判別分析實(shí)例匯總

1、判別分析實(shí)例匯總 例：人文與發(fā)展指數(shù)是聯(lián)合國開發(fā)計(jì)劃署于 1990 年5月發(fā)表的第一份人類發(fā)展報(bào)告中公布的。 該報(bào)告建議，目前對人文發(fā)展的衡量指標(biāo)應(yīng)當(dāng)以 人生的三大要素為重點(diǎn)。衡量人生的三大要素的 指標(biāo)分別為：實(shí)際人均 GDP指數(shù)、出生時的預(yù) 期壽命指數(shù)、受教育程度指數(shù)（由成人識字率指 數(shù)和綜合總?cè)藢W(xué)率指數(shù)按2/3、1/3的權(quán)重加權(quán)而 得），將一生三個指數(shù)合成為一個指數(shù)就是人文 發(fā)展指數(shù)。今從2007年世界各國人文發(fā)展指數(shù)（2005年）的排序中，選取高發(fā)展水平、中等發(fā)展水平和低發(fā)展水平國家各 6個作為三組樣 品，另選四個國家作為待判樣品，資料如下表所 示。試用判別分析過程對以下數(shù)據(jù)資料進(jìn)行判別

2、 分析，并據(jù)此對待選的四個國家進(jìn)行判別歸類。國家人均 GDP（美 元）出生時 的預(yù)期 壽命 （歲）成人識 字率 （%）初等、中等和 高等教 育入學(xué) 率（%）第美國4189077.999.593.3類：高德國2946179.199.288發(fā)展希臘2338178.99699水平 國家新加 坡2966379.492.587.3意大 利2852980.398.490.6韓國2202977.99996第一 類：中 等發(fā) 展水 平國家古巴600077.799.887.6羅馬 尼亞906071.997.376.8巴西840271.788.687.5泰國867769.692.671.2菲律 賓51377192

3、.681.1土耳 其840771.487.468.7第二 類：低 發(fā)展 水平 國家尼泊 爾155062.648.658.1尼日 利亞112846.569.156.2喀麥 隆229949.867.962.3巴基 斯坦237064.649.940越南307173.790.363.9印度 尼西 亞384369.790.468.2待判 組日本3126782.39985.9印度345263.76163.8中國675772.590.969.1南非1111050.882.477data develop;input type gdp life rate zhrate; cards ;1 4189077.999

4、.593.31 2946179.199.2881 2338178.996991 2966379.492.587.31 2852980.398.490.61 2202977.999962 6000 77.799.887.62 9060 71.997.376.82 8402 71.788.687.52 8677 69.692.671.22 5137 7192.681.12 8407 71.487.468.73 1550 62.648.658.13 1128 46.569.156.23 2299 49.867.962.33 2370 64.649.9403 3071 73.790.363.93 38

5、43 69.790.468.2.3126782.399 85.9.3452 63.76163.8.6757 72.590.969.1.1111050.882.4proc discrim simple wcov distance list ; /*simple:要求技術(shù)各類樣品的簡單描述統(tǒng)計(jì)量；選項(xiàng) WCO遮求計(jì)算類內(nèi)協(xié)方差陣；選項(xiàng) DISTANCE要求計(jì)算馬氏距離；選項(xiàng) LIST要求 輸出重復(fù)替換歸類結(jié)果。由于沒有給出方法選項(xiàng)，所以系統(tǒng)按缺省時的正態(tài)分布進(jìn)行有關(guān)參數(shù) 的估計(jì)和歸類。*/class type;var gdp life rate zhrate;run ;proc discrim p

6、ool=test slpool =0.05 list ; /*simple: */ class type;priors '1' =0.3 '2' =0.4 '3' =0.3 ;run ;proc discrim method =npar k = 2 list ; /*simple: */ class type;run ;proc candisc out =result ncan =2; /*simple: */ class type;var gdp life rate zhrate;run ;procgplot data =reult;plotc

