/* ====================================
SAS EXAMPLES ON PRINCIAP COMPONENTS ANALYSIS 
======================================*/


/* In SAS, you may perform a principal component analysis using either the PRINCOMP or FACTOR Procedures */

/* =========================
EXAMPLE 1: PCA BASED ON RAW DATA 
===========================*/

dm log 'clear';
dm output 'clear';
options nodate;

data PCA;
input X1 X2 X3 X4 X5 X6 X7 X8;
datalines;
6 7 2 5 8 7 8 8 
9 10 5 8 10 9 9 10 
7 8 3 6 9 8 9 7 
5 6 8 5 6 5 9 2 
6 8 8 8 4 4 9 5 
7 7 7 6 8 7 10 5 
9 9 8 8 8 8 8 8 
9 9 9 8 9 9 8 8 
9 9 7 8 8 8 8 5 
4 7 10 2 10 10 7 10 
4 7 10 0 10 8 3 9 
4 7 10 4 10 10 7 8 
6 9 8 10 5 4 9 4 
8 9 8 9 6 3 8 2 
4 8 8 7 5 4 10 2 
6 9 5 7 8 9 8 9 
8 7 7 7 9 5 8 6 
6 8 8 4 8 8 6 4 
6 7 8 4 7 8 5 4 
4 8 7 8 8 9 10 5 
;

PROC PRINCOMP DATA=PCA OUT=PCSCORES COVARIANCE n=8;
/* The option n=2 retains only 2 principal components. */
VAR X1--X8;
title 'Principal Component Analysis';
ods output eigenvalues=meigen;
RUN;

/* THE SCREE PLOT */
PROC PLOT DATA=meigen;
PLOT eigenvalue * Number;
run;


PROC FACTOR DATA=PCA 
METHOD=PRIN
NFACT=3
SCREE SIMPLE
ROUND
FLAG=.30 ;
VAR X1--X8;
TITLE2'Scree Plot of Eigenvalues';
RUN;

PROC CORR DATA=D2;
VAR FACTOR1 FACTOR2;
WITH X1 X2 X3 X4 X5 X6 X7 X8 FACTOR1 FACTOR2;
RUN;

PROC PRINT DATA=PCSCORES;
VAR prin1 prin2 prin3;
TITLE2 'VALUES OF THE FIRST THREE PRINCIPAL COMPONENT SCORES';
RUN;

proc univariate data=pcscores plot;
var prin1 prin2;
TITLE2 'Univariate Analysis on the first two Principal Components';
run;

proc gplot data=pcscores; 
plot prin2*prin1;
titles 'A Scatter Plot of the First Two Principal Component Scores';
run;
quit;






/* ===========================================
EXAMPLE 2: PCA WITH CORRELATION MATRIX AS INPUT 
============================================*/

DATA D1(TYPE=CORR) ;
INPUT _TYPE_ $  _NAME_ $ V1-V12 ;
CARDS;
N . 300 300 300 300 300 300 300 300 300 300 300 300
STD . 2.48 2.39 2.58 3.12 2.80 3.14 2.92 2.50 2.10 2.14 1.83 2.26
CORR V1 1.00 . . . . . . . . . . .
CORR V2 .69 1.00 . . . . . . . . . .
CORR V3 .60 .79 1.00 . . . . . . . . .
CORR V4 .62 .47 .48 1.00 . . . . . . . .
CORR V5 .03 .04 .16 .09 1.00 . . . . . . .
CORR V6 .05 -.04 .08 .05 .91 1.00 . . . . . .
CORR V7 .14 .05 .06 .12 .82 .89 1.00 . . . . .
CORR V8 .23 .13 .16 .21 .70 .72 .82 1.00 . . . .
CORR V9 -.17 -.07 -.04 -.05 -.33 -.26 -.38 -.45 1.00 . . .
CORR V10 -.10 -.08 .07 .15 -.16 -.20 -.27 -.34 .45 1.00 . .
CORR V11 -.24 -.19 -.26 -.28 -.43 -.37 -.53 -.57 .60 .22 1.00 .
CORR V12 -.11 -.07 .07 .08 -.10 -.13 -.23 -.31 .44 .60 .26 1.00
 ;
PROC FACTOR DATA=D1
METHOD=PRIN
PRIORS=ONE
MINEIGEN=1
SCREE
ROTATE=VARIMAX
ROUND
FLAG=.40 ;
VAR V1-V12;  
*VAR V1-V10 V12; /* IN ORDER TO HAVE A SIMPLER STRUCTURE */
RUN;