Lecture 3: Nonresponse issues and imputation

Transcription

1 Lectue 3: Noepoe ue ad mputato Souce of oepoe eal lfe eample Effect of oepoe ba Etmato method fo educg the effect of oepoe Weghtg, fo ut oepoe ol ve hot Imputato method, fo tem oepoe mal Nogoable epoe mecham

2 Noepoe occu almot all uve, eve compulo oe Labo Foce uve Nowa, quatel, 0% oepoe Peceved to have ceaed ecet ea Bede amplg eo, the mot mpotat ouce of eo amplg Noepoe mpotat to code becaue of Potetal ba wll almot alwa eult ba, ample ot epeetatve of the populato Iceaed ucetat the etmate

3 Noepoe the falue to obta complete obevato o the uve ample Ut oepoe: ut peo o houehold the ample doe ot epod Ca be ve hgh popoto, ca be a much a 70% potal uve 30% ot ucommo telephoe uve 50% the Nowega Coume Epedtue uve, up fom about 30% 5 ea ago Item oepoe: obevato o ome tem ae mg fo ut ample emede: Weghtg fo ut oepoe, mputato fo tem oepoe 3

4 Souce of ut oepoe No-cotact: falue to locate/detf ample ut o to cotact ample ut efual: ample ut efue to patcpate Iablt to epod: ample ut uable to patcpate, e.g. due to ll health, laguage poblem Othe: e.g. accdetal lo of data/quetoae 4

5 Souce of tem oepoe epodet: awe ot kow efual etve o elevat queto accdetal kp Itevewe: - doe ot ak the queto - doe ot ecod epoe Poceg epoe ejected at edtg Amout ome vaable ol -% Ofte hghet fo facal vaable, e.g. total houehold come ma have 0% mg data 5

6 The epoe ate the mot wdel epoted qualt dcato But eed ot be elated to how lage the ba ma be eample to llutate how oepoe ca lead to ve mleadg tattcal aal, eve whe the epoe ate hgh 6

7 . Clacal eample, epoe ate 8-85% Poltcal pollg befoe the Ameca pedetal electo 948 Democatc caddate: Tuma epublca caddate: Dewe Ittute: ope Suve : Jul, Augut, Septembe, Octobe Electo: Novembe 7

8 Jul Augut Sept Oct Electo Tuma Dewe Othe Sample ze epoe Noepoe Pecetage

9 Ba: Lage oepoe ate amog the ecoomcall pooe goup Compeatg fo oepoe: Model the pobablt of epoe depedet o whch caddate the peo wll vote fo, wth each oco-ecoomc goup Nogoable epoe mecham Gve Tuma 5% Method: Imputato, etmate 93-99% wll vote fo Tuma the oepoe goup 9

10 . Electo uve Nowa 993 Sample: 3000 peo Numbe of epoe, afte two callback: 403 Etmate the votg popoto Of the 403, 90 ad the voted Palamet electo: 84.8% Mag of eo: % Tue votg popoto 75.5% Etmate 84.8% baed becaue hghe oepoe ate amog ovote The epoe ample ot epeetatve of the oepoe goup tpcall the cae Mag of eo : SE

11 Effect of oepoe Fed populato model of oepoe: U fte populato of N ut f ut doe/would epod 0 f ot,..., N U U N N ' ae fed, ot adom M M { U { U : ze of U ze of : U } epodg ubpopulato 0} oepodg ubpopulato M

12 Ba of tadad etmato Smple adom ample of ze epoe Etmate Populato the ample: populato mea of U U mea adu M, ze N : N ad M q N N / NMM q q N N epected epoe ate M

13 Stadad etmato : obeved ample mea : Gve : the epoe ample E a adom ample fomu Ba E q q M q M No ba f ethe q o M 3

14 4 Mea quae eo: ] [ ] [ M q q N q E EVa E Va E σ We otce that eve f thee o ba, the ucetat ceae becaue of malle ample ze Epected ample ze deceae fom to q Fo eample, f we wat a ample of 000 ut ad we kow q : 000/q If epected epoe ate 60% : eed 000/

15 Ba E q M Poble coequee of oepoe:. Ba depedet of, ca ot be educed b ceag. Ba ceae wth ceag oepoe ate -q 3. Ba ceae whe M ceae 4. If : goable M oepoe mecham 5

16 Uealtc to aume M, But wth malle ubpopulato t ma ot be ueaoable, epecall f the vaable ued to patto the populato hghl coelated wth Called: pottatfcato Wdel ued tool to coect fo oepoe 6

