线性回归模型在SAS-EM中的应用实例

Chapter3PredictiveModelingUsingRegression3.1IntroductiontoRegression...............................................................................3-33.2RegressioninEnterpriseMiner........................................................................3-93-2错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。3-33.1IntroductiontoRegression2ObjectivesDescribelinearandlogisticregression.Exploredataissuesassociatedwithregression.Discussvariableselectionmethods.3-4错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。3LinearversusLogisticRegressionInputvariableshaveanymeasurementlevel.Inputvariableshaveanymeasurementlevel.Predictedvaluesaretheprobabilityofaparticularlevel(s)ofthetargetvariableatthegivenvaluesoftheinputvariables.Predictedvaluesarethemeanofthetargetvariableatthegivenvaluesoftheinputvariables.Targetisadiscrete(binaryorordinal)variable.Targetisanintervalvariable.LogisticRegressionLinearRegressionTheRegressionnodeinEnterpriseMinerdoeseitherlinearorlogisticregressiondependinguponthemeasurementlevelofthetargetvariable.Linearregressionisdoneifthetargetvariableisanintervalvariable.Inlinearregressionthemodelpredictsthemeanofthetargetvariableatthegivenvaluesoftheinputvariables.Logisticregressionisdoneifthetargetvariableisadiscretevariable.Inlogisticregressionthemodelpredictstheprobabilityofaparticularlevel(s)ofthetargetvariableatthegivenvaluesoftheinputvariables.Becausethepredictionsareprobabilities,whichareboundedby0and1andarenotlinearinthisspace,theprobabilitiesmustbetransformedinordertobeadequatelymodeled.Themostcommontransformationforabinarytargetisthelogittransformation.Probitandcomplementarylog-logtransformationsarealsoavailableintheregressionnode.错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。3-54LogisticRegressionAssumptionlogittransformationRecallthatoneassumptionoflogisticregressionisthatthelogittransformationoftheprobabilitiesofthetargetvariableresultsinalinearrelationshipwiththeinputvariables.3-6错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。5MissingValuesCasesInputs?????????Regressionusesonlyfullcasesinthemodel.Thismeansthatanycase,orobservation,thathasamissingvaluewillbeexcludedfromconsiderationwhenbuildingthemodel.Asdiscussedearlier,whentherearemanypotentialinputvariablestobeconsidered,thiscouldresultinanunacceptablyhighlossofdata.Therefore,whenpossible,missingvaluesshouldbeimputedpriortorunningaregressionmodel.Otherreasonsforimputingmissingvaluesincludethefollowing:Decisiontreeshandlemissingvaluesdirectly,whereasregressionandneuralnetworkmodelsignoreallobservationswithmissingvaluesonanyoftheinputvariables.Itismoreappropriatetocomparemodelsbuiltonthesamesetofobservations.Therefore,beforedoingaregressionorbuildinganeuralnetworkmodel,youshouldperformdatareplacement,particularlyifyouplantocomparetheresultstoresultsobtainedfromadecisiontreemodel.Ifthemissingvaluesareinsomewayrelatedtoeachotherortothetargetvariable,themodelscreatedwithoutthoseobservationsmaybebiased.Ifmissingvaluesarenotimputedduringthemodelingprocess,observationswithmissingvaluescannotbescoredwiththescorecodebuiltfromthemodels.错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。3-76StepwiseSelectionMethodsForwardSelectionBackwardSelectionStepwiseSelectionTherearethreevariableselectionmethodsavailableintheRegressionnodeofEnterpriseMiner.Forwardfirstselectsthebestone-variablemodel.Thenitselectsthebesttwovariablesamongthosethatcontainthefirstselectedvariable.Thisprocesscontinuesuntilitreachesthepointwherenoadditionalvariableshaveap-valuelessthanthespecifiedentryp-value.Backwardstartswiththefullmodel.Next,thevariablethatisleastsignificant,giventheothervariables,isremovedfromthemodel.Thisprocesscontinuesuntilalloftheremainingvariableshaveap-valuelessthanthespecifiedstayp-value.Stepwiseisamodificationoftheforwardselectionmethod.Thedifferenceisthatvariablesalreadyinthemodeldonotnecessarilystaythere.Aftereachvariableisenteredintothemodel,thismethodlooksatallthevariablesalreadyincludedinthemodelanddeletesanyvariablethatisnotsignificantatthespecifiedlevel.Theprocessendswhennoneofthevariablesoutsidethemodelhasap-valuelessthanthespecifiedentryvalueandeveryvariableinthemodelissignificantatthespecifiedstayvalue.3-8错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。Thespecifiedp-valuesarealsoknownassignificancelevels.错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading2应用于要在此处显示的文字。3-93.2RegressioninEnterpriseMiner8ObjectivesConductmissingvalueimputation.Examinetransformationsofdata.Generatearegressionmodel.FIN〉FOUT3-10错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。错误!使用“开始”选项卡将Heading1应用于要在此处显示的文字。Imputation,Transformation,andRegressionThedataforthisexampleisfromanonprofitorganizationthatreliesonfundraisingcampaignstosupporttheirefforts.Afteranalyzingthedata,asubsetof19predictorvariableswasselectedtomodeltheresponsetoamailing.Tworesponsevariableswerestoredinthedataset.Onere