【導讀】判別分析方法的任務是根據(jù)已掌握的一批分類明確的樣品，建立一個較好的判別函數(shù)，它來自哪個總體。20世紀30年代，近年來，在許多現(xiàn)代自然科學的各個分支和技術部門中得到廣泛的應用。判別分析方法通常要給出一個判別指標——判別函數(shù)，同時還要指定一種判別規(guī)則。或二次的距離判別函數(shù)。否則，將采用不基于任何分布假設的非參數(shù)方法。度可以估計時，屬于某組的后驗概率。，且組iG的概率密度為。kiip，那么根據(jù)貝葉斯。分別是第i組的均值和協(xié)方差陣。全相等若各組先驗概率不全相等若各組先驗概率?；蛘哌@個樣品x至第i組的廣義平方距離)(2xDi為最小值。樣品x判歸于除k組以外的其他組。為簡單起見，我們只考慮兩個總體的情況。若1u、2u和V已知，則)(yw是y的線性函數(shù)，稱為線性判別函數(shù)。使用線性判別函數(shù)還是二次判別函數(shù)進行判別分析取決于兩個總體的方差。其中，S為估計合并協(xié)方差陣，iS為第i組內(nèi)的估計協(xié)方差陣。下，接受原假設H0。

　　

【正文】 ca 50 Discriminant Analysis Test of Homogeneity of Within Covariance Matrices Notation: K = Number of Groups P = Number of Variables N = Total Number of Observations Number of Groups N(i) = Number of Observations in the i39。th Group 1 __ N(i)/2 || |Within SS Matrix(i)| V = N/2 |Pooled SS Matrix| _ _ 2 | 1 1 | 2P + 3P 1 RHO = | SUM | |_ N(i) N _| 6(P+1)(K1) DF = .5(K1)P(P+1) _ _ | PN/2 | | N V | Under null hypothesis:2 RHO ln | | | __ PN(i)/2 | |_ || N(i) _| is distributed approximately as chisquare(DF) Test ChiSquare Value = with 2 DF Prob ChiSq = Since the chisquare value is significant at the level, the within covariance matrices will be used in the discriminant function. Reference: Morrison, . (1976) Multivariate Statistical Methods p252. ed6e74e0641c5cc279a1942ed79030e9 商務數(shù)據(jù)分析 電子商務系列 上海財經(jīng)大學經(jīng)濟信息管理系 IS/SHUFE Page 19 of 70 Discriminant Analysis Univariate Test Statistics F Statistics, Num DF= 2 Den DF= 147 Total Pooled Between RSQ/ Variable STD STD STD RSquared (1RSQ) PETALLEN Univariate Test Statistics Variable F Pr F Label PETALLEN Petal Length in mm. Average RSquared: Unweighted = Weighted by Variance = Discriminant Analysis Classification Summary for Calibration Data: Resubstitution Summary using Quadratic Discriminant Function Generalized Squared Distance Function: 2 _ 1 _ D (X) = (XX )39。 COV (XX ) + ln |COV | j j j j j Posterior Probability of Membership in each SPECIES: 2 2 Pr(j|X) = exp( D (X)) / SUM exp( D (X)) j k k Number of Observations and Percent Classified into SPECIES: From SPECIES Setosa Versicolor Virginica Total Setosa 50 0 0 50 Versicolor 0 46 4 50 Virginica 0 3 47 50 Total 50 49 51 150 Percent Priors Error Count Estimates for SPECIES: Setosa Versicolor Virginica Total Rate Priors Discriminant Analysis Classification Results for Calibration Data: Crossvalidation Results using Quadratic Discriminant Function Generalized Squared Distance Function: 2 _ 1 _ D (X) = (XX )39。 COV (XX ) + ln |COV | ed6e74e0641c5cc279a1942ed79030e9 商務數(shù)據(jù)分析 電子商務系列 上海財經(jīng)大學經(jīng)濟信息管理系 IS/SHUFE Page 20 of 70 j (X)j (X)j (X)j (X)j Posterior Probability of Membership in each SPECIES: 2 2 Pr(j|X) = exp( D (X)) / SUM exp( D (X)) j k k Posterior Probability of Membership in SPECIES: Obs From Classified SPECIES into SPECIES Setosa Versicolor Virginica 12 Versicolor Virginica * 25 Virginica Versicolor * 63 Virginica Versicolor * 83 Virginica Versicolor * 118 Versicolor Virginica * 131 Versicolor Virginica * 148 Versicolor Virginica * * Misclassified observation Discriminant Analysis Classification Summary for Calibration Data: Crossvalidation Summary using Quadratic Discriminant Function Generalized Squared Distance Function: 2 _ 1 _ D (X) = (XX )39。 COV (XX ) + ln |COV | j (X)j (X)j (X)j (X)j Posterior Probabil