17 Etmato method fo educg the effect of oepoe Hadlg oepoe: educe the ze of oepoe, epecall b callback educe the effect of oepoe, b etmatg the ba ad coectg the ogal etmato deged fo a full ample Etmato method: Weghtg, fo ut oepoe Imputato, epecall fo tem oepoe 7

18 Weghtg Bac dea: Some pat of the populato ae udeepeeted the epoe ample Wegh thee pat up to compeate fo udeepeetato Populato-baed educe amplg eo Adjut fo ut oepoe 8

19 Pottatfcato. Statf ug vaable that patto the populato homogeeou goup. Statf accodg to vag epoe ate H pottata. Fo pottatum h, U h the epodg ubtatum ad U Mh the oepodg ubtatum q W h h h Mh epoe ate potatum h N h / N, whee N mea epoetatum h mea oepoetatum h h the ze of pottatum h 9

20 Smple adom ample ad etmatg E q H W q q h h h h h H q h W h h. compoet: Ba becaue of dffeet epoe ate the pottata, ca be etmated. Compoet ca ot be etmated f epoe ad oepoe mea ae dffeet Mh Pottatfcato etmate the ft compoet Chooe pottata uch that mot of the ba the ft compoet q h hould va a much a poble, ad h Mh 0

21 H h h h W : Ft compoet H h h h h W h : ubaed etmato fo th compoet : mea fom pottatum Obeved H h h h pot H h h h h H h h h h h pot N t N N W W ad fo the total, : adjuted etmato The pottatfed etmato h N h h h h the epoe ample potatum the ze of, / : Weght fo each obevato pottaum

22 Etmatg the umbe of oe-peo houehold, Nowega coume epedtue uve 99 Pottata: Fam. ze h Obeved ate wth houehold ze, z h z t pot f houehold ze 5 h N h z h 486,03 Compaed to uweghted etmate 390,50 Modelbaed etmate 595,46 ogoable oepoe Pottatfcato educe the ba about 50%

23 Imputato Ued fo tem oepoe Item oepoe ceate poblem eve whe the oepoe happe at adom, leave u wth few complete cae Imputato: fllg fo each mg data value b pedctg the mg value Fo a gve vaable, fo etmatg populato total o mea, ue etmato cotucted fo the full ample, baed o the obeved ad mputed data: Imputato baed etmato Need pope vaace etmate Alo wat to poduce complete data et that allow fo tadad tattcal aal Impotat that the mputed value eflect the ght vaato the data 3

24 . egeo-baed mputato method egeo mputato Aume a egeo model fo gve, whee avalable alo fo the oepoe goup f.e. Etmate β fom the epoe ample β E β β, Va σ, ad fo all oepoe goup, pedct wth wth Poblem: Not eough vaato to accout fo the vaablt the oepoe goup 4

25 edual egeo mputato Sce Va{ β / } σ Stadadzed obeved edual: e β / Fo, daw the value obeved edual the epoe ample e at adom fom the et of { e j : j } tadadzed Imputed -value gve b: e that : β β e / 5

26 6 If the model aumpto alo clude a dtbutoal aumpto, a omalt:, Daw mputed value fom the etmated N σ β Udelg aumpto o the epoe mecham: Mg at adom MA: Pobablt of epoe fo ut ma deped o, whle depedet of I X T X T, baed etmato become the the mputato -, the ato etmato, bac full ample etmato If

27 Stadad mputato method, much ued Natoal Stattcal Ittute Mea mputato Wth pottata: pottatfcato Hot-deck daw at adom wth eplacemet mputato tpcall wth pottata : fom the obeved value, Neaet eghbou mputato: Fd a doo the epoe ample baed o cloee of aula vaable 7

28 Nogoable oepoe : How to poceed The epoe pobablte ae aumed to deped o vaable of teet P, modeled, f, Populato model fo gve : Jot dtbuto of ad : f, f f, Codtoal dtbuto of gve oepoe, 0 f,, 0 f, 8

29 9 d P f P P P f f, 0 0 whee 0 /, 0 0,,,, Mamum lkelhood etmate:, Lkelhood fucto, depedece betwee, : 0,,,., ob ob P P f l Note: Lkelhood fucto could be qute flat, umecal dffculte fo fdg mamum. Imputed value: 0,, E o dawg a value fom the etmated codtoal dtbuto

30 30 Eample f 0 f P P Bomal cae P P P P P P P

31 3 Mamum lkelhood etmate Lkelhood fucto v the ze of ad "uccee" the epoe ample the umbe of, Let log log log log log, log ad 0,,., v v v v ob ob v v v l P P f l