7、an1*can2=type;run ;proc discrim data =result distance list class type;var can1 can2;run ;表1已知樣本分類水平信息Cbserva-tlonsVariablesClasses1843DF TotalDF ?'ilhin C1 asiesDF Belden Cllsisses：17152Class LevelInfarnait IonVariablePr iorNameFrequencyWeight PmriionProbabi I ity_166.Q00V0.3838885.333385J66.Q00

8、90.333933L333338JeG.OOOO 0.3999990.333333The DISCRIM Procedure1 n.ta Ou6 yp表2樣本統(tǒng)計(jì)量信息lithlrrCI&ss Covariance MatricesVariablegdp life rate ihnte沖49408692.97-123JJ2417?.07H1022J3type=1, DF = 5life-1234.12(M5-0488?J3rate417?.07-0.887,432J4zhrate-11022*03-2 . 092J42L13typeM, DF = 5Variableliferate2b

9、Me鑰p2642240.567-2026.117-2419.950-6404.957life-2026.1177.8868.86113,946rate-2419.8508.8E123,15114,327zhrate-6404.S5713,94614.32764,438tire=9, DF = 5Variable件liferatejh rate如87g170.86B77840 J70012B24.07834200.80S3I ife7840.7700117.6H073.1G6015.3 湖rate1S624J73373.1GG03科娜7136J0S77hrate4200.303315,3730m

10、.m96,0017Simple StatisticsVariablegdp life rate zhrateTotal-SampleStandard Deviation125639.694616.416816.2389N18181818Sun23489?127415591378Mean13050 70.76111 86.61667 78.43333Varianc98605269.50971283.70235type=1StandardVariableNSunMeanVarianceDeviationgdp6174953291594940858370291 ife647

11、3.5000078.916670.849670.9218rate6584.6000097.433337.484672.7287zhrate6554.2000092.3666721.186674.6029type=2StandardVariableNSumMeanVarianceDeviationgdp645683761426422411625life6433.3000072.216677.885672.8081rate8558.3000093.0500023.151004.8115zhrate6472.9000078.8166764.48767”3type - 3VariableNSumMea

12、nVarianceStandardDeviationsdp614281237?876171988.0186life6366.8000081,15000117.6110010.8449rate6418.2000069.36667888.6068718,4013zhrate6848.7000058.1166796.901878.8439b-Pooled Covariance Matrix IMomationNatural Log of the Covar iance Det errni nant of the Matrix Rank Covariance Matrix29.69428表3類間距離及

13、三類總體均值差異的顯著性檢 驗(yàn)Pai ise Squared Distances Between Groups 2_-1D (i U) = (X - X X COY (X - X ) i Ji JSquared Di stance to typeFrom type1231037.5C2S8?5 J?S032婚.6 眈蛇010.91436375.97G0310.914280F SIslI 1st ics, NDF=4, CDF=12 for Squared Distance to typeFrom tge1J910?2.5497348/8562222.54973U8J4時7845.585626.

14、54857。Prob > Mahalanobis Di stance far Squsred Distance to tv口日From type1I311.0000<.0001<,00012<.0001LOOOO0.00493<QQ1O.QU羽1,0900Pairwise Ceri&ral ized Squared D istance Be4weefi Croups2 ,_ _ -I _ _D (i |j) = (X - X )h CO? (X - X 0I 4k hI J J表3給出了類1與類2之間的馬氏距離為 37.58288,類1與類3之間的馬氏距離

15、為 75.97603,類2與類3之間的馬氏距離為10.91428. 類與類之間總體均值的F檢驗(yàn)統(tǒng)計(jì)量值分布為22.54978, 45.58562, 22.54973,對應(yīng)的檢驗(yàn)概 率分別為<0.0001, <0.0001,<0.0001,說明三類總 體均值兩輛之間的差異是顯著的，因此判別分析 有意義。表4線形判別函數(shù)LinearDiscriminartFunct ion fortypeVariable12Constant-157.18S32-S3.12840-62.22473沖0.00204O.Q0O625O0.0002E7B1 ifeL66562L31631rate“708

