## Amanothi ezembalo

Ngicabanga ukuthi indlela engcono kakhulu ukuqonda ucwaningo yilona engaba imiphumela nohlaka (okuyinto Ngixoxisene amanothi zezibalo esahlukweni 2). Umhlahlandlela weziphumo ongase ube nawo ubuhlobo obuseduze nemibono evela kwisampula esekelwe kumklamo (Aronow and Middleton 2013; Imbens and Rubin 2015, chap. 6) esahlukweni 3 (Aronow and Middleton 2013; Imbens and Rubin 2015, chap. 6) . Lesi sithasiselo sibhaliwe ngendlela yokugcizelela lokho kuxhumano. Lokhu kugcizelelwa kuyinto engeyona yendabuko, kodwa ngicabanga ukuthi ukuxhumana phakathi kwesampula kanye nokuhlolwa kuyasiza: kusho ukuthi uma wazi okuthile mayelana nesampuli bese wazi okuthile mayelana nokuhlolwa nokuphambene nalokho. Njengoba ngizobonisa kula manothi, uhlaka lwemiphumela engaba khona lwembula amandla wezilingo ezilawulwa ngokungahleliwe zokulinganisela imiphumela ye-causal, futhi ibonisa ukulinganiselwa kwalokho okungenziwa ngezilingo eziphelele ngisho nokuhlolwa.

Kulesi sithasiselo, ngizochaza ukuhlelwa kokuhlelwa kwemiphumela, ukuphinda ezinye zezinto ezivela kumanothi ezembalo esahlukweni 2 ukuze wenze lezi zimpawu zibe ngaphezulu. Khona-ke ngizochaza imiphumela ewusizo mayelana nokulinganisa kokulinganisa kwemiphumela yokwelashwa ejwayelekile, kufaka phakathi ingxoxo yokwabiwa okulinganayo kanye nokulinganisa okungafani kwamanani. Lesi sithasiselo sidonsela kakhulu ku- Gerber and Green (2012) .

Uhlaka lokubheka imiphumela

Ukuze sibonise ukuhlelwa kohlelo olungenzeka, ake sibuyele ku-Restivo nokuzama kukaVan de Rijt ukulinganisa umphumela wokwamukela ukugcinwa kwemali eminikelweni ezayo kwi-Wikipedia. Umhlahlandlela weziphumo ongenzeka unamakhemikhali amathathu okuyinhloko: amayunithi , ukwelashwa , kanye nemiphumela engenzeka . Endabeni ye-Restivo ne-van de Rijt, amayunithi ayengabahleli abafanelekayo-labo abangaphezulu kwezingu-1% zabanikeli-ababengakakutholi imali. Singabhalisa laba abahleli nge- $$i = 1 \ldots N$$ . Imithi yokwelashwa ekuhlolweni kwabo yayiyi-"barnstar" noma "ayikho inqolobane," futhi ngizobhala $$W_i = 1$$ uma umuntu $$i$$ esesimweni sokwelashwa futhi $$W_i = 0$$ kungenjalo. Isici sesithathu sohlaka lokubaluleka komphumela kubaluleke kakhulu: imiphumela engaba khona . Lezi zinkimbinkimbi kakhulu ngoba zibandakanya imiphumela "engaba khona" -zinto ezingenzeka. Ngomhleli ngamunye we-Wikipedia, umuntu angacabangela inani lokuhlela ayezokwenza esimweni sokunakekelwa ( $$Y_i(1)$$ ) nenombolo angayenza esimweni sokulawula ( $$Y_i(0)$$ ).

Qaphela ukuthi lokhu kukhetho kwamayunithi, ukwelashwa, nemiphumela kuchaza ukuthi yini engayifunda kulolu vivinyo. Isibonelo, ngaphandle kokucabanga okungeziwe, i-Restivo ne-van de Rijt abakwazi ukusho lutho ngemiphumela yamabhakhadi kuwo wonke abahleli be-Wikipedia noma kwimiphumela efana nekhwalithi yokuhlela. Ngokuvamile, ukhetho lwamayunithi, ukwelashwa, nemiphumela kufanele lusekelwe emigomweni yocwaningo.

