## Zolemba masamu

Ndikuganiza kuti njira yabwino yodziwiritsira ntchito zowonjezera ndizokhazikika zomwe zingatheke (zomwe ndinakambirana pazamasamba pamutu 2). Zomwe zikhoza kukhazikitsidwa zili ndi mgwirizano wapamtima ndi malingaliro ochokera ku zitsanzo zomwe ndinapanga mu mutu 3 (Aronow and Middleton 2013; Imbens and Rubin 2015, chap. 6) . Zowonjezera izi zalembedwa m'njira yosonyeza kugwirizana kumeneko. Kugogomezera uku ndi pang'ono osati mwambo, koma ndikuganiza kuti kugwirizana pakati pa sampuli ndi kuyesera kumathandiza: zikutanthauza kuti ngati mukudziwa zina zokhudzana ndi zitsanzo ndikudziwa zina zokhudzana ndi mayesero komanso mosiyana. Monga momwe ndisonyezere muzinthu izi, zida zowonjezera zomwe zimawoneka zimasonyeza mphamvu za zowonongeka zowonongeka pofuna kulingalira za zotsatira zake, ndipo zikuwonetseratu zolephera za zomwe zingatheke ndi mayesero omwe anayesedwa mwangwiro.

Muzowonjezereka izi, ndikufotokozera zotsatira zopezeka, ndikuwongolera zina mwazinthu za masamu mu chaputala 2 kuti mupange zolembazo zambiri. Kenaka ndikufotokozera zotsatira zothandiza zenizeni zenizeni za zotsatira za mankhwala, kuphatikizapo zokambirana zapadera komanso zosiyana-siyana. Zowonjezera izi zimayandikira kwambiri Gerber and Green (2012) .

Ndondomeko ya zotsatira

Pofuna kufotokozera zotsatira zomwe zingatheke, tiyeni tibwerere ku Restivo ndi kuyesa kwa van de Rijt kuti tiwone zotsatira za kulandira nkhokwe pamisonkhano yotsatira ya Wikipedia. Zokambirana zomwe zingatheke zimakhala ndi zinthu zitatu zazikuluzikulu: magawo , mankhwala , ndi zotsatira zabwino . Pankhani ya Restivo ndi van de Rijt, maunitelo anali oyenerera olemba-omwe anali opambana 1% mwa opereka-omwe sanalandire nkhokwe. Titha kulemba olemba awa ndi $$i = 1 \ldots N$$ . Mankhwala omwe adawapeza anali "nkhokwe" kapena "palibe nkhokwe," ndipo ndidzalemba $$W_i = 1$$ ngati munthu $$i$$ ali mu chikhalidwe cha chithandizo ndi $$W_i = 0$$ mwinamwake. Gawo lachitatu la zofunikira zopezera zotsatira ndizofunikira kwambiri: zotsatira zomwe zingatheke . Izi ndi zovuta kwambiri kuti zikhale zovuta chifukwa zimaphatikizapo "zotsatira" zomwe zingatheke. Kwa mlembi aliyense wa Wikipedia, amatha kulingalira momwe angapangire kusintha kwake ( $$Y_i(1)$$ ) ndi chiwerengero chimene angapange mu chikhalidwe cholamulira ( $$Y_i(0)$$ ).

Tawonani kuti kusankhidwa kwa mayunitsi, mankhwala, ndi zotsatira kumatanthawuza zomwe mungaphunzire kuchokera kuyesayesa. Mwachitsanzo, popanda lingaliro linalake, Restivo ndi van de Rijt sangathe kunena kanthu za zotsatira za mabarnstars onse olemba Mabaibulo kapena zotsatira monga kusintha khalidwe. Kawirikawiri, kusankha masuniti, mankhwala, ndi zotsatira ziyenera kukhazikitsidwa pa zolinga za phunzirolo.

