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& && &&&小弟最近在阅读Treatment effect的一些文章，无奈才疏学浅，对于模型有几点疑问，欢迎各位高手指教：
15:27:53 上传
& & 请问这个MTE在实证研究中具体该怎么计算？U1i U0i Us具体怎么计算？非常感谢。
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论坛法律顾问：王进律师Treatment Effect97-第5页
上亿文档资料，等你来发现
Treatment Effect97-5
StataTechnicalBulletin21；Options；sensvar；specvar#speci?esthevalue；#speci?esthecon?dencelev；fromshowingtheiterationl；reportstheestimatedcoef?；#,#,and#specifythede?nit；isthedefault.；
StataTechnicalBulletin21
specvar#speci?esthevalueorthenameofthesensitivityvariable.Sensitivityshouldbebetween0and1.#speci?esthevalueorthenameofthespeci?cityvariable.Speci?cityshouldbebetween0and1.
#speci?esthecon?dencelevel,inpercent,forcon?denceintervals.Thedefaultis
fromshowingtheiterationlog.orassetby.speci?esthattheHuber/White/sandwichestimatorofvarianceistobeusedinplaceofthetraditionalcalculation.prevents
reportstheestimatedcoef?cientsinsteadofoddsratios.Thisoptionaffectshowresultsaredisplayed,nothowtheyareestimated.maybespeci?edatestimationorwhenredisplayingpreviouslyestimatedresults.
#,#,and#specifythede?nitionofconvergence.
isthedefault.
Convergenceisdeclaredwhen
fortwoconsecutiveEMsteps.Inaddition,iterationstopswhen
“convergencenotachieved”arepresented.Thereturncodeisstillsetto0.;inthatcase,resultsalongwiththemessage
Optionsforpredict
,thedefault,calculatestheprobabilityofapositiveoutcome.
calculatesthelinearprediction.
calculatesthestandarderrorofthelinearprediction.
numbersthecovariatepatterns―observationswiththesamecovariatepatternhavethesame.Observationsnotusedinestimationhavethepredictionsettomissing.The“?rst”covariatepatternisnumbered1,thesecond2,andsoon.Remarks
Traditionallogitorlogisticregressionassumesthattheoutcomevariableismeasuredwithouterror.Insomestudies,however,theoutcomevariableisnotmeasuredperfectly.Thiscanoccur,forexample,whenusingadiagnostictesthavingsensitivityand/orspeci?citylowerthan100%.Theresultingmisclassi?cationcanleadtobiasinthecoef?cientsestimatedandrelatedstatistics(Copeland,etal.1977).
MagderandHughes(1997)proposedanEMalgorithmthatincorporatesthevaluesofthesensitivityandspeci?cityoftheclassi?cationtestintotheestimationofthelogisticparameters.Theyshowedthatinthepresenceofmisclassi?cation,theirprocedureproducedunbiasedestimatesofboththecoef?cientsandtheirvariances.ItisthisEMalgorithmthatwehaveimplementedin.Notethatwhensensitivityandspeci?cityarebothsettoone,andproducethesameestimates.
Tosetto,etal.(1999)conductedacaseCcontrolstudytodeterminetheimportanceoftheprothrombingenealleleG20210Aasariskfactorinvenousthromboembolism(VTE).Thestudyconsistedof116VTEpatientsand232healthyindividualsascertainedrandomlyfromawellde?nedpopulation.Foreachsubjectinthestudy,theyobtainedinformationregardingpreviousdiagnosisofVTEusingasurveytoolwithanestimatedsensitivityof71.3%andspeci?cityof98.9%.
Eachsubjectinthestudywasalsotypedattheprothrombinlocus.Nohomozygouscarriersofthemutatedallele(G20210A)werefound.Thirteen(3.7%)subjectswereheterozygousforthemutationandtheremaining335subjectsdidnothavethemutation.
Inourdata,indicateswhetherthepatienthasbeendiagnosedwithVTE,and
mutation.Herearetheresultsfrom:whethertheindividualhasthe
22StataTechnicalBulletinSTB-55andthosefromincorporatingthesensitivityandspeci?city:
NeithermodelprovidesevidencesupportingthehypothesisofanassociationbetweenthemutatedalleleandVTE.Notethat
islarger―furtherfromthenull―thanthatreportedbystandardlogisticregression,althoughtheoddsratioreportedby
itsstandarderrorislarger,re?ectingtheaddeduncertaintyabouttheoutcomevariable.Thisisaknownnamely,theEMalgorithmtypicallyproduceslargeroddsratiosandlargervariances.