32 3 Lkelhood equato: v v v v v v v v l 0 0 / 0 0 l/ II 0 0 / I I

33 33 v v Note: < P E E A eaoable etmate would atf MLE that :,

34 34 0 0,,, P E Etmate the total umbe of uccee the populato, N T Bac etmato wthout oepoe: N T Imputato-baed etmate: } { N N N t I

35 35 What happe f we eoeoul aume goable epoe mecham? The N t P Etmate :, } { N : Ba E T T E I T T E N Appomatel ubaed fo lage

36 Lectue 4: Vaace etmato the peece of mputed value Code mplet poble cae Smple adom ample adom oepoe No aula fomato Two poble mputato method mea mputato : hot-deck mputato : daw at adom fom the obeved wth eplacemet value, 36

37 Mea mputato ca ot be ued f the completed data et hall eflect epected vaato the oepoe goup Look at tadad deg-baed aal baed o the completed ample: obeved ad mputed data Poblem : Etmate σ ample mea f the whole ample obeved 37

38 Lage,N- Stadad 95% cofdece teval: CI : ±.96 σ N Wth oepoe: Stadad CI baed o the completed data et wth obeved ad mputed value: CI : ±.96 σ N, σ :, σ baed o the completed ample wth obeved ad mputed value 38

39 Coveage wth mea mputato W σ N ~ N0, appomatel CI σ uch that ±.96 σ N σ Cofdece level: C P CI P W.96 Noepoe % Cof. level

40 40 Coveage wth hot-deck mputato La m m m data Va data E σ N N Va data EVa data VaE data EVa Va data EE E m σ σ σ

41 4 σ σ E appomatel 0, ~ N N W σ Cofdece level:.96/ /.96 W P N N W P C

42 Cofdece level of CI*: Noepoe % Mea mputato Hot-deck mputato

43 Oe poble oluto: Multple mputato m epeated hot-deck mputato fo each mg value: m completed ample, σ fo,..., m, σ baed o the m completed ample m m Aveage: / m ad σ σ / A dect tadad CI: CI Alo too hot : ±.96σ N m 43

44 σ N meaue the vaato ol wth the ample It ecea to clude a meaue of vaato betwee the m ample; to meaue the ucetat due to mputato B m m ub MI method combe the tadad aale a follow: eplace σ wth : σ ad coepodg 95% CI: V B N m ±. 96 V 44

45 eque that the mputato ae baed o a Baea model, dawg mputed value fom the poteo dtbuto gve oepoe How doe t wok fo hot-deck mputato? Deped o f m the oepoe ate It ca be how that the cofdece level appomatel equal to, whe m > : C m P N0,.96 m f f m m f m Deceag a m ceae!! 45

46 Note that fo m : C P N0,.96/ P N0,.96 f m f m f m P N0,.96 f m f f m m f f m m 46

47 Cofdece level Noepoe % m Hot-deck m ft

48 Qute a appovemet ove gle mputato, but th tadad MI pocedue doe ot qute acheve the deed cofdece level. eao: The hot-deck mputato do ot dpla eough vaablt. I ub tem, the mputato mut be pope. The betwee-mputato compoet mut be gve a lage weght k tha /m. 48

49 No-Baea multple mputato Fomulato of poblem o-baea multple mputato fo vaace etmato A appoach fo developg a geeal theo fo o-baea MI how to combe tadad pocedue Smple eample Fo a gve data model ad mputed value: Ca the ame combato of tadad pocedue be ued fo a etmato poblem? 49

50 Suggeted appoach Full ample:,, Plaed data:,..., Objectve: Etmate epoe ample of ze Obeved: ob { :, } 50

51 Etmato baed o the full ample data : Vaace etmato: V Fo we mpute b ome method: Completed data: * :,, Baed o *: * * V V * m epeated mputato: m completed data-et wth m etmate, ad elated vaace etmate V,,..., m,..., m. 5

52 5 The combed etmate: The wth-mputato vaace: ad the betwee-mputato compoet : m m / m V V m / m m B The total etmated vaace of : Mut deteme k uch that B m k V W Va W E

53 Tpcall: E V Va E B ob Va ob E W Va E k EVa ob m appomatel Va Va ob ob / m E ob E ob { } { Va E Va ob Va E ob } m 53

54 54 } { Va VaE EVa k E VaE EVa m EVa m k E Va ob ob ob ob ob ob ob EVa Va VaE k E