Chifukwa cha zotsatirazi zomwe zingatheke-zomwe zafotokozedwa mwachidule pa gome 4.5-mmodzi akhoza kufotokozera za mankhwala omwe amachititsa munthu kukhala ndi mankhwala $$i$$ monga

$\tau_i = Y_i(1) - Y_i(0) \qquad(4.1)$

Kwa ine, kulinganirana uku ndi njira yowonekera yofotokozera zotsatira zake, ndipo, ngakhale kuti ziri zosavuta kwambiri, dongosololi limakhala lodziwika bwino mu njira zambiri zofunika ndi zosangalatsa (Imbens and Rubin 2015) .

Table 4.5: Mndandanda wa Zotsatira Zowoneka
Munthu Kusintha mu chikhalidwe cha mankhwala Kusinthidwa mu chikhalidwe cholamulira Chithandizo cha mankhwala
1 $$Y_1(1)$$ $$Y_1(0)$$ $$\tau_1$$
2 $$Y_2(1)$$ $$Y_2(0)$$ $$\tau_2$$
$$\vdots$$ $$\vdots$$ $$\vdots$$ $$\vdots$$
N $$Y_N(1)$$ $$Y_N(0)$$ $$\tau_N$$
tanthauzo $$\bar{Y}(1)$$ $$\bar{Y}(0)$$ $$\bar{\tau}$$

Tikafotokozera zachinyengo mwa njirayi, timakhala ndi vuto. Pafupifupi nthawi zonse, sitimayesetsa kuona zomwe zingatheke. Izi zikutanthauza kuti mkonzi wina wa Wikipedia angalandire nkhokwe kapena ayi. Choncho, tikuwona chimodzi mwa zotsatira zomwe zingatheke- $$Y_i(1)$$ kapena $$Y_i(0)$$ -koma osati zonse. Kulephera kuwona zotsatira zonse zomwe zingatheke ndi vuto lalikulu lomwe Holland (1986) linadzitcha kuti Fundamental Problem of Causal Inference .

Mwamwayi, pamene tikufufuza, tilibe munthu m'modzi, tili ndi anthu ambiri, ndipo izi zimapereka njira yozungulira vuto lalikulu la Causal Inference. M'malo moyesera kulingalira za momwe munthu amathandizira mankhwala, timatha kulingalira momwe mankhwala amathandizira:

$\text{ATE} = \frac{1}{N} \sum_{i=1}^N \tau_i \qquad(4.2)$

Izi zikufotokozedwabe ponena za $$\tau_i$$ zomwe sizingatheke, koma ndi algebra (Eq 2.8 ya Gerber and Green (2012) ) timapeza

$\text{ATE} = \frac{1}{N} \sum_{i=1}^N Y_i(1) - \frac{1}{N} \sum_{i=1}^N Y_i(0) \qquad(4.3)$

Aone kuti pali 4.3 limasonyeza kuti ngati ife tingakhoze amati anthu pafupifupi zotsatira pansi chithandizo ( $$N^{-1} \sum_{i=1}^N Y_i(1)$$ ) ndi anthu pafupifupi zotsatira pansi pa ulamuliro ( $$N^{-1} \sum_{i=1}^N Y_i(1)$$ ), ndiye tikhoza kulingalira momwe mankhwala amathandizira, ngakhale popanda kulingalira momwe mankhwala amachitira munthu wina aliyense.

Tsopano kuti ndatanthauzira chiwerengero chathu-chinthu chomwe tikuyesera kuti tiyese-ndikuyang'ana momwe tingathe kuwerengera ndi deta. Ndimakonda kuganizira za vutoli ngati lingaliro laling'onoting'ono (ganizirani kumbuyo kwa masamu pamutu 3). Tangoganizani kuti timasankha mwachangu anthu ena kuti azisamalira pa chithandizo cha mankhwala ndipo nthawi zina timasankha anthu kuti azisunga muzolamulira, ndiye tikhoza kulingalira kuti zotsatira zake ndizochitika:

$\widehat{\text{ATE}} = \underbrace{\frac{1}{N_t} \sum_{i:W_i=1} Y_i(1)}_{\text{average edits, treatment}} - \underbrace{\frac{1}{N_c} \sum_{i:W_i=0} Y_i(0)}_{\text{average edits, control}} \qquad(4.4)$

kumene $$N_t$$ ndi $$N_c$$ ndi chiwerengero cha anthu omwe ali ndi chithandizo ndi zoletsa. Kuwerengera 4.4 ndi kulingalira kwa kusiyana-kwa-njira. Chifukwa cha kupangidwa kwa sampulumu, tikudziwa kuti nthawi yoyamba ndi yosakondera mosayenerera pamapeto pa chithandizo pakutha mankhwala ndipo nthawi yachiwiri ndiyesa kulingalira mosaganizira.

