Efficiently Screening Predictor Variables for Logistic Models

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1、NESUG2012Statistics,ModelingandAnalysisPaperSA9EfficientlyScreeningPredictorVariablesforLogisticModelsStevenRaimi,MarketingAssociates,Detroit,MIandWilmington,DEBruceLund,MarketingAssociates,Detroit,MIandWilmington,DEABSTRACTThispaperdiscussesthesituationwhe

2、reamodelermustfitamultinomiallogisticmodelwithnominaltargetandhasavailablehundredsofpotentialpredictorvariables.Suchsituationsmayoccurwhenthird-partydatasetsareaddedtoin-housetransactionaldatafordirectmarketingapplications.Thepaperdiscussesstatisticalmeasur

3、esforevaluatingthepredictivepowerofnumericpredictorvariablesandwhethertheeventualuseofthepredictorinthemodelcouldbeimprovedviaanon-monotonictransformation.Muchofourfocusisonthecasewherethetargetisbinary.Simulatedprobabilitydistributionsforthesestatisticalme

4、asuresarealsodiscussed.Finally,weprovideamethodologyandatoolkit(usingSAS®macros)thatidentifiesasubsetofpredictorsforfurtherstudyandeventualusageinfittingamodel.INTRODUCTIONThepaperdiscussestwostepsintheprocessofidentifyingandpreparingnumericpredictorvariabl

5、esforuseinalogisticregressionmodelwithnominalmultinomialtarget.1.Identifyingwhichnumericvariableshavesufficientpredictivepowertomeritfurtherstudy.2.Fromamongthesevariables,findingwhichhaveanon-monotonicrelationshiptothetargetvariable.Thec-statisticandan"x-s

6、tatistic"(tobedefined)arecomputedfornumericpredictorvariables.ASASmacrocalled%XC_STATisprovidedtoefficientlycomputec-statisticsandx-statisticsforanynumberofthesevariables.ThispaperisanextensionofworkbyRaimiandLund(2011).Cherrie(2007)alsodiscussestheproblemo

7、fpredictorvariablescreeningoflargecollectionsofpotentialpredictorsformultinomiallogisticregression.AgeneralreferenceforadiscussionofvariablescreeningandtransformingisFinlay(2010).C-STATISTICConsideranumeric(orordered)predictorX,andabinarytargetvariableYwith

8、values0and1.LetMgivethecountofpairsofobservationswhereoneobservationhasY=0andtheotherhasY=1.Suchpairsarecalled“informativepairs”.DefineCandTasfollows:C(forConcordant):Countofinformativepairswithahighe