logistic回歸分析實例操作

1、Logistic回歸分析二分類（因變量Y有（如發(fā)病1與未發(fā)病0）兩種可能出現(xiàn)的結(jié)果）資料的Logistic回歸分析，至于多分類Logistic回歸分析，與二分類操作過程類似，只是在數(shù)據(jù)編制及分析方法選擇處不同。分析的一般步驟：變量的編碼啞變量的設(shè)置和引入各個自變量的單因素分析變量的篩選交互作用的引入建立多個模型選擇較優(yōu)的模型模型應(yīng)用條件的評價輸出結(jié)果的解釋實例操作11.1某研究人員在探討腎細(xì)胞癌轉(zhuǎn)移的有關(guān)臨床病理因素研究中，收集了一批行根治性腎切除術(shù)患者的腎癌標(biāo)本資料，現(xiàn)從中抽取26例資料作為示例進(jìn)行l(wèi)ogistic回歸分析。1.各變量及其賦值說明x1：確診時患者的年齡（歲）x2：腎細(xì)胞癌血管

2、內(nèi)皮生長因子（VEGF）,其陽性表述由低到高共3個等級（1-3）x3：腎細(xì)胞癌組織內(nèi)微血管數(shù)（MVC）x4：腎癌細(xì)胞核組織學(xué)分級，由低到高共4級（1-4）X5：腎細(xì)胞癌分期，由低到高共4期（1-4）y：腎細(xì)胞癌轉(zhuǎn)移情況（有轉(zhuǎn)移y=1;無轉(zhuǎn)移y=0）。為二分類變量。若作單因素的Logistic回歸分析，也就是分別作Y與各自變量間的回歸分析如Y與X1、Y與X2等的單因素Logistic回歸分析。2.建立數(shù)據(jù)庫擔(dān)fogisiit回歸f理雪B陰冒|Data5ecl-IBMSPSSStatisticsDataEd如FieEdrLView旦EtaTransformAialyzeDirectMarkfUrr

3、gGraphsytirties.fdd-onsV/indowHeti目昌”嚅鮎韁紐扇露奄國/坊邯Nam&X1T?P&WitsnDecimalsLabelValuesMissingColumnsAlignMeasureRole12bJumeric80惟淒時崽咅的Non仔MonaS二Righ:Seals%llnputX2FJumericB0譽(yù)疋甩痙血蹩1,+1-NoneS石Right我:NominalInpul34X3Numeric81None時已8Right/Scale%InpulX4hljmerica0(1一蜩忖QflP8二Right罷Noninallinpul5X5rjume

4、ricB0譽(yù)筑胞応寸期一詢None8垂Right<Nominal%Inpul67yb-lumeric80腎細(xì)胞念轉(zhuǎn)夠Nonas二Right亀Nominal粘llnputPRE_1r-Jumeric115PredictedptdbNon&Nme13-Right/ScaleInpul8PGR_1Numeric80Predctedgroup(0.無搏穆None8RightdbNominal+Inpuly1Q_111213iaviewv»d»bitV|*舊村SPSSStatistic:弓Racessonsrea3分析步驟(1)靈*logi電c

5、回歸作業(yè)-gSJS.sayjGtSata王切-FileEditVievfDataTransf°rrnAnalyzeDire匚t塑日廣ketingGraphsUtilitiesAdd-onsWindowHelpAReportsDescripliveStatisticsTablesGompareMeans卜GeneralLinearModel#G呂DEr引i至巳lLinearModels#MixedModels卜CorrelateR&gressionLoglinearkNeuralNetworksClassifyDimensionReductionScale#Nonpararne

6、tricTests卜ForecastingSurvival加MultipleResponseElMissingValueAnalysis.MultipleImputation卜ComplexSamplesQualityControl卜IdROCCurveAutomati匚Linearr/lodeling血Linear.CurveEstimationISPartialLeastSquares1BinaryLogistic制MultinomialLogisticOOrdinalProbitNonlinear.疇WeightEstimadon.-甌2-StageLeastSquares-.Optim

7、alScaling(CATREG)(2)logistic回歸徑k-數(shù)S.iavDataSetllBM!ljSPSSStalisticsDataEditorFile-EditViewDataTransformAnalyzeDirectMarketingGraphsUblibesAdd-onsWindoMVHelpZ3Id捕區(qū)1Qr上圖中若為單因素回歸分析，只需在Covariates協(xié)變量框內(nèi)導(dǎo)入單一自變量如X1即可。(3)2腕占試目i曰諭威克.冊卩那呦口-BMSPSSStisticsDataEd；torAleEditViewDataTrarieformAtialyzeDirectMarketin

