线性回归模型在SASEM中的应用实例.docx

线性回归模型在SASEM中的应用实例.docx

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线性回归模型在SASEM中的应用实例

Chapter3PredictiveModelingUsingRegression

3.1IntroductiontoRegression

TheRegressionnodeinEnterpriseMinerdoeseitherlinearorlogisticregressiondependinguponthemeasurementlevelofthetargetvariable.

Linearregressionisdoneifthetargetvariableisanintervalvariable.Inlinearregressionthemodelpredictsthemeanofthetargetvariableatthegivenvaluesoftheinputvariables.

Logisticregressionisdoneifthetargetvariableisadiscretevariable.Inlogisticregressionthemodelpredictstheprobabilityofaparticularlevel（s）ofthetargetvariableatthegivenvaluesoftheinputvariables.Becausethepredictionsareprobabilities,whichareboundedby0and1andarenotlinearinthisspace,theprobabilitiesmustbetransformedinordertobeadequatelymodeled.Themostcommontransformationforabinarytargetisthelogittransformation.Probitandcomplementarylog-logtransformationsarealsoavailableintheregressionnode.

Recallthatoneassumptionoflogisticregressionisthatthelogittransformationoftheprobabilitiesofthetargetvariableresultsinalinearrelationshipwiththeinputvariables.

Regressionusesonlyfullcasesinthemodel.Thismeansthatanycase,orobservation,thathasamissingvaluewillbeexcludedfromconsiderationwhenbuildingthemodel.Asdiscussedearlier,whentherearemanypotentialinputvariablestobeconsidered,thiscouldresultinanunacceptablyhighlossofdata.Therefore,whenpossible,missingvaluesshouldbeimputedpriortorunningaregressionmodel.

Otherreasonsforimputingmissingvaluesincludethefollowing:

∙Decisiontreeshandlemissingvaluesdirectly,whereasregressionandneuralnetworkmodelsignoreallobservationswithmissingvaluesonanyoftheinputvariables.Itismoreappropriatetocomparemodelsbuiltonthesamesetofobservations.Therefore,beforedoingaregressionorbuildinganeuralnetworkmodel,youshouldperformdatareplacement,particularlyifyouplantocomparetheresultstoresultsobtainedfromadecisiontreemodel.

∙Ifthemissingvaluesareinsomewayrelatedtoeachotherortothetargetvariable,themodelscreatedwithoutthoseobservationsmaybebiased.

∙Ifmissingvaluesarenotimputedduringthemodelingprocess,observationswithmissingvaluescannotbescoredwiththescorecodebuiltfromthemodels.

TherearethreevariableselectionmethodsavailableintheRegressionnodeofEnterpriseMiner.

Forwardfirstselectsthebestone-variablemodel.Thenitselectsthebesttwovariablesamongthosethatcontainthefirstselectedvariable.Thisprocesscontinuesuntilitreachesthepointwherenoadditionalvariableshaveap-valuelessthanthespecifiedentryp-value.

Backwardstartswiththefullmodel.Next,thevariablethatisleastsignificant,giventheothervariables,isremovedfromthemodel.Thisprocesscontinuesuntilalloftheremainingvariableshaveap-valuelessthanthespecifiedstaypvalue.

Stepwiseisamodificationoftheforwardselectionmethod.Thedifferenceisthatvariablesalreadyinthemodeldonotnecessarilystaythere.Aftereachvariableisenteredintothemodel,thismethodlooksatallthevariablesalreadyincludedinthemodelanddeletesanyvariablethatisnotsignificantatthespecifiedlevel.Theprocessendswhennoneofthevariablesoutsidethemodelhasap-valuelessthanthespecifiedentryvalueandeveryvariableinthemodelissignificantatthespecifiedstayvalue.

Thespecifiedp-valuesarealsoknownassignificancelevels.

3.2RegressioninEnterpriseMiner

FIN〉FOUT

Imputation,Transformation,andRegression

Thedataforthisexampleisfromanonprofitorganizationthatreliesonfundraisingcampaignstosupporttheirefforts.Afteranalyzingthedata,asubsetof19predictorvariableswasselectedtomodeltheresponsetoamailing.Tworesponsevariableswerestoredinthedataset.Oneresponsevariablerelatedtowhetherornotsomeonerespondedtothemailing（TARGET_B）,andtheotherresponsevariablemeasuredhowmuchthepersonactuallydonatedinU.S.dollars（TARGET_D）.

Name

ModelRole

MeasurementLevel

Description

AGE

Input

Interval

Donor'sage

AVGGIFT

Input

Interval

Donor'saveragegift

CARDGIFT

Input

Interval

Donor'sgiftstocardpromotions

CARDPROM

Input

Interval

Numberofcardpromotions

FEDGOV

Input

Interval

%ofhouseholdinfederalgovernment

FIRSTT

Input

Interval

Elapsedtimesincefirstdonation

GENDER

Input

Binary

F=female,M=Male

HOMEOWNR

Input

Binary

H=homeowner,U=unknown

IDCODE

ID

Nominal

IDcode,uniqueforeachdonor

INCOME

Input

Ordinal

Incomelevel（integervalues0-9）

LASTT

Input

Interval

Elapsedtimesincelastdonation

LOCALGOV

Input

Interval

%ofhouseholdinlocalgovernment

MALEMILI

Input

Interval

%ofhouseholdmalesactiveinthemilitary

MALEVET

Input

Interval

%ofhouseholdmaleveterans

NUMPROM

Input

Interval

Totalnumberofpromotions

PCOWNERS

Input

Binary

Y=donorownscomputer（missingotherwise）

PETS

Input

Binary

Y=donorownspets（missingotherwise）

STATEGOV

Input

Interval

%ofhouseholdinstategovernment

TARGET_B

Target

Binary

1=donortocampaign,0=didnotcontribute

TARGET_D

Target

Interval

Dollaramountofcontributiontocampaign

TIMELAG

Input

Interval

Timebetweenfirstandseconddonation

ThevariableTARGET_Disnotconsideredinthischapter,soitsmodelrolewillbesettoRejected.

