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comsvybrr—BalancedrepeatedreplicationforsurveydataDescriptionQuickstartMenuSyntaxOptionsRemarksandexamplesStoredresultsMethodsandformulasReferencesAlsoseeDescriptionsvybrrperformsbalancedrepeatedreplication(BRR)estimationofspeciedstatistics(orex-pressions)foraStatacommandorauser-writtenprogram.
ThecommandisexecutedonceforeachreplicateusingsamplingweightsthatareadjustedaccordingtotheBRRmethodology.
AnyStataes-timationcommandlistedin[SVY]svyestimationmaybeusedwithsvybrr.
User-writtenprogramsthatmeettherequirementsin[P]programpropertiesmayalsobeused.
QuickstartEstimatepopulationmeanofv1usingBRRstandard-errorestimateswithsamplingweightwvar1andreplicateweightsinvariableswithprexrwvarsvyset[pweight=wvar1],brrweight(rwvar*)svybrr_b:meanv1BRRestimateofthestandarderrorofthedifferencebetweenthemeansofv2andv3svybrr(_b[v2]-_b[v3]):meanv2v3Asabove,butnametheresultdiffandsaveresultsfromeachreplicationtomydata.
dtasvybrrdiff=(_b[v2]-_b[v3]),saving(mydata):meanv2v3Sameasabovebrrdiff=(_b[v2]-_b[v3]),saving(mydata):meanv2v3Note:AnyestimationcommandmeetingtherequirementsspeciedintheDescriptionmaybesubstitutedformeanintheexamplesabove.
MenuStatistics>Surveydataanalysis>Resampling>Balancedrepeatedreplicationsestimation12svybrr—BalancedrepeatedreplicationforsurveydataSyntaxsvybrrexplist,svyoptionsbrroptionseformoption:commandsvyoptionsDescriptionif/insubpop(varnameif)identifyasubpopulationReportinglevel(#)setcondencelevel;defaultislevel(95)noheadersuppresstableheadernolegendsuppresstablelegendnoadjustdonotadjustmodelWaldstatisticnocnsreportdonotdisplayconstraintsdisplayoptionscontrolcolumnsandcolumnformats,rowspacing,linewidth,displayofomittedvariablesandbaseandemptycells,andfactor-variablelabelingcoeflegenddisplaylegendinsteadofstatisticscoeflegendisnotshowninthedialogboxesforestimationcommands.
brroptionsDescriptionMainhadamard(matrix)Hadamardmatrixfay(#)Fay'sadjustmentOptionssaving(lenamesaveresultstolename;savestatisticsindoubleprecision;saveresultstolenameevery#replicationsmseuseMSEformulaforvarianceReportingverbosedisplaythefulltablelegendnodotssuppressreplicationdotsdots(#)displaydotsevery#replicationsnoisilydisplayanyoutputfromcommandtracetracecommandtitle(text)usetextastitleforBRRresultsAdvancednodropdonotdropobservationsreject(exp)identifyinvalidresultsdof(#)designdegreesoffreedomsvyrequiresthatthesurveydesignvariablesbeidentiedusingsvyset;see[SVY]svyset.
commanddenesthestatisticalcommandtobeexecuted.
Thebyprexcannotbepartofcommand.
See[U]20Estimationandpostestimationcommandsformorecapabilitiesofestimationcommands.
Warning:Usingiforinrestrictionswilloftennotproducecorrectvarianceestimatesforsubpopulations.
Tocomputeestimatesforsubpopulations,usethesubpop()option.
svybrr—Balancedrepeatedreplicationforsurveydata3explistspeciesthestatisticstobecollectedfromtheexecutionofcommand.
explistisrequiredunlesscommandhasthesvybprogramproperty,inwhichcaseexplistdefaultstob;see[P]programproperties.
Theexpressionsinexplistareassumedtoconformtothefollowing:explistcontains(name:elist)elisteexpelistcontainsnewvarname=(exp)(exp)eexpisspecname[eqno]specnamespecnameisbb[]sese[]eqnois##nameexpisastandardStataexpression;see[U]13Functionsandexpressions.