8、gGraphs蛍ililiaAdd-onsWindowHelpLAJ"-X4L21：X1X2PRE:17lnr:：'idi.-!consignir:rriQr!i?l111-probabiiif/血StepwiseEntry:晌|Remavat|d.hj|©AllcasesDisplay-Attachsiep'AtlaststepStatisticsndPlotsV：Glass帀tatianplSwICasewiselistngofresidualsPGR_1t-LogisticRegression:OptionsX1Lci&ticRegressio

9、n電411212CorrationsofestimatesINosmer-Lenneshcgoodness-of-filOishersoutside-.2:tddevZiJtefstianhistory站Clfor卻(B)B5Classificationculofr0.5MaKimumllerahons2C4分析結(jié)果(1)數(shù)據(jù)描述SelectedCasesIncludedinAnalysis26100.0MissingCases0.0Total26100.0UnselectedCases0.0Total26-100.0-a.Ifweightisineffect,seeclassificatio

10、ntableforthetotalnumberofcases.無轉(zhuǎn)移0轉(zhuǎn)移1(2)Block1:Method=ForwardStepwise(LikelihoodRatio)川SigStep1Step15.5381.000Block15.5381.0001qcopinon17277.000Step2Step6.1781.013Block21.7162.000Model21716000表示兩步變量的引入均有統(tǒng)計學(xué)意義，方法合理。NagelkerkeRCox&SnellR118.004a.450.621211.826b.566.781a.Estimationterminatedatiter

11、ationnumber6becauseparameterestimateschangedbylessthan.001.b.Estimationterminatedatiterationnumber7becauseparameterestimateschangedbylessthan.001.可見第二步比第一步變量引入后決定系數(shù)有所增加，表明第二步變量引入后模型的擬合效果更好。3)a.Thecutvalueis.500theEquation95%C.I.fprEXP(B)BSEWalddfExp(B)Step1aX22.563.9167.829100512.9782.15578.154Const

12、ant-6.2562.2897.4681.006.002Step2bX22.4131.1964.0721.04411.1721.072116.454X42.0961.0883.7131.0548.136.96568.62312328543151541023000a. Variable(s)enteredonstep1:X2.b. Variable(s)enteredonstep2:X4.模型最后引入X2(腎細(xì)胞癌血管內(nèi)皮生長因子(VEGF)和X4(腎癌細(xì)胞核組織學(xué)分級)兩個變量，雖然X4引入后的參數(shù)檢驗顯示P=0.540.05且其OR值的95%CI中包括1,但是考慮到其0R=8.136較大，且

13、由上一表可知引入變量X4后，用模型進(jìn)行預(yù)測時的percentageCorrect從84.6%提高到96.2%，因此綜合考慮后還是應(yīng)將變量X4引入模型。(4)eEquationdfSigStep1VariablesX1.8061.369X3.1881.664X46.1991.013X53.6891.055OverallStatistics8.8764.064Step2VariablesX11.3981.237X3.7261.394X51.6621.197OvorallStatistics5.0973.165可見當(dāng)其他變量引入模型后的參數(shù)檢驗均無統(tǒng)計學(xué)意義。5)16+Scpnumber:1Obse

14、rvedGroupsandPredictedProbabilitiesFREQu十ENCY12十IOI0I8+0I0I0I04+I0I0I011000000Prob:O.1.2.5.4.5.6.7.S.91Group:OaOOOOaOOODOOOOOOOOOOQOOOOOQOOOOOOOOOOOOOOOOOOOOOOLlllLllllLLlllLLLllLLlllLLllllLLllllllllLLl11111L1PredictedProbabilityisofMembershipfor妄移heCutValueis.50Smbal£!Q_無發(fā)柱_1-胳EachSymbolRprsents1Stpnumber:2ObservedCroupsandPredictedProbabilities16+FIR12十EIQIU10Ea+oN10C10¥104+0010010D1000+I十III+III1十.I1IQIPredicted+-4+Prob!0.1.23.4.5.E.7.8.91Group：OOGODODOODOOOODOOODOOOODOOOOOOOODOOQDDOflODOOOODOOO11111111111111111111111111111111111111111111111111Pr