of Stattc and Survey of Santa Fe, Roaro, Argentna julana_merello@yahoo.com.ar Abtract In large comple urvey ung multlevel amplng wth conglomerate, dfferent level of tratfcaton, electon probablte proportonal to ze, etc., one of the man problem relate to ba. Comple amplng degn, uch a thoe jut mentoned, ometme do not allow for ba control, becaue dfferent electon probablte are nvolved for amplng unt, and ample are not elf-weghed. All uch ba-related dffculte mpede a correct readng of etmaton or mae outcome comparon mpoble. Conequently, the uual practce to correct or adjut baelne epanon factor or wegh (uually, regreon of electon probablte) baed on aulary nown data or nformaton preet from eternal ource or record. The purpoe of th paper to mae baelne weght adjutment by mean of the calbraton of fed margnal probablte technque n the Uo de Tempo (Tme Uage) urvey, carred out n the Cty of Roaro, Santa Fe Provnce (Argentna 2010). Th technque wa appled a per Devlle and Särndal' [1992] method. Baed on a general approach, uch technque ntroduce new weght a a reult of adjutng or calbratng baelne weghtng et at the degn phae by olvng out a problem of numercal mnmzaton. The problem defned by the electon of a dtance between the new fed margnal probablte and the baelne one, and the ue of a et of retrcton on the aulary varable nvolved n the adjutment. The calbraton performed ept amplng degn ued n the urvey. Therefore, t wa appled to the baelne epanon factor for each amplng unt (houehold n the Tme Uage Survey), whch were corrected a per non-repone, nce th wa the lat amplng unt of the degn. Regardng aulary nformaton ued for calbraton and adjutment of the amplng nner chema, data were retreved from the Ceno Naconal de Poblacón, Hogare y Vvenda 2001 (2001 Natonal Survey on Populaton, Houng and Houehold). Keyword: Calbraton, Epanon Factor, Multlevel Samplng, Etmaton. 1. Introducton The Uo de Tempo (Tme Uage) urvey, carred out n the Cty of Roaro, Santa Fe Provnce durng May, June and July 2012, provded wth repreentatve nformaton of people +15 year old from the Cty of Roaro, regterng the equencng and duraton of daly actvte carred out by one peron durng a pecfc perod of tme, uually 24 hour, uch a job, ether profeonally or at home, educaton, free tme, voluntarm, etc. for weeday (from Monday to Frday), for weeend and for the whole wee. By mean of a urvey, the am analyzng the behavor of a partcular feature and etmatng t populaton total, but the amount of tem oberved wll not be the ame a t populaton total, and, to etmate uch total, weghtng wll be ued to get the frt etmaton.

2 By etmatng a varable for whch a populaton dtrbuton nown, uch a gender and age, and not tang them nto account durng the creenng proce, t hghly lely that, due to the amplng randomne or the lac of repone, etmated dtrbuton are erroneou. The total of men and women n the ample were calculated, and they mmatched wth the populaton dtrbuton, o, f th urvey fal to repreent populaton by gender and age, t wll not be vald for provdng any other type of data ether. Baelne weght were adjuted ung re-weghtng technque, uch a calbraton method developed by Devlle and Säfrndal (1992) and chedulng degned by Devlle, Särndal and Sautory (1993) wthn the SAS oftware, whch tattc-pecfc, under the name CALMAR (CALage ur MARge). 2. Method The followng paragraph nclude a ummarzed dea of the theoretcal approach eplaned by Devlle, Särndal and Sautory (1993). The technque of etmaton by calbraton wa ntroduced by Devlle and Särndal n The dea to ue aulary nformaton to obtan a better etmate of a populaton tattc. Frt, conder a fnte populaton U of ze N wth unt label 1, 2,...,N. Let y, = 1,...,N be the tudy varable and, = 1,...,N be the -dmenonal vector of aulary varable aocated wth unt. Suppoe we are ntereted n etmatng the populaton total: N t y y 1 We draw a ample = {1, 2,..., n} U ung a probablty amplng degn P, where the frt and econd order ncluon probablte are =Pr ( ) and j =Pr (,j ) repectvely. An etmate of t y the Horvtz-Thompon (HT) etmator: tˆ d y HT where d =1/ the amplng weght, defned a the nvere of the ncluon probablty for unt. An attractve property of the HT etmator that t guaranteed to be unbaed regardle of the amplng degn P. It varance under P gven a N N y y j V (tˆ ) ( ) p HT 1 j 1 j j Now let u uppoe that {, = 1,...,N} avalable and, nown. Ideally, we would le X: d t but often tme th not true. j t N 1 the populaton total for The dea behnd calbraton etmator to fnd weght w, = 1,... n cloe to d, baed on a dtance functon, uch that X: w t We wh to fnd weght w mlar to d o a to preerve the unbaed property of the HT etmator. Once w found, the calbraton etmator for t y tˆ w y To formalze th procedure, a dtance functon to meaure promty of potental calbraton factor et to baelne weght defned. By mathematcal development, generalzed regreon epreon of etmator reached (Särndal, Swenon and Wretman,1992). c