Distinguishbetween[],whicharetobetyped,and,whichindicateoptionalarguments.
Optionssvyoptions;see[SVY]svy.
Mainhadamard(matrix)speciestheHadamardmatrixtobeusedtodeterminewhichPSUsarechosenforeachreplicate.
fay(#)speciesFay'sadjustment(Judkins1990),where0≤#≤2,butexcluding1.
Thisoptionoverridesthefay(#)optionofsvyset;see[SVY]svyset.
Optionssaving(lename,suboptions)createsaStatadatale(.
dtale)consistingof(foreachstatisticinexplist)avariablecontainingthereplicates.
doublespeciesthattheresultsforeachreplicationbesavedasdoubles,meaning8-bytereals.
Bydefault,theyaresavedasfloats,meaning4-bytereals.
Thisoptionmaybeusedwithoutthesaving()optiontocomputethevarianceestimatesbyusingdoubleprecision.
every(#)speciesthatresultsbewrittentodiskevery#threplication.
every()shouldbespeciedinconjunctionwithsaving()onlywhencommandtakesalongtimeforeachreplication.
Thiswillallowrecoveryofpartialresultsshouldsomeothersoftwarecrashyourcomputer.
See[P]postle.
replacespeciesthatlenamebeoverwrittenifitexists.
Thisoptiondoesnotappearinthedialogbox.
msespeciesthatsvybrrcomputethevariancebyusingdeviationsofthereplicatesfromtheobservedvalueofthestatisticsbasedontheentiredataset.
Bydefault,svybrrcomputesthevariancebyusingdeviationsofthereplicatesfromtheirmean.
4svybrr—BalancedrepeatedreplicationforsurveydataReportingverboserequeststhatthefulltablelegendbedisplayed.
nodotsanddots(#)specifywhethertodisplayreplicationdots.
Bydefault,onedotcharacterisdisplayedforeachsuccessfulreplication.
Ared'x'isdisplayedifcommandreturnsanerror,andan'e'isdisplayedifatleastonevalueinexplistismissing.
Youcanalsocontrolwhetherdotsaredisplayedusingsetdots;see[R]set.
nodotssuppressesdisplayofthereplicationdots.
dots(#)displaysdotsevery#replications.
dots(0)isasynonymfornodots.
noisilyrequeststhatanyoutputfromcommandbedisplayed.
Thisoptionimpliesthenodotsoption.
tracecausesatraceoftheexecutionofcommandtobedisplayed.
Thisoptionimpliesthenoisilyoption.
title(text)speciesatitletobedisplayedabovethetableofBRRresults;thedefaulttitleis"BRRresults".
eformoption;see[R]eformoption.
Thisoptionisignoredifexplistisnotb.
Advancednodroppreventsobservationsoutsidee(sample)andtheifandinqualiersfrombeingdroppedbeforethedataareresampled.
reject(exp)identiesanexpressionthatindicateswhenresultsshouldberejected.
Whenexpistrue,theresultingvaluesareresettomissingvalues.
dof(#)speciesthedesigndegreesoffreedom,overridingthedefaultcalculation,df=NpsuNstrata.
Remarksandexamplesstata.
comBRRwasrstintroducedbyMcCarthy(1966,1969a,1969b)asamethodofvarianceestimationfordesignswithtwoPSUsineverystratum.
TheBRRvarianceestimatortendstogivemorereasonablevarianceestimatesforthisdesignthanthelinearizedvarianceestimator,whichcanresultinlargevaluesandundesirablywidecondenceintervals.
InBRR,themodelistmultipletimes,onceforeachofabalancedsetofcombinationswhereonePSUisdroppedfromeachstratum.
Thevarianceisestimatedusingtheresultingreplicatedpointestimates.
AlthoughtheBRRmethodhassincebeengeneralizedtoincludeotherdesigns,Stata'simplementationofBRRrequirestwoPSUsperstratum.
Toprotecttheprivacyofsurveyparticipants,publicsurveydatasetsmaycontainreplicate-weightvariablesinsteadofvariablesthatidentifythePSUsandstrata.
