安庆师范学院    胡云峰

习题 用对应分析法，对我国16个地区农民1982年支出情况的6项指标进行分类。

16个地区农民生活水平的调查数据（单位:元）

程序：

x=[190.33 43.77 9.73 60.54 49.01 9.04;135.20 36.40 10.47 44.16 13.49 3.94;...

    95.21 22.83 9.30 22.44 22.81 2.80;104.78 25.11 6.40 9. 18.17 3.25;...

    128.41 27.63 8.94 12.58 23.99 3.27;145.68 32.83 17.79 27.29 39.09 3.47;...

    159.37 33.38 18.37 11.81 25.29 5.22;116.22 29.57 13.24 13.76 21.75 6.04;...

    221.11 38. 12.53 115.65 50.82 5.;144.98 29.12 11.67 42.60 27.30 5.74;...

    169.92 32.75 12.72 47.12 34.35 5.00;153.11 23.09 15.62 23.54 18.18 6.39;...

    144.92 21.26 16.96 19.52 21.75 6.73;140.54 21.5 17. 19.19 15.97 4.94;...

    115.84 30.26 12.20 33.61 33.77 3.85;101.18 23.26 8.46 20.2 20.5 4.3];

[n p]=size(x);

T=sum(sum(x));

xliehe=zeros(1,p);

xhanghe=zeros(1,n);

for k=1:p

    xliehe(k)=sum(x(:,k));

end

for l=1:n

    xhanghe(l)=sum(x(l,:));

end

Z=zeros(p,p);

for i=1:1:n

    for j=1:1:p

        Z(i,j)=(x(i,j)-xhanghe(i)*xliehe(j)/T)/((xhanghe(i)*xliehe(j))^(1/2));

    end

end

A=Z'*Z

输出结果

A =

    0.0042    0.0003    0.0032   -0.0090   -0.0026    0.0012

    0.0003    0.0034    0.0001   -0.0044    0.0004    0.0000

    0.0032    0.0001    0.0055   -0.0091   -0.0016    0.0010

   -0.0090   -0.0044   -0.0091    0.0284    0.0014   -0.0029

   -0.0026    0.0004   -0.0016    0.0014    0.0055   -0.0008

0.0012    0.0000    0.0010   -0.0029   -0.0008    0.0014

然后求A的特征值及特征向量

程序

[X B]=eig(A)

输出结果

X =

    0.7547   -0.3203    0.3733    0.0438    0.3135    0.2972

    0.3441    0.1587   -0.4490    0.7199   -0.3485    0.1227

    0.2253    0.1520   -0.7095   -0.5207    0.2386    0.3078

    0.3628    0.0685   -0.1587   -0.0255    0.2293   -0.8861

    0.3311   -0.0066    0.1281   -0.4555   -0.8120   -0.0850

    0.1417    0.91    0.3377   -0.0243    0.1071    0.0970

B =

    0.0000         0         0         0         0         0

         0    0.0010         0         0         0         0

         0         0    0.0016         0         0         0

         0         0         0    0.0033         0         0

         0         0         0         0    0.0069         0

         0         0         0         0         0    0.0357

（0.0357+0.0069）/（0.0357+0.0069+0.0033+0.0016+0.0010）*100%=87.83%

前两个方差的累计贡献率已达87%，因此，选前两个特征值分别计算R型与Q型的因子载荷阵如下

程序

F=zeros(p,2);

for t=1:1:p

    F(t,1)=(0.0357^0.5)*(X(t,6));

    F(t,2)=(0.0069^0.5)*(X(t,5));

end

F

G=Z*F

输出结果

F =

    0.0562    0.0260

    0.0232   -0.02

    0.0582    0.0198

   -0.1674    0.0191

   -0.0161   -0.0674

    0.0183    0.00

G =

   -0.0079   -0.0021

   -0.0054    0.0024

   -0.0001   -0.0013

    0.0075   -0.0011

    0.0080   -0.0012

    0.0035   -0.0024

    0.0128    0.0001

    0.0083   -0.0007

   -0.0246    0.0012

   -0.0044    0.0006

   -0.0042    0.0000

    0.0062    0.0027

    0.0077    0.0018

    0.0080    0.0028

   -0.0030   -0.0025

0.0018   -0.0007

最后我们在因子轴平面上左变量点和样品点

程序

h1=F(:,1);

g1=F(:,2);

h2=G(:,1);

g2=G(:,2);

plot(h1,g1,'o')

hold on

plot(h2,g2,'+')

legend('变量点','样品点');

输出结果下载本文