Njira yina yoganizira momwe ntchitoyi ikuyendera ndikutsimikizira kuti kuyerekezera pakati pa magulu ndi machitidwe otsogolera ndi owongoka chifukwa chakuti nthawi zonse zimakhala zogwirizana kuti magulu awiriwo adzafanana. Kufanana kumeneku kumagwiritsira ntchito zinthu zomwe taziyeza (nenani chiwerengero cha kusintha kwa masiku 30 asanayese) ndi zinthu zomwe sitinaziyerekeze (kunena za kugonana). Luso limeneli kuonetsetsa bwino pa mfundo onse anaona ndiponso unobserved n'zofunika. Kuti tiwone mphamvu yodzigwiritsira ntchito pazinthu zomwe sizinachitike, tiyeni tiyerekeze kuti kafukufuku wam'tsogolo amapeza kuti abambo ambiri amamvera mphoto kuposa akazi. Kodi izi zikanathetsa zotsatira za Restivo ndi kuyesa kwa van de Rijt? Ayi. Mwachidziwitso, iwo anaonetsetsa kuti zonse zosayenerera zingakhale zogwirizana, kuyembekezera. Chitetezo ichi pazomwe sichidziwika ndi champhamvu kwambiri, ndipo njira yofunikira yomwe kuyesera kuli kosiyana ndi njira zomwe sizinayesedwe pamutu 2.

Kuwonjezera pa kufotokozera zotsatira za mankhwala kwa anthu onse, ndizotheka kufotokoza zotsatira zothandizira anthu. Izi nthawi zambiri zimatchedwa zochitika zofunikira zothandizira mankhwala (CATE). Mwachitsanzo, mu phunziro la Restivo ndi van de Rijt, tiyerekeze kuti $$X_i$$ ndikuti mkonzi anali pamwamba kapena pansi pa kusintha kwapakati pa masiku 90 isanayambe kuyesedwa. Mmodzi akhoza kuwerengera zotsatira zothandizira mosiyana kwa okonza awa olemera ndi olemera.

Zomwe zingatheke kukwaniritsa ndi njira yabwino yoganizira za chidziwitso komanso zoyesera. Komabe, pali zina ziwiri zovuta zomwe muyenera kukumbukira. Zowopsya ziwirizi zimagwiritsidwa palimodzi pansi pa Stable Unit Treatment Value Assumption (SUTVA). Gawo loyamba la SUTVA ndilo lingaliro lakuti chinthu chokha chomwe chili chofunikira kwa munthu $$i$$ 's' zotsatira zake ndi ngati munthuyo anali kuchipatala kapena chikhalidwe. M'mawu ena, akuganiza kuti munthu $$i$$ sakhudzidwa ndi mankhwala operekedwa kwa anthu ena. Izi nthawi zina zimatchedwa "zosokoneza" kapena "palibe zowonongeka", ndipo zingathe kulembedwa monga:

$Y_i(W_i, \mathbf{W_{-i}}) = Y_i(W_i) \quad \forall \quad \mathbf{W_{-i}} \qquad(4.5)$