55 Thee eample Etmatg populato aveage wth hot-deck mputato Etmatg egeo coeffcet wth edual mputato ato model Lea egeo model Noepoe mecham: MCA 55

56 Populato aveage wth hot-deck mputato p P E k p k f m, f m / 56

57 egeo coeffcet wth edual mputato ato model: β ε Va ε σ,, All ' ae kow, alo the oepoe ample The full data etmato of β : β / Etmate baed o obeved ample : β 57

58 Imputato method The tadadzed edual: e β / Fo : Daw e at adom fom the et of obeved edual e, The mputed -value: β e 58

59 59 All codeato : codtoal o ad X f X k X X X X X X X X f /

60 60 egeo coeffcet wth edual mputato Lea egeo model: j j j j e Va, Obeved edual:,...,,, β α σ ε ε β α wth eplacemet at adom fom the obeved edual, : Daw Fo e The mputed -value: e β α / m f k

61 Futue eeach:. Fo the ame tuato ad mputato method: Ue the ame k fo all etmad? Geeal awe: No Illutato b eample, hot-deck mputato Fo etmatg populato mea wth ample mea: k /- f m Th k ot vald fo all othe etmato poblem Stat b look at th poblem the mplet cae 6

62 MCA, the epoe vaable ae depedet Hot-deck mputato No aumpto o amplg deg, geeal p Thee poble cae:. a ample fom a fte populato wth deg model. The obeved tochatc vaable ae, ad ob equvalet to,. Same a cae, but wth a populato model. The ob { :,, } 3. Obevatoal tud whee modeled ad ob { :, } p P 6

63 Oe obvou equemet : E, Cae: E Cae : E, Cae 3: E : Code etmate lea : a Theoem atfe E, f ad ol f a a fo all ad the E k / p ad we ca ue k / f m 63

64 64. egeo coeffcet fo egeo though the og: / β a / / m f k. a / ample mea, k /-f m 3. A cae whee * doe ot hold : egeo coeffcet lea egeo ot though the og: β j j a β β p E

65 I cae 3 we kow fom eale that we ca ue k/-f m wth edual hot-deck mputato Fo egula egeo poblem hot-deck mputato caot wok. Obvoul: Whe coelated to kow oepoe goup: Oe hould utlze th the mputato egadle of the etmato poblem oe code. Need to geealze thee eult: To othe epoe mecham, at leat MA, whee the epoe pobablte deped o aula vaable, kow fo the whole ample To moe geeal mputato method, lke eaet eghbouhood 65

66 Futue eeach: Othe ue to be tuded obute of the choce k /-f m, mulato tude k a meaue of the popoto of mg fomato the epoe ample a compaed to the full ample. Geealze th b defg elevat meaue of mg fomato Stud of coveage of cofdece teval Mg data eplaato vaable ae commo obevatoal tude lke epdemologcal eeach. Some tal mulato dcate that k /-f m ca be ued th cae wth edual hot-deck mputato 66

67 Compae th MI method wth alteatve method fo vaace etmato wth mputed data jackkfe,boottap Codto ude whch the appoache ae vald Eted to whch the method povde ufed appoache fo et of etmad Stadad ctea: effcec of pot ad vaace etmato Computatoal bude 67

68 Some efeece- afte topc Stadad mputato method Ludtöm ad Sädal 00. Etmato the peece of Noepoe ad Fame Impefecto, ch.7. CBM, Stattc Swede Nogoable oepoe Bake ad Lad 988. egeo aal fo categocal vaable wth outcome ubject to ogoable oepoe. Joual of the Ameca Stattcal Aocato, 83, Fote ad Smth 998. Model-baed feece fo categocal uve data ubject to ogoable oepoe wth dcuo. Joual of the oal Stattcal Socet B, 60, Geelee, eece ad Zechag 98. Imputato of mg value whe the pobablt of epoe deped o the vaable beg mputed. 68

69 Lttle 98. Model fo oepoe ample uve. Joual of the Ameca Stattcal Aocato,77, Belb, Bjøtad ad Zhag 005. Modelg ad Etmato Method fo Houehold Sze the Peece of Nogoable Noepoe. Appled to the Nowega Coume Epedtue Suve. Suve Methodolog,3, 97-. Vaace etmato wth o-baea mputed data Bjøtad 007. No-Baea Multple Imputato wth dcuo. Joual of Offcal Stattc, 3, Shao ad Stte 996. Boottap fo mputed uve data. Joual of the Ameca Stattcal Aocato, 9,