SavedResults
numberofobservations
loglikelihood
loglikelihood,constant-onlymodel
modeldegreesoffreedom
pseudo-squared
nameofdependentvariable
;typeofmodeltest
coef?cientvector
varianceCcovariancematrixoftheestimators
marksestimationsampleFunctions
MethodsandFormulas
Let1ifindividualtrulyhastheoutcomeofinterest(diseased)and0otherwise(nondiseased).Letifindividualisclassi?edashavingtheoutcomeand0otherwise.Assumethatistheprobabilitythatthethindividualtrulyhasthe
and1covariatevector.Thenifindividualisclassi?edashavingtheconditionbeingstudiedgiventhevaluesof
whereisa1coef?cientvectortobeestimated,and
StataTechnicalBulletin23
TheEMalgorithmbeginsby?rstsetting
expectationstep.toanarbitraryvalueandcomputingforeachobservation.Thisisthe
Thedataarethenduplicatedandeachobservationincludedtwice,oncewiththeoutcomevariablesetto1andanother
iftheoutcomevariableiswiththeoutcomesettozero.Aweightedlogisticregressionmodelis?ttedwithweightsequalto
ifitiszero.Thisconstitutesthemaximizationstep.1and
Thenew’sobtainedfromthe?ttedlogisticmodelareusedtocalculatenew
isdeclared.’sandtheprocessrepeateduntilconvergence
References
Copeland,K.T.,H.Checkoway,A.J.Michael,andR.H.Holbrook.1977.Biasduetomisclassi?cationintheestimationofrelativerisk.American
JournalofEpidemiology105:488C495.
Magder,L.S.andJ.P.Hughes.1997.Logisticregressionwhentheoutcomeismeasuredwithuncertainty.AmericanJournalofEpidemiology146:
Tosetto,A.,E.Missiaglia,M.Frezzato,andF.Rodeghiero.1999.TheVITAproject:prothrombinG20210Amutationandvenousthromboembolism
inthegeneralpopulation.ThrombHaemost82:.
sg140TheGumbelquantileplotandatestforchoiceofextrememodels
ManuelG.Scotto,UniversityofLisbon,arima@mail.telepac.pt
Abstract:Somestatisticaltoolsforexploratorydataanalysisarepresented.TheGumbelquantileplotisdescribedasaninformal
waytotestiftheGumbeldistributionprovidesagood?tfordata.Furthermore,weincludeamethodofstatisticalchoiceamongthethreeextremevaluedistributions.
Keywords:Generalizedextremevaluedistribution,hypothesistesting,Gumbelquantileplot.
varnameexprange
Introduction
Themaingoalofthisworkisindealingwiththestatisticalchoiceofextrememodels.Thisisessentialinapplicationswheretheattentionisfocusedatrarelyoccurringevents,suchasanannualmaximal?oodexceedingdykes,oraseasonalminimaltemperaturebelowthecriticalvalueforcropproduction.Werestrictourselvestotheone-dimensionalcaseandstartwithadiscussionoftheproblem.
Letbeindependentandidenticallydistributedrandomvariableswithunderlyingmarginaldistributiongivenbywhichisthewell-knowngeneralizedextremevaluedistribution(GEV).Theparametersandarethelocationandscaleparametersrespectivelyandistheshapeparameterandmaybeusedtomodelawiderangeoftailbehaviors.Therearethreeparticularformsofcorrespondingto0(Fr′echetdistribution),0(Weibulldistribution),and0beinginterpreted
0,widelycalledtheGumbeldistribution.WeusetheGumbelquantileplot(GQP)andthestatistic?rstasthelimitas
introducedbyGumbelanddevelopedbyTiagodeOliveiraandGomes(1984),hereafterreferredtoasOG.foraquickstatisticalchoicebetweentheextrememodels.
ThequantileplotfortheGumbeldistribution
Probabilityplottingpapersarecommonlyusedtoassess,inaninformalway,whetherasamplecomesfromaparticulardistribution.FortheGumbeldistribution,thequantilefunctionisgivenby
whichleadstosocalleddoublelogarithmicplotting.Tothisend,we?rsttaketheorderedsampleandplot
versus,where1istheclassicalplottingposition.IftheGumbeldistributionprovidesagood?ttoourdata,thentheGQPshouldlookroughlylinear.Furthermore,bothFr′echetandWeibullmodelscanalsobevalidatedby
24StataTechnicalBulletinSTB-55meansoftheGQP.IftheplothasadownsideconcavitywecanassumeaFr′echetmodelwhereasanupsideconcavityindicatesaWeibullmodel.Finally,notethat
Usinglinearregression,quickestimatesfor
estimatorscanbeobtainedbymeansoftheandcanbededucedfromtheslopeandtheintercept.MaximumlikelihoodcommandintroducedinScottoandTobias(1998).
Statisticalchoicebetweentheextrememodels
StatisticalchoiceamongtheextrememodelsgivesacentralandpreeminentpositiontotheGumbeldistributionduetothesimplicityofinferencesassociatedwiththisdistribution.WepresentatestforH:intheGEVmodel.Weconsiderthestatistic,
whichislocationanddispersion-parameterfree.UnderthevalidityofH,itwasshownbyOGthatthereexist0andsuchthat.Onechoiceis2and22.OGproposedasimpledecidingruleinordertodecideachoose0anddecidefortheGumbeldistributionwhen,fortheFr′echetdistributionwhen,andfortheWeibulldistributionwhen.Thevaluesofandcorrespondingtotheusualsigni?cancearegiveninthetablebelow.