pomwe $$\mathbf{W_{-i}}$$ ndivector of statuses mankhwala m'malo aliyense $$i$$ . Njira imodzi yomwe izi zikhoza kuphwanyidwa ngati mankhwala ochokera kwa munthu mmodzi athawira kwa munthu wina, kaya zabwino kapena zoipa. Kubwerera ku Restivo ndi kuyesa kwa van de Rijt, ganizirani abwenzi awiri $$i$$ ndi $$j$$ ndipo munthu ameneyo $$i$$ amalandira barnstar ndipo $$j$$ satero. Ngati $$i$$ kulandira zifukwa zowonjezera $$j$$ kusintha zambiri (popanda mpikisano) kapena kusintha pang'ono (popanda kutaya mtima), ndiye SUTVA waphwanyidwa. Ikhoza kuphwanyidwa ngati zotsatira za chithandizocho zimadalira chiwerengero cha anthu ena omwe akulandira chithandizo. Mwachitsanzo, ngati Restivo ndi van de Rijt atapereka ndalama zokwana 1,000 kapena 10,000 m'malo mwa 100, izi zikhoza kukhudza zotsatira za kulandira nkhokwe.

Nkhani yachiwiri yomwe imagwiritsidwa ntchito ku SUTVA ndikulingalira kuti chithandizo chokha chofunikira ndi chomwe mfufuzi amapereka; lingaliro ili nthawi zina limatchedwa mankhwala osabisika kapena osasamala . Mwachitsanzo, ku Restivo ndi van de Rijt, zikhoza kukhala choncho kuti powapatsa zikalata ochita kafukufuku amachititsa olemba kuti aziwonekera pamasamba otchuka otchuka komanso kuti akukhala pa tsamba lokonzekera otchuka - zomwe zinapangitsa kusintha kwa khalidwe la kusintha. Ngati izi ndi zoona, ndiye kuti zotsatira za barnstar sizikusiyanitsa ndi zotsatira za kukhala pa tsamba lokonzanso. Inde, sizikuwonekera ngati, kuchokera ku sayansi, izi ziyenera kuonedwa kukhala zokongola kapena zosasangalatsa. Izi zikutanthauza kuti mungaganize kuti wochita kafukufuku akunena kuti zotsatira za kulandira nkhokwe zimaphatikizapo mankhwala onse omwe amachokera. Kapena mungaganizire zochitika zomwe kafukufuku angafune kupatula zotsatira za mabanki a zinthu zina zonsezi. Njira imodzi yoganizira izi ndi kufunsa ngati pali china chilichonse chomwe chimachititsa Gerber and Green (2012) (p. 41) kuyitana "kusokoneza"? Mwa kuyankhula kwina, kodi pali china chilichonse kupatula chithandizo chimene chimachititsa anthu kuchipatala ndi kulamulira zinthu kuti azichitiridwa mosiyana? Kuda nkhawa za kuswa kwazing'onoting'ono ndizo zomwe zimawatsogolera odwala mu gulu lolamulira mu mayesero azachipatala kuti atenge mapiritsi a placebo. Njirayi, ofufuza akhoza kutsimikiza kuti kusiyana kokha pakati pa zinthu ziwirizi ndi mankhwala enieni komanso osati kumwa piritsi.

Kuti mudziwe zambiri pa SUTVA, onani gawo 2.7 la Gerber and Green (2012) , gawo 2.5 la Morgan and Winship (2014) , ndi gawo 1.6 la Imbens and Rubin (2015) .

Kukonzekera

M'mbuyomu, ndalongosola momwe ndingagwiritsire ntchito kuchuluka kwa mankhwala. M'gawo lino, ndikupereka malingaliro a kusiyana kwa mawerengero amenewo.

Ngati mukuganiza za kuyerekezera kuchuluka kwa mankhwalawa poyerekeza kusiyana pakati pa njira ziwiri, ndiye kuti n'zotheka kusonyeza kuti zolakwika zofanana ndi zotsatira zake ndi:

$SE(\widehat{\text{ATE}}) = \sqrt{\frac{1}{N-1} \left(\frac{m \text{Var}(Y_i(0))}{N-m} + \frac{(N-m) \text{Var}(Y_i(1))}{m} + 2\text{Cov}(Y_i(0), Y_i(1)) \right)} \qquad(4.6)$