Thesereplicate-weightvariablesareadjustedcopiesofthesamplingweights.
ForBRR,thesamplingweightsareadjustedfordroppingonePSUfromeachstratum;see[SVY]Varianceestimationformoredetails.
Example1:BRRreplicate-weightvariablesThesurveydesignfortheNHANESIIdata(McDowelletal.
1981)isspecicallysuitedtoBRR;therearetwoPSUsineverystratum.
svybrr—Balancedrepeatedreplicationforsurveydata5.
usehttps://www.
stata-press.
com/data/r16/nhanes2.
svydescribeSurvey:Describingstage1samplingunitspweight:finalwgtVCE:linearizedSingleunit:missingStrata1:strataSU1:psuFPC1:#ObsperUnitStratum#Units#Obsminmeanmax12380165190.
0215221856792.
511832348149174.
019942460229230.
023152252105126.
0147(outputomitted)292503215251.
5288302365166182.
5199312308143154.
0165322450211225.
0239316210,35167167.
0288Hereisaprivacy-consciousdatasetequivalenttotheoneabove;allthevariablesandvaluesremain,exceptstrataandpsuarereplacedwithBRRreplicate-weightvariables.
TheBRRreplicate-weightvariablesarealreadysvyset,andthedefaultmethodforvarianceestimationisvce(brr).
.
usehttps://www.
stata-press.
com/data/r16/nhanes2brr.
svysetpweight:finalwgtVCE:brrMSE:offbrrweight:brr_1.
.
brr_32Singleunit:missingStrata1:SU1:FPC1:Supposethatwewereinterestedinthepopulationratioofweighttoheight.
Hereweusetotaltoestimatethepopulationtotalsofweightandheightandthesvybrrprextoestimatetheirratioandvariance;weusetotalinsteadofratio(whichisotherwisepreferablehere)toillustratehowtospecifyanexplist.
6svybrr—Balancedrepeatedreplicationforsurveydata.
svybrrWtoH=(_b[weight]/_b[height]):totalweightheight(runningtotalonestimationsample)BRRreplications(32)12345BRRresultsNumberofobs=10,351Populationsize=117,157,513Replications=32Designdf=31command:totalweightheightWtoH:_b[weight]/_b[height]BRRCoef.
Std.
Err.
tP>|t|[95%Conf.
Interval]WtoH.
4268116.
0008904479.
360.
000.
4249957.
4286276ThemseoptioncausessvybrrtousetheMSEformoftheBRRvarianceestimator.
ThisvarianceestimatorwilltendtobelargerthanthepreviousbecauseoftheadditionofthefamiliarsquaredbiastermintheMSE;see[SVY]Varianceestimationformoredetails.
TheheaderforthecolumnofstandarderrorsinthetableofresultsisBRR*fortheBRRvarianceestimatorusingtheMSEformula.
.
svybrrWtoH=(_b[weight]/_b[height]),mse:totalweightheight(runningtotalonestimationsample)BRRreplications(32)12345BRRresultsNumberofobs=10,351Populationsize=117,157,513Replications=32Designdf=31command:totalweightheightWtoH:_b[weight]/_b[height]BRR*Coef.
Std.
Err.
tP>|t|[95%Conf.
Interval]WtoH.
4268116.
0008904479.
360.
000.
4249957.
4286276Thebiastermhereistoosmalltoseeanydifferenceinthestandarderrors.
Example2:Surveydatawithoutreplicate-weightvariablesForsurveydatawiththePSUandstratavariablesbutnoreplicationweights,svybrrcancomputeadjustedsamplingweightswithinitsreplicationloop.
Herethehadamard()optionmustbesuppliedwiththenameofaStatamatrixthatisaHadamardmatrixofappropriateorderforthenumberofstratainyourdataset(seethefollowingtechnicalnoteforaquickintroductiontoHadamardmatrices).
Thereare31stratainnhanes2.
dta,soweneedaHadamardmatrixoforder32(ormore)tousesvybrrwiththisdataset.