16、5-0.09262-0.009402 hr it a1.726511.195590.05253由表4可寫出線形判別函數(shù)如下:高發(fā)展水平:y1=-157.18932+0.00204gdp+1.66582life-0.37085r ate+1.72851zhrate中等發(fā)展水平Y(jié)2=-99.12840+0.0006250gdp+1.49389life-0.0926 2rate+1.19559zhrate 低發(fā)展水平：Y3=-62.22473+0.0002576gdp+1.31631life-0.0894 0rate+0.85253zhrate表5:用距離判別法判別分析結(jié)果Resubstituti&

17、amp;n Results using Linear DTscriifnaint FunctionGenera I ized Squared Di stance Funct ion2- -I _D (X) - (K-X y CO? cx-x)fcaPosterior Pnimbi I ity of Membership in Encti type? 1Pr(j|X)=字沖卜/D (X) / SUM 冢p(=J 0 ()0)j kkPosterior Probtbi I ity af Membersh p in typeFrom ClassifiedObstype：into t/pe123111

18、Lmo，叩印 0,0000211i .順。MWU 0.00003111.0000o.oooo o.nooo411i.moQ .叩 QU0.0000511i-Dono0.00000.0000g111.0000D.QOQO O.uOuu122Q.OOQQPJ999 0.DQQ1022O.DOOOD.99470.0053S22O.OOflOa.39S80.0002IC22O.OQQO0,94110.058311220.00000,99400.0060122to.oodo0 .幽0,104213330.0000Q.00430.995714330.0000Q.00010.990915330.00000.

19、00280.9977IC33o.mo00001.0000173a0.00000.25790.7421IES30.00000.49780.5022191杷1.0000O.COOD U .皿00203 M0.00000.06710.932321t小0.00110(M 眥M34022.2部O.OOQO0.91250.0871* Misclassified observation由表5得，最后四個觀測的歸類結(jié)果為19 號（日本）觀測為高發(fā)展水平國家，第20號（印 度）為第3類，即低發(fā)展水平國家，21號（中 國）和22號（南非）歸為中等發(fā)展水平國家。表6距離判別法判別分析結(jié)果小結(jié)Rifeaubst it

20、u+ ion £uift加ary usi Lirasir Di ser i m inflirit Funct i anGeneral ised Squa red DI st arce Fund Ian2-1 .d m =(x-x y coy cx-x 】j jjPosterior ProLabi I ily of Membership in Each typePr(j IX) = sup(-.5 F OO) J SUW exc(-.5 F OO)j kkNumberFrom tpeofObser7at iTalalPriors25.006 ICO.000D.00QOJO731.820

21、.33333and Percent2250.000 o.ocE100.0000.00g36.360.3333SCl ass if i ed125.UOn- -uo OO086100.0031,820.33383into typeTotsil41010.008100.CDg ioo.no6100.0022 i oio. coError Count E與七 iMtes for type28 FotalR七3PriorsO.ODDO0.33830.0000U.OOOO0.383311.3933O.OtlOiJ表6給出了分類錯誤信息，由輸出結(jié)果可知 分類錯誤的比率為0,即正確的比率為100%。本程序中

22、第二個判別分析過程的選項(xiàng) “pool=test ;要求進(jìn)行類內(nèi)協(xié)方差陣一致性檢驗(yàn)，檢驗(yàn)的顯著性水平由選項(xiàng)"slpool=0.05”給出為0.05. priors語句給出了各發(fā)展水平國家的 先驗(yàn)概率。表7分類信息及類內(nèi)協(xié)方差陣一致性檢驗(yàn)結(jié)果Cl ass： LevelInf ormat iontypeVariableFrequenc：Weight ProporlionPriorRrobabi lily123,1_2_3$ 6&6*00000.3333336.00000.3333336,09000.3333330.300000 ouooooo 0.300000帕thin Corei

23、r ianceMatrix Informat iontypeGovirianceHat r i x Ra.nkNadural Loe of the Det erm I riant of the Covariance Mal ri x1ZFboledA d4421.8181922.790952645543228.69428Ghi-SquareOF Pr ? GhiSq點(diǎn)4日5昵曉3 20IN口8Since the Chi -Stiuare value is s ivn if icant at the 0.05 I eve I > the within Qvarigince Prices w