0.001-1.....001
WeappliedboththeGQPandthestatisticaltestdescribedabove,totheannualmaximumsealevelsinVenicedatasetduringtheperiod1981C82(Smith1986).
ThisgivesrisetothegraphinFigure1.
(Graphonnextpage)
StataTechnicalBulletin25
Figure1.References
Scotto,M.G.andA.Tobias.1998.TechnicalBulletinReprints,vol.Smith,R.L.1986.ExtremevalueTiagodeOliveira,J.andM.I.J.TiagodeOliveira.Dordrecht:sg141Abstract:ThisarticledescribesestimatesatreatmenteffectsmodelconsiderstheconditionalontwosetsofeffectsmodelandcompletehowthecommandisusedKeywords:Probit,endogenousSyntax
Basicsyntax
depvarvarlistFullsyntaxformaximumdepvarvarlist#Fullsyntaxfortwo-stepdepvarvarlists,ands,s,isspeci?ed.sharesthefeaturesofall
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请教连老师2sls和处理效应模型
&本帖最后由 arlionn 于
20:30 编辑
& &2SLS 是一类估计方法的统称，也即我们平时所言的两阶段最小二乘法，我想细节和过程不必赘述。
& &Treatment Effect Model 可以视为一个特殊的内生性问题，其特征是内生变量为 0/1 变量。因此，第一阶段的回归不能再用 OLS，而是使用了 Logit 或 Probit，并以此为基础得到所谓的 hazard ratio；在第二步的回归中，在原有模型设定的基础上，加入 Hazard ratio 来调整内生性导致的偏误（详情 help treatreg，查看电子说明书中有关 Method 部分的说明）。
& &所以，你提到的文献中的处理方法，从严格意义上来讲，是不对的。至于二者之间的偏差有多大，由于没有做过相关的模拟，也没有看到相关的文献，目前还不得而知。
*==============Appendix===================
& && &&&*--------
& && &&&*-4.2.1.2&&处理效应 Treatment effect
& && && & *-& &Y = X*b1 + D*b2 + U
& && && & *& & D is 0/1 变量, 内生
& && && & *
& && && & *-本质：一个内生的 0/1 变量 (一个特殊的 IV 问题)
& && && && &
& && && & * 例 1：Y=ROA, D=是否实施股权激励(Yes=1, No=0)
& && && & * 例 2：Y=Wage,D=是否大学毕业(Yes=1, No=0)
& && && & *
& && && & * 内生性问题的根源：业绩好的公司更倾向于实施股权激励
& && && & *& && && && && && & 能力强的人更可能顺利读完大学
& && &*-其它例子：
& && && & *-&&是否读博士？
& && && & *-&&是否建立政治关联？(游说, 贿赂, 当选人大代表等)
& && && & *-&&是否实施多元化经营, 交叉上市, 兼并收购？&&
&&*-------------------
&&*-4.2.3 处理效应模型&&Treatment Effect Model
& & *--------
& & *-4.2.3.1&&二元模型设定
& && &help treatreg& &// Also see | Manual: [R] treatreg
& && &shellout "$R\Stata_Treatreg.pdf"&&
& &*-Primary regression equation:
& &*& && &y_j = X_j*b1 + T_j*b2 + e_j& &&&(1)&&e_j~N(0,sigma^2)
& &*-Treatment equation
& &*& && &T_j* = W_j*gamma + u_j& && && & (2)&&Latent variable
& &*& && && && && && && && && && && && && && & u_j~N(0,1)
& &*-Decision rule:
& &*& && && && &{ 1&&if (T_j*&0)
& &*& && &T_j = {& && && && && && && &Note: T_j 是可以观察到的
& &*& && && && &{ 0&&otherwise
& &*& &Corr(e_j, u_j) = rho& &// 内生性的根源
& &*- rho&0，表明 OLS 低估了 T_j 对 y_j 的边际影响;
& &*- rho&0，表明 OLS 高估了 T_j 对 y_j 的边际影响;
& & *--------
& & *-4.2.3.2&&估计方法
& && &*-最大似然估计 (Maxlikelihood Estimation, MLE)
& && && && &*-基于二元联合正态分布函数
& && &*-两步法 (Two-step Estimation)
& && && &&&
& && && && &*-Step1: Probit (Treat Equation) --& Prob(Z=1)
& && && && &*& && &&&probit T w
& && && && &*& && && &&&{ H = normden(wb)/normal(wb)& && &&&if T=1
& && && && &*& &Hazard: {
& && && && &*& && && &&&{ H = -normalden(wb)/(1-normal(wb)) if T=0
& && && && && &
& && && && &*-Step2: reg y X z H&&// regression Equation 中加入 hazard
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