dm "output;clear;log;clear";
******************************************************;
* bpdemo.sas -- Biplot Demonstration Using 2-D Data. *;
******************************************************;
Options PS=55 LS=90 NoNumber NoDate
FORMCHAR='|----|+|---+=|-/\<>*';
Title1 "Biplot Examples";
Data One;
Input Id $ X1-X2;
Datalines;
O 0 0
A 2 0
B 0 2
C 1.5 1.8
D 2.0 1.9
E 1.7 1.6
;
Proc Corr Data=One Cov;
Var X1-X2;
Run;
Proc Iml;
Reset Nolog NoPrint;
Use One;
Read All Var{X1 X2} Into X;
Close One;
N=NRow(X);
One=J(n,1,1);
Xbar=(X`*One)/n; /* Find the Centroid */
XTilde=X-One*Xbar`; /* Center the Data */
Call SVD(u,l,v,XTilde); /* Compute SVD */
Title2 "Biplot Analysis -- Alpha=0 With n-1 Scaling";
DGamma=diag(l); /* Construct DGamma */
G=U*sqrt(n-1); /* Form G and H */
H=V*DGamma*(1/sqrt(n-1));
GGprime=G*G`;
HHprime=H*H`;
Print X,XTilde,U,DGamma,V,G,H,GGprime,HHprime;
Create Obs From G; /* Output the vectors for plotting */
Append From G;
Close Obs;
Create Vars From H;
Append From H;
Close Vars;
Quit;
Data Obs;
Merge Obs One; /* Merge Back the ID information */
Run;
Data Vars;
Set Vars;
Id=Put(_N_,1.); /* Just Number the Variables */
Run;
Data Both; /* Need Both Together for the Biplot */
Set Vars Obs;
Run;
Title3 "Biplot Data -- Row and Column Coordinates";
Proc Print Data=Both;
Var Id Col1 Col2;
Run;
Proc Plot Data=Both;
Title2 "Observations in Original Variable Space";
Plot X1*X2 $ Id="*" / VRef=0 HRef=0 Box
VAxis=By 0.5 HAxis=By 0.5 VPos=30 HPos=60;
Run;
Title2 "Observations and Variables in Biplot";
Plot Col2*Col1 $ Id="*" / VRef=0 HRef=0 Box
VAxis=By 0.5 HAxis=By 0.5 VPos=40 HPos=60;
Run; Quit;
Biplot Examples
Correlation Analysis
2 'VAR' Variables: X1 X2
Covariance Matrix DF = 5
X1 X2
X1 0.9000000000 0.0920000000
X2 0.0920000000 0.9056666667
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
X1 6 1.20000 0.94868 7.20000 0 2.00000
X2 6 1.21667 0.95167 7.30000 0 2.00000
Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 6
X1 X2
X1 1.00000 0.10190
0.0 0.8477
X2 0.10190 1.00000
0.8477 0.0
Biplot Examples
X
0 0
2 0
0 2
1.5 1.8
2 1.9
1.7 1.6
XTILDE
-1.2 -1.216667
0.8 -1.216667
-1.2 0.7833333
0.3 0.5833333
0.8 0.6833333
0.5 0.3833333
U
-0.766173 -0.007212
-0.141927 0.7059029
-0.122406 -0.698703
0.2814024 -0.094718
0.4696523 0.0489865
0.2794503 0.0457429
DGAMMA
2.2303329 0
0 2.013442
V
0.6961385 0.7179076
0.7179076 -0.696138
G
-1.713214 -0.016126
-0.317357 1.5784468
-0.273707 -1.562347
0.6292348 -0.211795
1.0501744 0.1095371
0.6248698 0.1022843
H
0.694353 0.6464317
0.7160663 -0.62683
Biplot Examples
Biplot Analysis -- Alpha=0 With n-1 Scaling
GGPRIME
2.9353637 0.518247 0.4941138 -1.074599 -1.80094 -1.072185
0.518247 2.5922101 -2.379219 -0.534 -0.160382 -0.036857
0.4941138 -2.379219 2.5158436 0.1586713 -0.458575 -0.330835
-1.074599 -0.534 0.1586713 0.4407936 0.6376069 0.3715265
-1.80094 -0.160382 -0.458575 0.6376069 1.1148647 0.6674262
-1.072185 -0.036857 -0.330835 0.3715265 0.6674262 0.4009243
HHPRIME
0.9 0.092
0.092 0.9056667
Biplot Examples
Biplot Analysis -- Alpha=0 With n-1 Scaling
Biplot Data -- Row and Column Coordinates
OBS ID COL1 COL2
1 1 0.69435 0.64643
2 2 0.71607 -0.62683
3 O -1.71321 -0.01613
4 A -0.31736 1.57845
5 B -0.27371 -1.56235
6 C 0.62923 -0.21180
7 D 1.05017 0.10954
8 E 0.62487 0.10228
Biplot Examples
Observations in Original Variable Space
Plot of X1*X2$ID. Symbol used is '*'.
--+-------------+-------------+-------------+-------------+---
X1 | | |
2.0 + * A * D +
| | |
| | |
| | |
| | * E |
| | |
| | |
1.5 + | * C +
| | |
| | |
| | |
| | |
| | |
| | |
1.0 + | +
| | |
| | |
| | |
| | |
| | |
| | |
0.5 + | +
| | |
| | |
| | |
| | |
| | |
| | |
0.0 +-*-O-----------------------------------------------------*-B+
--+-------------+-------------+-------------+-------------+---
0.0 0.5 1.0 1.5 2.0
X2
NOTE: 2 obs had missing values.
Biplot Examples
Observations and Variables in Biplot
Plot of COL2*COL1$ID. Symbol used is '*'.
--+-------+-------+-------+-------+-------+-------+-------+---
COL2 | | |
| | |
| | |
| | |
2.0 + | +
| | |
| | |
| * A | |
1.5 + | +
| | |
| | |
| | |
1.0 + | +
| | |
| | |
| | * 1 |
0.5 + | +
| | |
| | |
| | * E * D |
0.0 +------*-O------------------------+--------------------------+
| | |
| | * C |
| | |
-0.5 + | +
| | * 2 |
| | |
| | |
-1.0 + | +
| | |
| | |
| | |
-1.5 + * B | +
| | |
| | |
| | |
-2.0 + | +
| | |
| | |
| | |
--+-------+-------+-------+-------+-------+-------+-------+---
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
COL1