24、ill bw uwmd in the discriminmt function.Reference: Morrisron, D.F. (197G) Multivi-iate Statistical Methods p252>表7表明3個類的先驗(yàn)概率分別為0.3,0.4, 0.3,類內(nèi)協(xié)方差陣行列式的自然對數(shù)不相等， 表明類內(nèi)協(xié)方差陣不相等，而卡方統(tǒng)計(jì)量值為 46.068898,對應(yīng)的概率是 0.0008,在0.05的顯 著性水平下是顯著的，即類內(nèi)協(xié)方差陣存在顯著 差異。由于類內(nèi)協(xié)方差陣不等，所以判別函數(shù)應(yīng) 是二次函數(shù)。表8類間配對廣義馬氏距離The DISCRIM ProcedurePa

25、 IrwIse Genaral i zed Squired D istances Batwesn Groups2_ _-1 _ _,Di|J二裒-X ) CW (X - X ) In ICOV I - 2 In ffilOR iiiIJJIJJJGeneral ized Squired Distance to type P row typsI2S124.22114315.049?G2C1S?23C.6759324.62353132.51537913E486.8748128,S722B由表8可知，類內(nèi)廣義馬氏距離不再為0,而且類間的廣義馬氏距離也不再相等， 因而類內(nèi) 協(xié)方差和先驗(yàn)概率對后驗(yàn)概率的

26、計(jì)算是起作用 的。表9用Bayes判別法得到的判別分析部分結(jié)果Resub st 1 tul I on Results using Quadrat i c Di scrim I rant Fund i oriGenerali ized Squared Di stance Funct II on2-1D W=(x-x y cov(X-X ) + In ICOV IjJJJjPosteriorPrababi lity ofMembershipin Each type2Pr(j|X)=exp(-.5 D 00) / SUM exp(-.5 D CX)jkVPoster ior Probbi 1 ity

27、of Membership in iypeFromC1 ass： i f ied0b$lypeinto type1231111.00000.00000.00002111.00000.00000.00008111.000001.00011O.OOOD4111.00000.0000O.flOOO511i.ooaoo.oooc0400006111.oooo0.00000,00007220.00001.00000.00008220.00001 JOO。0.00008220.00001.00000.0000102?0.00001.0000D.OOOD11220.00000.999S0.000112220

28、.00001,0000O.OOOtJ13330.0000o.ooocLD00914330,00000.0000L000915330.00000.0000LOODB16330.00000.0000LOOOO17S30.00000.00010.99 附18330.00000,02720.972Sa1 *1.00400.00000.0000203 *0.0000oi.oood1.000D212 *0.00001 .000(1O.OOOD222宗0.00001.00000.0000HlMLscI a«si f ladobseion由表9可知，用BAYES判別法對待判樣品 的判別結(jié)果與距離判別

29、法結(jié)果一致。本程序中的第三個過程要求進(jìn)行非參數(shù)分析，即對類密度函數(shù)進(jìn)行非參數(shù)估計(jì)。選項(xiàng)K=2 要求用最近鄰的兩個樣品進(jìn)行密度函數(shù)估計(jì)， 選 項(xiàng)list要求輸出重復(fù)替換歸類結(jié)果。該過程運(yùn)行結(jié)果如下:表10用NPAR方法得到的判別分析部分結(jié) 果Squared Distance Function2-1D WY) ： (X-Y)= W (X-V)PQsteriQr Probability of Nenbrship in E冬sh typem (X - Pnopcrt icn of ols in 宅qup k in 2k n&& rest rei ghbars of XPr(J|X) =

30、 n 00 PRIOR ，SUM(巾(X) PRIOR )4I-|IPosterior Probabi I Itjrof Uembership in typeOhsFrom C1 jlssif i ed l/pei nlo type123111eoooq0JI0000.0000?11I.OOOQojjoqo0.00003111.0DCQD.00000.0000411LODCQ0.0000o.aooo8111,00050.00000.0000611i.cooa0.00000.00Ofl?220,00001.00000.0000322o.oooa1.0000O.QOOA922o.oooaIJiOO