3 Y cal Y B' (X X ) Ŷ GREG B The CALMAR macro calculate fnal weght for each of the cae, baed on t feature, tang nto account baelne weght (nvere of ample ncluon probablty). 2.1 Objectve The man objectve of the urvey wa etmatng the amount of people performng any type of voluntary wor n the Cty of Roaro. And to quantfy the tme pent worng for the maret, houehold wor and other actvte related to tudyng, free tme and ret, etc. Voluntary wor defned a the unpad actvty performed baed on one' own decon wth the ntenton of renderng beneft to other wth no underlyng duty nor oblgaton derved from famly relaton or frendhp. 2.2 Target populaton Data about the ue of tme by men and women lvng n houehold n the Cty of Roaro wa collected. Houehold member who were 15 year old or older were probed, and they were aed to fll n an actvty dary and an ndvdual quetonnare. 2.3 Surveyng mechanm Two urveyng mechanm were ued: an ndvdual quetonnare --where houehold member were recorded, along wth the peronal trat of each of them-- and the Actvty Dary. The Actvty Dary cover a24-hour tme pan, tartng at 4.00 a.m. on the day before the ntervew and endng at 4.00 a. m. of the ntervew day. It contan mnute tme et, n whch up to three actvte can be ncluded, 6 overlappng code for the econd and thrd actvty, and localzaton code for all actvte. The Actvty Dary alo ncluded three verfcaton queton, degned to render actvte that are uually forgotten, or to help codng; and a control queton about the type of day (typcal day/non-typcal day). The Actvty Dary wa flled n by urveyor wth actvte done by the repondent durng the ntervew performed baed on a gude of queton pecfcally degned. Queton "What were you dong yeterday between and? and then, Were you dong anythng ele? repeated for each tme et, ecept for the leepng tme (conderng the Dary tarted at the tme the repondent woe up and ended at the tme he/he went to leep), and the tme pent on worng for the maret, for whch a pecal et of queton wa degned. 2.4 Samplng Mult-phaed tudy wth prmary unt tratfcaton. Prmary unt tratfcaton wa performed baed on a prevou paper, where radue were clutered accordng to a cluter tattcal analy, analyzng a et of varable from the 2001 Natonal Populaton and Houehold Cenu ("Socal Map"). Prmary unt: radue (area). Selecton wa done wth a probablty whch wa proportonal to the tratum ze, meaured by the number of houehold. Secondary unt: bloc, ngle randomzaton, wth probablty baed on the number of bloc n each radu. Tertary unt: houehold, ytematc amplng. Selecton of 10 houehold baed on a ytematc amplng wth random tart. ( d ' ) 1 d y