kumene anthu $$m$$ amagawira mankhwala ndi $$Nm$$ kuti awonetsetse (onani Gerber and Green (2012) , tsamba 3.4). Choncho, poganizira za anthu angapo omwe angapereke chithandizo ndi momwe angapatsire kulamulira, mungathe kuona kuti ngati $$\text{Var}(Y_i(0)) \approx \text{Var}(Y_i(1))$$ , ndiye mukufuna $$m \approx N / 2$$ , malinga ngati ndalama zothandizira ndi kulamulira zili zofanana. Equation 4.6 ikufotokozera chifukwa chake mapangidwe a Bond ndi anzake (2012) ayesa zotsatira za chidziwitso cha anthu pa kuvota (chifaniziro 4.18) sichinali chokwanira. Kumbukirani kuti anali ndi 98 peresenti ya odwala pa chikhalidwe cha mankhwala. Izi zikutanthauza kuti khalidwe lodziwika mu chikhalidwe choyendetsa silinayesedwe molondola monga momwe likanakhalira, zomwe zikutanthauza kuti kusiyana kwakukulu pakati pa chithandizo ndi chidziwitso sichinali choyenera momwe chingakhalire. Kuti mudziwe zochuluka za momwe mungagwiritsire ntchito gawoli, kuphatikizapo zomwe zimasiyanasiyana, onani List, Sadoff, and Wagner (2011) .

Potsirizira pake, m'mawu akuluakulu, ndinalongosola momwe kulingalira mosiyana-kosiyana-siyana, komwe kawirikawiri kamagwiritsidwira ntchito popangidwe, kungawononge kusiyana kochepa kusiyana ndi kuyerekezera mosiyana-siyana, komwe kumagwiritsidwa ntchito pakati pa kupanga. Ngati $$X_i$$ ndi mtengo wa zotsatira zisanachitike chithandizo, ndiye kuti kuchuluka komwe tikuyesera kuyerekezera ndi kusiyana kwake ndi kusiyana ndi:

$\text{ATE}' = \frac{1}{N} \sum_{i=1}^N ((Y_i(1) - X_i) - (Y_i(0) - X_i)) \qquad(4.7)$

Zolakwitsa zazomwezo ndi (onani Gerber and Green (2012) , eq. 4.4)

$SE(\widehat{\text{ATE}'}) = \sqrt{\frac{1}{N-1} \left( \text{Var}(Y_i(0) - X_i) + \text{Var}(Y_i(1) - X_i) + 2\text{Cov}(Y_i(0) - X_i, Y_i(1) - X_i) \right)} \qquad(4.8)$

Kuyerekeza kwa eq. 4.6 ndi eq. 4.8 amavomereza kuti kusiyana-kosiyana-siyana kudzakhala ndi zolakwika zochepa (onani Gerber and Green (2012) , tsamba 4.6)

$\frac{\text{Cov}(Y_i(0), X_i)}{\text{Var}(X_i)} + \frac{\text{Cov}(Y_i(1), X_i)}{\text{Var}(X_i)} > 1\qquad(4.9)$

Nthawi zambiri, pamene $$X_i$$ kwambiri za $$Y_i(1)$$ ndi $$Y_i(0)$$ , ndiye mukhoza kupeza malire osiyana-siyana kusiyana ndi kusiyana- a-amatanthauza chimodzi. Njira imodzi yoganizira izi mu nkhani ya Restivo ndi kuyesa kwa van de Rijt ndikuti pali kusiyana kwakukulu kwa chilengedwe cha ndalama zomwe anthu amasintha, choncho izi zikufanizira chithandizo ndi kuchepetsa zovuta zovuta: n'zovuta kupeza wachibale Zing'onozing'ono phokoso lamtundu wa phokoso. Koma ngati musiyanitsa-kutuluka kwachibadwa, ndiye kuti pali kusiyana kwakukulu, ndipo zimakhala zosavuta kupeza zotsatira zochepa.

Onani Frison and Pocock (1992) kuti mudziwe bwino kusiyana kwa njira, kusiyana-siyana, ndi njira za ANCOVA zomwe zimakhalapo pa malo ambiri omwe ali ndi chithandizo chambiri chisanachitike. Makamaka, amalangiza ANCOVA mwamphamvu, zomwe sindinaziphimbe pano. Komanso, onani McKenzie (2012) kuti akambirane za kufunikira kwa njira zambiri zotsatila mankhwala.