SAS典型判別過程

FisherFisher判別法（典型判別法）#典型判別分析SAS/STAT/Candisc過程典型判別分析的思路從幾何的概念來說，是將高維空間的樣本點投影到低維空間，利用低維空間的變量做判別分析，從而使分析更加直觀，即對原始數(shù)據(jù)進(jìn)行坐標(biāo)變換，尋求能使總體盡可能分開的方向。從代數(shù)的概念來說，就是根據(jù)一個分類變量和幾個定量變量，通過典型判別過程得出典型變量，典型變量是定量變量的線性組合。典型判別分析得出與組有最大可能多重相關(guān)的變量的線性組合，最大的多重相關(guān)叫做第一典型相關(guān)，其線性組合稱為第一典型變量U],線性組合的相關(guān)系數(shù)稱為典型系數(shù)，次大的叫做第二典型相關(guān)，其線性組合稱為第二典型變量u。2Candisc過程可使用的語句為：Proccandisc<options>;（必需語句）Classvariable;（必需語句）Byvariables;Freqvariable;Varvariables;Weightvariable;數(shù)據(jù)集選項：DATA=SAS-data-set（SAS數(shù)據(jù)集）：指定欲分析的數(shù)據(jù)集。OUT=SAS-data-set（SAS數(shù)據(jù)集）：生成一個包含原始數(shù)據(jù)和典型變量得分的數(shù)據(jù)集。OUTSTAT=SAS-data-set（SAS數(shù)據(jù)集）：生成一個type=corr包含各種統(tǒng)計量的輸出數(shù)據(jù)集。典型變量選項：NCAN=n：指定將被計算的典型變量的個數(shù)。n的值必須小于或等于變量的個數(shù)。打印選項：BCORR:類間相關(guān)系數(shù)。PCORR:合并類內(nèi)相關(guān)系數(shù)。TCORR全樣本相關(guān)系數(shù)。WCORR每一類水平的類內(nèi)相關(guān)系數(shù)。BCOV：類間協(xié)方差。PCOV：合并類內(nèi)協(xié)方差。TCOV：全樣本協(xié)方差。WCOV：每一類水平的類內(nèi)協(xié)方差。BSSCP:類間SSCP矩陣。PSSCP：合并類內(nèi)修正SSCP矩陣。TSSCP：全樣本修正SSCP矩陣。WSSCP:每一類水平的類內(nèi)修正SSCP矩陣。ANOVA:檢驗總體中每一個變量類均值相等的假設(shè)的單變量統(tǒng)計量。SIMPLE：全樣本合類內(nèi)的簡單描述性統(tǒng)計量。ALL:產(chǎn)生以上所有的打印選項。NOPRINT：不打印。一般語句Byvariables;By語句與Proccandisc一起使用可以對由BY變量分組的觀測進(jìn)行獨(dú)立分析。Classvariable;Class變量的值定義分析的組，類水平由有格式的Class變量的值確定。Class變量可以是數(shù)字變量也可以是字符變量。Varvariables;Var語句指定分析中包括的定量變量。如果省略Var語句，分析包括未在其他語句中列出的全部變量。程序示例：該例是Fisher的Iris數(shù)據(jù)進(jìn)行典型判別分析。數(shù)據(jù)從三種剛毛弋尾花品種各采集了50各樣本。測量其萼片長度、萼片寬度、花瓣長度和花瓣寬度。做典型判別分析并觀察第一和第二個典型變量的散點圖，是否與原始數(shù)據(jù)的結(jié)果相符。datairis;inputsepallensepalwidpetallenpetalwidspecies@@;labelsepallen='SepalLengthinmm.'sepalwid='SepalWidthinmm.'petallen='PetalLengthinmm.'petalwid='PetalWidthinmm.';cards;數(shù)據(jù)行；proccandiscdata=irisncan=2out=outcandistanceanova;classspecies;varsepallensepalwidpetallenpetalwid;procprintdata=outcan;run;procplot;plotcan2*can1=species;run;