31、Oo_aooc10220.00001.0000o.aooo1122o.oooa1.00000.0100012220.00001.00000.0100013S30.00000.0000LQOOC14330,00000.11000LOOOO1b930-00090JI000LOOOOIB330.0000o.rjoooLOOOO1733O-ODCQ0.00001.00001333O.ODCQ0.00001.000018, 1 *LOCOO0.00000.0000£0,Othar Io.oooa0.5000Q 咖02112 *0,00001.0000O.OOOQ22,Other I0,0000

32、Q.50MO.OOU< Misclas®If ied observat i onT 1le for 1argest probabi1 H-y由表10可知，4個待判的樣品中19號和21 號歸類結(jié)果與BAYES判別歸類結(jié)果是一致的， 但20號和22號所屬類別則不能確定，這是與前 面2中判別方法結(jié)果不一致的地方。第四種FISHER判別：第一個過程執(zhí) 行典型判別分析。第二個過程要求繪制第一個典 型變量CAN1和第二個典型變量 CAN2的散點(diǎn) 圖，以便更加直觀了解分類情況。第一、二個過 程輸出結(jié)果如下：表11典型相關(guān)的多變量檢驗(yàn)結(jié)果The CANDISC ProcedureMult iv

33、arits ist io nd F pprQKimati onsS=2M=，5N=5Stat i st. i cYsIub F Value Nuri DF Den DF Pr > FWilks' LambdaPillai% TnceHotel I ine-Lftttley TraceRoy? s Greatest Root0.C340C739I.3S75S414 16.68642648 15.8E1449477 3 4 220 35242E1519<.0001<.0001<.CD01<.0001NOTE： F Stsit ist ic for Roy 等

34、Greatest Root i s an upper bound.NOTE： F Stat iat ic for 陰 Iks' Lambda is exact.由上表對相關(guān)陣的顯著性檢驗(yàn)結(jié)果可知，至少有表12典型相關(guān)與特征值The CANDISC ProcedureCanon 1ca1 Carrel at ionAdi mtedCemon i 1CorrelationApproximateStandardErrorSquaredCanon 1ca 1 Corrfilat ion1 QJ63 陰 5Q J64192QJ14393Q-4065820533960,6163610.18B991

35、0.42S926Test of HD：The canon 1 eft 1 cornel*!i ons InElaemvalues of InvCE)*HIhe current row and 亂11 that fol lew are zero-GanRsq/tl-CeinRsq)LikaIihood Approxi帕富teEigenvalue Difference Proportion Cmulative Rat io F Yalue Nlb DF Den OF Pr > F115.6514 15JQG5 0.95510.S5&I 0.0340073919.27024 <,

36、000120J4500.04431.0000 O.573O73783.23813 0.05?7上表可知，第一典型相關(guān)為0.969875,而第 二典型相關(guān)為0.653396。第一個特征值為 15.8514,所占比例為95.51%,第二個特征值為 0.7450,所占比例僅有4.49%,說明只需用第一 個典型變量即可。表13原始變量的典型相關(guān)系數(shù)Raw Cnonlcl Cceff ic leritaVariablegdp life rate zhraleCan I0.0002096S440.0382360552-.03463722600.0988009194Can2*.0001135495 0.03

37、94378902 O.U5O065G861 0.0990509184由表12可得兩個典型變量分別為:CAN1=0.0002096544gdp+0.0382960552life-0.0346472260rate+0.0988009134zhrateCan2=-0.0001135485gdp+0.0394378902life+0.0500655661rate+0.0390500134zhrate表14類間馬氏距離及各類總體均值的顯著生檢驗(yàn)CroupsPeiirviu Squared Dist&nces BetweenV (i Ij) = (x - y cov 8-Squared Distance to tj/peFrom tvm0 378288 75,3760337.5B2B8010.3142675.97S0310.91429 DF $3t博tig,NDF=2, N)F=14 for Squared Di虱4nm to typeFran type063.S1B04106.3664552.61604 0