Njengoba kunikezwe lezi ziphumo ezingenzeka-ezifingqiwe etafuleni le-4.5-eyodwa ingachaza umphumela we-causal wokwelashwa komuntu $$i$$ njenge

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

Kuye, lokhu kulingana kuyindlela ecacile yokuchaza umphumela wokuba nomphumela, kanti, nakuba ulula kakhulu, loluhlaka (Imbens and Rubin 2015) ezindleleni eziningi ezibalulekile nezithakazelisayo (Imbens and Rubin 2015) .

Ithebula 4.5: Ithebula Lemiphumela Ebonakalayo
Umuntu Ihlela esimweni sokwelapha Ihlela esimweni sokulawula Umphumela wokwelapha
1 $$Y_1(1)$$ $$Y_1(0)$$ $$\tau_1$$
2 $$Y_2(1)$$ $$Y_2(0)$$ $$\tau_2$$
$$\vdots$$ $$\vdots$$ $$\vdots$$ $$\vdots$$
N $$Y_N(1)$$ $$Y_N(0)$$ $$\tau_N$$
kusho $$\bar{Y}(1)$$ $$\bar{Y}(0)$$ $$\bar{\tau}$$

Uma sichaza isimo salo ngale ndlela, noma kunjalo, sibhekene nenkinga. Cishe zonke izimo, asikwazi ukugcina imiphumela emibili. Lokhu kungukuthi, umhleli othile we-Wikipedia uthole i-barnstar noma cha. Ngakho-ke, sibona omunye wemiphumela $$Y_i(1)$$ noma $$Y_i(0)$$ -kodwa hhayi kokubili. Ukuhluleka ukugcina imiphumela emibili ingaba inkinga enkulu Holland (1986) eyayibiza ngokuthi yiNkinga Eyisisekelo Ye-Causal Inference .

Ngenhlanhla, uma senza ucwaningo, asinalo umuntu oyedwa kuphela, sinabantu abaningi, futhi lokhu kunikeza indlela ejikeleze Inkinga Eyisisekelo Ye-Causal Inference. Esikhundleni sokuzama ukulinganisa umphumela womuthi ngamunye, singalinganisa umphumela wokwelapha isilinganiso:

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

Lokhu $$\tau_i$$ ngokwemibandela ye- $$\tau_i$$ engenakugodwa, kodwa ngezinye i-algebra (Eq 2.8 ye- Gerber and Green (2012) ) sithola

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

I-Equation 4.3 ibonisa ukuthi uma singakwazi ukulinganisa umphumela wesilinganiso sabantu ngaphansi kokwelashwa ( $$N^{-1} \sum_{i=1}^N Y_i(1)$$ ) nomphumela wesilinganiso womphakathi ngaphansi kokulawulwa ( $$N^{-1} \sum_{i=1}^N Y_i(1)$$ ), khona-ke singakwazi ukulinganisa umphumela wokwelapha isilinganiso, ngisho ngaphandle kokulinganisa umphumela wokwelapha komuntu othile.

Manje njengoba ngichaze ukulinganisela kwethu-into esizama ukuyiqhathanisa-ngizophendukela ukuthi singayilinganisa kanjani ngempela nedatha. Ngithanda ukucabanga ngalokhu inselelo yokulinganisa njengenkinga yesampula (cabanga emuva kumanothi ezembalo esahlukweni 3). Cabanga ukuthi sithatha abantu abathile ukuba bahlale esimweni sokwelapha futhi sikhetha abanye abantu ukuba bagcine esimweni sokulawula, khona-ke singalinganisa umphumela wesilinganiso esimweni ngasinye:

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

lapho $$N_t$$ ne $$N_c$$ yizinombolo zabantu $$N_c$$ kanye nezimo zokulawula. I-Equation 4.4 i-estimator-difference-of-means. Ngenxa yesakhiwo sampula, siyazi ukuthi isikhathi sokuqala singumlinganisi ongakhethi emiphakathini yomphumela wesilinganiso lapho ukwelashwa kanti i-term yesibili isilinganiso sokungabi namandla ngaphansi kokulawula.