Hereweuseh32(fromthefollowingtechnicalnote)toestimatethepopulationratioofweighttoheightbyusingtheBRRvarianceestimator.
svybrr—Balancedrepeatedreplicationforsurveydata7.
usehttps://www.
stata-press.
com/data/r16/nhanes2.
svybrr,hadamard(h32):ratio(WtoH:weight/height)(runningratioonestimationsample)BRRreplications(32)12345Survey:RatioestimationNumberofstrata=31Numberofobs=10,351NumberofPSUs=62Populationsize=117,157,513Replications=32Designdf=31WtoH:weight/heightBRRRatioStd.
Err.
[95%Conf.
Interval]WtoH.
4268116.
0008904.
4249957.
4286276TechnicalnoteAHadamardmatrixisasquarematrixwithrrowsandcolumnsthathasthepropertyHrHr=rIrwhereIristheidentitymatrixoforderr.
GeneratingaHadamardmatrixwithorderr=2piseasilyaccomplished.
StartwithaHadamardmatrixoforder2(H2),andbuildyourHrbyrepeatedlyapplyingKroneckerproductswithH2.
HereistheStatacodetogeneratetheHadamardmatrixforthepreviousexample.
matrixh2=(-1,1\1,1)matrixh32=h2forvaluesi=1/4{matrixh32=h2#h32}svybrrconsumesHadamardmatricesfromlefttoright,soitisbesttomakesurethatrisgreaterthanthenumberofstrataandthatthelastcolumnistheoneconsistingofall1s.
ThiswillensurefullorthogonalbalanceaccordingtoWolter(2007).
8svybrr—BalancedrepeatedreplicationforsurveydataStoredresultsInadditiontotheresultsdocumentedin[SVY]svy,svybrrstoresthefollowingine():Scalarse(Nreps)numberofreplicationse(Nmisreps)numberofreplicationswithmissingvaluese(kexp)numberofstandardexpressionse(keexp)numberofb/seexpressionse(kextra)numberofextraestimatesaddedtobe(fay)Fay'sadjustmentMacrose(cmdname)commandnamefromcommande(cmd)samease(cmdname)orbrre(vce)brre(brrweight)brrweight()variablelistMatricese(bbrr)BRRmeanse(V)BRRvarianceestimatesWhenexplistisb,svybrrwillalsocarryforwardmostoftheresultsalreadyine()fromcommand.
MethodsandformulasSee[SVY]VarianceestimationfordetailsregardingBRRvarianceestimation.
ReferencesJudkins,D.
R.
1990.
Fay'smethodforvarianceestimation.
JournalofOfcialStatistics6:223–239.
McCarthy,P.
J.
1966.
Replication:Anapproachtotheanalysisofdatafromcomplexsurveys.
InVitalandHealthStatistics,series2.
Hyattsville,MD:NationalCenterforHealthStatistics.
.
1969a.
Pseudoreplication:Furtherevaluationandapplicationofthebalancedhalf-sampletechnique.
InVitalandHealthStatistics,series2.
Hyattsville,MD:NationalCenterforHealthStatistics.
.
1969b.
Pseudo-replication:Half-samples.
Revuedel'InstitutInternationaldeStatistique37:239–264.
McDowell,A.
,A.
Engel,J.
T.
Massey,andK.
Maurer.
1981.
PlanandoperationoftheSecondNationalHealthandNutritionExaminationSurvey,1976–1980.
VitalandHealthStatistics1(15):1–144.
Wolter,K.
M.
2007.
IntroductiontoVarianceEstimation.
2nded.
NewYork:Springer.
Alsosee[SVY]svypostestimation—Postestimationtoolsforsvy[SVY]svybootstrap—Bootstrapforsurveydata[SVY]svyjackknife—Jackknifeestimationforsurveydata[SVY]svysdr—Successivedifferencereplicationforsurveydata[SVY]Calibration—Calibrationforsurveydata[SVY]Poststratication—Poststraticationforsurveydata[SVY]Subpopulationestimation—Subpopulationestimationforsurveydata[SVY]Varianceestimation—Varianceestimationforsurveydata[U]20Estimationandpostestimationcommands