/* Filename: 	PCAvsCASeriation.sas                                                     */
/* Purpose:		Generate 4 fake battle-shipshaped curves and perform a PCA then a CA      */
/* Last Update:	FDN 4.23.02								    			   			      */

data seriation;
step=.1;
m1=2;
m2=4 ;
m3=6;
m4=8;
do i = 2 to 8 by step;
	t1= probnorm(i-(m1-step))-probnorm(i-m1) ; 
	t2= probnorm(i-(m2-step))-probnorm(i-m2) ; 
	t3= probnorm(i-(m3-step))-probnorm(i-m3) ; 
	t4= probnorm(i-(m4-step))-probnorm(i-m4) ; output;

end;
keep i t1 t2 t3 t4;	


data seriationpct; set seriation;
total= sum(of t1 t2 t3 t4);
array pct {*} t1 t2 t3 t4;
do j=1 to dim(pct);
	pct(j)= pct(j)/total;
end;
drop j total;


proc gplot;
 	plot t1*i t2*i t3*i t4*i/ overlay;
	run;

proc g3d;
	scatter t1*t2 = t3;
run; 


proc print;
run;

/* do the pca -- note we use the COV matrix */
proc princomp  data =seriation out=pca outstat=eigenstructure  covariance;
var t1 t2 t3 t4;
proc plot;
plot prin2*prin1 '*' $ i ;
run;
/* plot the eigenvectors */
data eigenvectors; set eigenstructure;
where _type_='SCORE';
proc transpose data = eigenvectors out=eigenvectors name=type; 
proc print data=eigenvectors;
proc plot data=eigenvectors;
plot prin2*prin1= '*' $ type;
run;


/* do a ca  and compare the results */

proc corresp data=seriation out=ca;
id i;
var t1 t2 t3 t4;

proc plot;
where _type_= 'OBS';
plot dim2*dim1 = '*' $ i ;

proc plot;
where _type_= 'VAR';
plot dim2*dim1 = '*' $ i ;

run;