4 2.4.1 Sample ze Allocaton To determne ample ze, certan nowledge of the populaton n term of bac feature of the ubject of the tudy and the daggregaton level ntended to analyze data wa neceary. Baed on prevou tude, data collected about the rate of people performng voluntary wor at the level of 2-dgt daggregaton were analyzed. Conderng the need to provde data at the level of the Cty of Roaro, a ample ze of 1040 houehold wa defned; a ample of 10 houehold wa defned n the elected area. Wth uch a ze, a varaton coeffcent below 15% wa epected for the man actvte Sample electon A a framewor for ample electon, a geographcal area frame wa ued; uch area conted of cenu radue ued n the 2001 Populaton and Houehold Cenu, grouped n 5 trata. Cenu radue were elected for each tratum wth a probablty whch wa proportonal to ther ze; bloc by ngle randomzaton and houehold wth probablty by ytematc amplng wth random tart. 3. Outcome The followng table depct fnal ample of prmary unt and of econd phae, dtrbuted by trata. Table # 1: Fnal ample of prmary unt and econd phae, dtrbuted by trata Stratum Total Houehold Rate n the ample Amount of elected radue 1 7, , , , , Total 268,071 1, Baelne weghtng and etmator To calculate weghtng, the probablty of electon of the area, bloc and houehold wa taen nto account. When the houehold elected and all houehold member are probed, weghtng derved from electon probablty the ame for the houehold and all the people lvng theren, nce no creenng proce wa done n the houehold. When calculatng total for baelne weghtng, t wa noted thee dd not match wth the populaton total. Therefore, the re-weghtng technque wa ued n order to adjut ample dtrbuton to the populaton dtrbuton reported by eternal ource. Snce there wa no cenu recent nformaton avalable, populaton projecton wa ued, by age and gender, n the year the urvey wa performed. Applyng newly calbrated weght, etmaton were calculated, and a more content pattern wa found.

5 Table #2 and #3: Etmated populaton wth baelne weghtng Gender Total % Total 789, % Male 374, % Female 415, % Age group Total % Total 789, % ,990 22% ,837 15% ,562 22% ,471 12% ,053 15% ,704 7% ,967 7% Table #4: Etmated populaton wth calbrated weghtng Gender Total % Age group Total % Total 909, % Total 909, % Male 430, % , % Female 479, % , % , % , % , % , % , % Table #5: Populaton Projecton Total Men Women Column % Row %a Total 909, , , , , , , , , , , , , , , , , , , , , , , ,

6 4. Concluon In pte of all the logcal lmtaton of th tudy, we can aume that ung etmator wth aulary nformaton generally offer the beneft of accuracy of ome of the etmaton, and t hardly ever woren the baelne tuaton. Th a relevant fact, nce urvey uually have multple objectve and, therefore, t not eay to fnd a et of aulary nformaton approprate for all of them. By mean of ung the Calmar oftware, total populaton adjutment wa attaned by age group and total populaton baed on gender. However, f we am at etmaton at even lower daggregaton level, uch a "Populaton total by age group and gender", alternatve method wll have to be condered. 5. Bblography J.C.Devlle and C.E.Särndal - (1992) - Calbraton Etmator n Survey Samplng Document # F Inttuto Naconal de Etadítca y Etudo Económco de Franca - (1993) - Calmar macro Arrero C.P. - Calbratng a houehold Survey by ung the Calmar Program Wu C., Sttter R.R. - (2001) - A model-calbraton approach to ung complete aulary nformaton from urvery data Equvel, Valera - (2009) - Uo del Tempo en la Cudad de Bueno Are - 1 Edc.Lo Polvorne: Unverdad Naconal Gral. Sarmento. Budlender D., Chobooane N. and Mpethen Y. - (2001) - A urvey of tme ue: How South Afrcan women and men pend ther tme Stattc South Afrca. Pretora Lele Kh - (1972) - Muetreo de Encueta Cochran, W.C. - (1982) - Técnca de Muetreo