Enye indlela yokucabanga ukuthi i-randomization inikeza kanjani ukuthi iqinisekisa ukuthi ukuqhathanisa phakathi kwama-ARV kanye namaqembu okulawula kuhle ngoba ukuhlelwa kwe-randomization kuqinisekisa ukuthi amaqembu amabili azofana. Lokhu kufana nokubhekisele ezintweni esizilinganisile (zisho inani lokuhlelwa ezinsukwini ezingu-30 ngaphambi kokuzama) nezinto esingazange sizilinganise (kusho ubulili). Leli khono ukuze kube lokulingana ku kokubili izici ebuka futhi unobserved kubalulekile. Ukuze ubone amandla okulinganisa okuzenzekelayo ngezizathu ezingenakubalwa, ake sicabange ukuthi ucwaningo lwesikhathi esizayo luthola ukuthi amadoda aphendula kakhulu kumiklomelo kunabesifazane. Ingabe lokho kungavimbela imiphumela ye-Restivo nokuhlolwa kuka-van de Rijt? Cha. Ngokungahleliwe, baqinisekisa ukuthi wonke ama-unobservables angaba nokulinganisela, kulindeleke. Lokhu kuvikelwa okungaziwa kunamandla kakhulu, futhi kuyindlela ebalulekile ukuthi izivivinyo zihlukile kumasu okungewona okuhlola okuchazwe esahlukweni 2.

Ngaphandle kokuchaza umphumela wokwelashwa kuwo wonke umuntu, kungenzeka ukuchaza umphumela wokwelashwa wesigatshana somuntu. Lokhu ngokuvamile kubizwa ngokuthi umphumela wesiphakamiso wesilinganiso esimaphakathi (CATE). Isibonelo, esifundweni se-Restivo no-van de Rijt, ake sithi $$X_i$$ kungakhathaliseki ukuthi umhleli $$X_i$$ noma ngaphansi kwenombolo ephakathi kokuhlelwa phakathi kwezinsuku ezingu-90 ngaphambi kokuhlolwa. Omunye angakwazi ukubala umphumela wokwelapha ngokwehlukana kulabahleli abaqondayo nabanzima.

Uhlaka lwendlela yokusebenza lungaba yindlela enamandla yokucabanga nge-causal inference kanye nokuhlolwa. Nokho, kunezinkinga ezimbili ezengeziwe okumelwe uzigcine engqondweni. Lezi zinkimbinkimbi ezimbili zivame ukuhlanganiswa ngaphansi kwegama elithi Stable Unit Treatment Value Assumption (SUTVA). Ingxenye yokuqala ka-SUTVA yimbono yokuthi into eqondene nomuntu $$i$$ 's umphumela ukuthi ngabe lowo muntu usesimweni sokuphatha noma sokulawula. Ngamanye amazwi, kucatshangwa ukuthi umuntu $$i$$ akathinteki ukwelashwa okunikezwe kwabanye abantu. Lokhu ngezinye izikhathi kuthiwa "akukho ukuphazanyiswa" noma "akukho ukuphazamiseka", futhi kungabhalwa ngokuthi:

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

lapho $$\mathbf{W_{-i}}$$ iyimvamisa yemigomo yokwelashwa komuntu wonke ngaphandle komuntu $$i$$ . Enye indlela lokhu kungaphula ngayo uma ukwelashwa okuvela kumuntu oyedwa kuchitha omunye umuntu, kungaba kuhle noma okungalungile. Ukubuyela ku-Restivo nokuzama kuka-van de Rijt, cabanga abangani ababili $$i$$ kanye $$j$$ futhi lowo muntu $$i$$ uthola inqolobane futhi $$j$$ ayikho. Uma $$i$$ ethola izimbangela zokugcina $$j$$ ukuhlela ngaphezulu (ngaphandle komqondo wokuncintisana) noma uhlele kancane (ngaphandle kokuphelelwa ithemba), i-SUTVA iphuliwe. Kungaphula futhi uma umthelela wezokwelapha uncike kwinani labanye abantu abathola ukwelashwa. Isibonelo, uma i-Restivo ne-van de Rijt benikeze amabarnstars angama-1,000 noma ayi-10,000 esikhundleni se-100, lokhu kungase kuthinte umphumela wokuthola isikhwama.

Ukukhishwa kwesibili okufakwe ku-SUTVA kungukuthi ukuphathwa okufanele kuphela yilowo umcwaningi oletha; lokhu kuthathwa ngezinye izikhathi kuthiwa akukho ukwelashwa okufihliwe noma ukungabandakanyi . Isibonelo, e-Restivo nase-van de Rijt, kungenzeka ukuthi bekukhona ukuthi ngokunikeza umcwaningi abacwaningi babangela abahleli ukuba babonakale ekhasini elihleliwe labahleli nokuthi likhona ekhasini labahleli abadumile-kunokuba bathole i-barnstar- okwenze ushintsho ekuziphatheni kokuhlela. Uma lokhu kuyiqiniso, umphumela we-barnstar awukwazi ukuhlukaniswa nomphumela wokuba ekhasini elihleliwe labahleli. Yiqiniso, akucaci ukuthi, ngokombono wesayensi, lokhu kufanele kubhekwe njengokukhangayo noma ukungathandeki. Okungukuthi, ungacabanga ukuthi umcwaningi uthi umphumela wokwamukela ibhakha uhlanganisa zonke izifo ezalandela ezikhusayo. Noma ungase ucabange isimo lapho ucwaningo luzofuna ukuhlukanisa umphumela wamabhastars avela kuzo zonke ezinye izinto. Enye indlela yokucabanga ngayo ukubuza ukuthi kukhona yini okuholela kulokho i- Gerber and Green (2012) (iphe. 41) ebiza ngokuthi "ukuhlukana kokulinganisa"? Ngamanye amazwi, ingabe kukhona okunye ngaphandle kokwelashwa okubangela abantu ukuthi babe nokuphathwa kwezimo zokwelashwa nokulawula ukuphathwa ngendlela ehlukile? Ukukhathazeka mayelana nokuphulwa kwe-symmetry yilokho okuhola iziguli eqenjini lokulawula ezinkulweni zezokwelapha ukuthatha ipilisi ye-placebo. Ngaleyo ndlela, abacwaningi bangaqiniseka ukuthi umehluko kuphela phakathi kwezimo ezimbili ngumuthi wangempela futhi awunalo ulwazi lokuthatha iphilisi.

Ukuze uthole okwengeziwe ku-SUTVA, bheka isigaba 2.7 se- Gerber and Green (2012) , isigaba sesi-2.5 Morgan and Winship (2014) , nesigaba 1.6 sika- Imbens and Rubin (2015) .

Ukucabangela

Esigabeni esandulele, ngichazile indlela yokulinganisela umphumela wokwelapha ovamile. Kulesi sigaba, ngizohlinzeka ngemibono mayelana nokuhluka kwalezi zilinganiso.