Acardpromotionisonewherethecharitableorganizationsendspotentialdonorsanassortmentofgreetingcardsandrequestsadonationforthem.

TheMYRAWdatasetintheCRSSAMPlibrarycontains6,974observationsforbuildingandcomparingcompetingmodels.Thisdatasetwillbesplitequallyintotrainingandvalidationdatasetsforanalysis.

BuildingtheInitialFlowandIdentifyingtheInputData

1.OpenanewdiagrambyselectingFileNewDiagram.

2.OntheDiagramssubtab,namethenewdiagrambyright-clickingonUntitledandselectingRename.

3.NamethenewdiagramNon-Profit.

4.AddanInputDataSourcenodetothediagramworkspacebydraggingthenodefromthetoolbarorfromtheToolstab.

5.AddaDataPartitionnodetothediagramandconnectittotheInputDataSourcenode.

6.Tospecifytheinputdata,double-clickontheInputDataSourcenode.

7.ClickonSelect…inordertochoosethedataset.

8.Clickonthe

andselectCRSSAMPfromthelistofdefinedlibraries.

9.SelecttheMYRAWdatasetfromthelistofdatasetsintheCRSSAMPlibraryandthenselectOK.

Observethatthisdatasethas6,974observations（rows）and21variables（columns）.Evaluate（andupdate,ifnecessary）theassignmentsthatweremadeusingthemetadatasample.

1.ClickontheVariablestabtoseeallofthevariablesandtheirrespectiveassignments.

2.ClickontheNamecolumnheadingtosortthevariablesbytheirname.Aportionofthetableshowingthefirst10variablesisshownbelow.

Thefirstseveralvariables（AGEthroughFIRSTT）havethemeasurementlevelintervalbecausetheyarenumericinthedatasetandhavemorethan10distinctlevelsinthemetadatasample.Themodelroleforallintervalvariablesissettoinputbydefault.ThevariablesGENDERandHOMEOWNRhavethemeasurementlevelbinarybecausetheyhaveonlytwodifferentnonmissinglevelsinthemetadatasample.Themodelroleforallbinaryvariablesissettoinputbydefault.

ThevariableIDCODEislistedasanominalvariablebecauseitisacharactervariablewithmorethantwononmissinglevelsinthemetadatasample.Furthermore,becauseitisnominalandthenumberofdistinctvaluesisatleast2000orgreaterthan90%ofthesamplesize,theIDCODEvariablehasthemodelroleid.IftheIDvaluehadbeenstoredasanumber,itwouldhavebeenassignedanintervalmeasurementlevelandaninputmodelrole.

ThevariableINCOMEislistedasanordinalvariablebecauseitisanumericvariablewithmorethantwobutnomorethantendistinctlevelsinthemetadatasample.Allordinalvariablesaresettohavetheinputmodelrole.

Scrolldowntoseetherestofthevariables.

ThevariablesPCOWNERSandPETSbothareidentifiedasunaryfortheirmeasurementlevel.Thisisbecausethereisonlyonenonmissinglevelinthemetadatasample.Itdoesnotmatterinthiscasewhetherthevariablewascharacterornumeric,themeasurementlevelissettounaryandthemodelroleissettorejected.

Thesevariablesdohaveusefulinformation,however,anditisthewayinwhichtheyarecodedthatmakesthemseemuseless.BothvariablescontainthevalueYforapersonifthepersonhasthatcondition（petownerforPETS,computerownerforPCOWNERS）andamissingvalueotherwise.Decisiontreeshandlemissingvaluesdirectly,sonodatamodificationneedstobedoneforfittingadecisiontree;however,neuralnetworksandregressionmodelsignoreanyobservationwithamissingvalue,soyouwillneedtorecodethesevariablestogetatthedesiredinformation.Forexample,youcanrecodethemissingvaluesasaU,forunknown.YoudothislaterusingtheReplacementnode.

IdentifyingTargetVariables

NotethatthevariablesTARGET_BandTARGET_Daretheresponsevariablesforthisanalysis.TARGET_Bisbinaryeventhoughitisanumericvariablesincethereareonlytwonon-missinglevelsinthemetadatasample.TARGET_Dhastheintervalmeasurementlevel.Bothvariablesaresettohavetheinputmodelrole（justlikeanyotherbinaryorintervalvariable）.ThisanalysiswillfocusonTARGET_B,soyouneedtochangethemodelroleforTARGET_BtotargetandthemodelroleTARGET_Dtorejectedbecauseyoushouldnotusearesponsevariableasapredictor.

1.