輸出結(jié)果：PlotofCanonicalVariables

CanonicalDiscriminantAnalysis150Observations149DFTotal4Variables147DFWithinClasses3Classes2DFBetweenClasses類水平信息：包括分類變量取值，每類的頻數(shù)、頻率和權(quán)重ClassLevelInformationSPECIESFrequencyWeightProportion15050.00000.33333325050.00000.33333335050.00000.333333類間的馬氏平方距離PairwiseSquaredDistancesBetweenGroupsD(i/j)2=(x一x)'cov—i(x-x)

ijijSquaredDistancetoSPECIESFromSPECIES1231089.86419179.38471289.86419017.201073179.3847117.201070FStatistics,NDF=4,DDF=144forSquaredDistancetoSPECIESFromSPECIES12310550.1888910982550.188890105.3126531098105.312650Prob>MahalanobisDistanceforSquaredDistancetoSPECIESFromSPECIES12311.00000.00010.000120.00011.00000.000130.00010.00011.0000單變量檢驗的統(tǒng)計量，當(dāng)P>F的值小于5%,則說明每個變量在類間的差異是非常顯著的。rUnivariateTestStatisticsFStatistics,NumDF=2DenDF=147TotalPooledBetweenRSQ/VariableSTDSTDSTDR-Squared(1-RSQ)FPr>FSEPALLEN8.28075.14797.95060.6187061.6226119.26450.0001SEPALWID4.35873.39693.36820.4007830.668849.16000.0001PETALLEN17.65304.303320.90700.94137216.05661180.16120.0001PETALWID7.62242.04658.96730.92888313.0613960.00710.0001AverageR-Squared:Unweighted=0.7224358WeightedbyVariance=0.8689444

多元變量檢驗的統(tǒng)計量，當(dāng)p>F的值小于5%,則說明聯(lián)合檢驗，變量在類間的差異是非常顯著的。rMultivariateStatisticsandFApproximationsS=2M=0.5N=71StatisticValueFNumDFDenDFPr>Wilks'Lambda0.02343863199.14582880.0001Pillai'sTrace1.1918988353.46682900.0001Hotelling-LawleyTrace32.47732024580.53282860.0001Roy'sGreatestRoot32.191929201166.95741450.0001NOTE:FStatisticforRoy'sGreatestRootisanupperbound.NOTE:FStatisticforWilks'Lambdaisexact.EigenvaluesofINV(E)*HAdjustedApproxSquared=CanRsq/(1-CanRsq)CanonicalCanonicalStandardCanonicalCorrelationCorrelationErrorCorrelationEigenvalueDifferenceProportionCumulative10.9848210.9845080.0024680.96987232.191931.90650.99120.991220.4711970.4614450.0637340.2220270.2854.0.00881.0000總體中當(dāng)前的典型相關(guān)及更小的典型相關(guān)為零的檢驗，p>F的值小于5%時，可以認(rèn)為當(dāng)前的典r型相關(guān)顯著不為零。LikelihoodTestofH0:ThecanonicalcorrelationsintheLikelihoodRatioApproxFNumDFDenDFPr>F10.02343863199.145382880.000120.7779733713.793931450.0001currentrowandallthatfollowarezero全樣本的標(biāo)準(zhǔn)化的典型系數(shù)Total-SampleStandardizedCanonicalCoefficientsCAN1CAN2SEPALLEN-0.6867795330.019958173SepalLengthinmm.SEPALWID-0.6688250750.943441829SepalWidthinmm.PETALLEN3.885795047-1.645118866PetalLengthinmm.PETALWID2.1422387152.164135931PetalWidthinmm.原始典型相關(guān)系數(shù)PlotofCanonicalVariablesCanonicalDiscriminantAnalysisRawCanonicalCoefficientsCAN1CAN2SEPALLEN-.08293776420.0024102149SepalLengthinmm.SEPALWID-2164521235SepalWidthinmm.PETALLEN0.2201211656-.0931921210PetalLengthinmm.PETALWID0.28104603090.2839187853PetalWidthinmm.典型變量的類均值ClassMeansonCanonicalVariables

SPECIESCAN1CAN21-7.6075999270.21513301721.825049490-0.72789962235.7825504370.512766605PlotofCanonicalVariablesOBSSEPALLENSEPALWIDPETALLENPETALWIDSPECIESCAN1CAN2150331421-7.67197-0.1348926428562236.800150.58090PlotofCAN2*CAN1.SymbolisvalueofSPECIES.CAN2,,1,,,1,,2,111,1,11111,11,1111111333333333333333223233