Uma ucabanga ngokulinganisela umphumela wokwelashwa olinganiselwe njengokulinganisa umehluko phakathi kwezindlela ezimbili zesampula, kungenzeka ukuthi ukhombise ukuthi iphutha elijwayelekile lomphumela wokwelapha isilinganiso:

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

lapho $$m$$ abantu banikezwe ukwelashwa futhi $$Nm$$ ukulawula (bona i- Gerber and Green (2012) , eq. 3.4). Ngakho-ke, uma ucabanga ukuthi bangaki abantu abazokwabela ukwelashwa nokuthi bangaki abazokwabela ukulawula, ungabona ukuthi uma $$\text{Var}(Y_i(0)) \approx \text{Var}(Y_i(1))$$ , bese ufuna $$m \approx N / 2$$ , uma nje izindleko zokwelashwa nokulawula zifana. I-Equation 4.6 icacisa ukuthi kungani ukuklama kweBond kanye nozakwethu (2012) ukuzama mayelana nemiphumela yolwazi lomphakathi ekuvotweni (isibalo 4.18) kwakungenakubalwa ngokulinganayo. Khumbula ukuthi kwaba no-98% wabathintekayo esimweni sokwelapha. Lokhu kusho ukuthi ukuziphatha okusebenzayo esimweni sokulawula kwakungalinganiswanga ngokunembile njengoba kwakungenzeka, okwakusho ukuthi umehluko olinganisiwe phakathi kwendlela yokwelapha nokulawula ayingacatshangwanga ngokunembile njengoba kungenzeka. Ukuze uthole ukwaziswa okungaphezulu mayelana nokwabiwa okuphelele kwabahlanganyeli ezimweni, kufaka phakathi uma izindleko zihluka phakathi kwezimo, bheka List, Sadoff, and Wagner (2011) .

Ekugcineni, embhalweni oyinhloko, ngachaza indlela ukulinganisela okungafani ngayo, okujwayelekile okusetshenziselwa ukuklanywa okungafani, kungabangela ukuhlukahluka okuncane kunomlinganiso we-umehluko, okuvame ukusetshenziselwa phakathi kwezifundo ukuklama. Uma $$X_i$$ yomphumela ngaphambi kokwelashwa, khona-ke inani esilinga ukulilinganisa nendlela yokungafani-umahluko:

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

Iphutha elijwayelekile leleyo nhlobo (bheka i- Gerber and Green (2012) , eq. 4.4)

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

Ukuqhathaniswa kweq. 4.6 kanye neq. I-4.8 yembula ukuthi indlela eyahlukahlukana ngokungafani kuyoba nephutha elincane elijwayelekile lapho (bheka i- Gerber and Green (2012) , eq. 4.6)

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

Kakhulu, uma $$X_i$$ ukubikezela kakhulu kwe- $$Y_i(1)$$ kanye $$Y_i(0)$$ , khona-ke ungathola ukulinganisa okucacile okungafani nakwehlukahlukana- of-kusho eyodwa. Enye indlela yokucabanga ngalokhu kumongo we-Restivo nokuhlolwa kukaVan de Rijt ukuthi kukhona ukuhlukahluka kwemvelo emalini abantu abahlela ngayo, ngakho lokhu kuqhathanisa nokwelashwa nezimo zokulawula kunzima: kunzima ukubona isihlobo umphumela omncane kwimiphumela yomphumela womsindo. Kodwa uma uhlukanisa-lokhu kuhlukahluka ngokwemvelo, khona-ke kukhona ukuhluka okuncane kakhulu, futhi lokho kwenza kube lula ukubona umphumela omncane.

Bheka i- Frison and Pocock (1992) ukuze uqhathanise ngokucacile umehluko-we-izindlela, umehluko-we-umehluko, kanye nezindlela ezisekelwe ku-ANCOVA ngendlela ejwayelekile kakhulu lapho kunezilinganiso eziningi zokwelashwa ngaphambi kokunakekelwa nokwelapha. Ngokuyinhloko, batusa kakhulu i-ANCOVA, engingazange ngiyibeke lapha. Ngaphezu kwalokho, bheka McKenzie (2012) ukuze uthole ingxoxo ngokubaluleka kwezinyathelo eziningi zokwenza umphumela wezokuthutha.