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ballantine.sas
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ballantine.sas
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* Draw ballantine diagram for three variables;
* From Earl Hunt,
The design of ballantines
Behav. Research Methods, Instru. & Computers, 1986 18:3, 277-284 article;
**-- Enter the three correlations here;
%include data(therapy);
proc corr data=therapy nosimple;
var therapy perstest intext;
*include goptions;
goptions vsize=7 in hsize=7 in;
%gsize(hsize=6, vsize=6, options=htext=1.8);
**-- Enter the three correlations here;
%let ryx1 = .60;
%let ryx2 = .77974;
%let rx1x2 = .0513;
**-- Names of the three variables, response var in the middle;
%let vars ='X1' 'Y' 'X2';
%macro ballantine(data=_last_, y=, x1=, x2=,
colors=red black green,
patterns = m2n45 empty m2n135
);
proc iml;
reset fw=6;
start centdist( r );
*-- Compute distance between centers of circles from rsq;
if r = 1 then return( 0 ); /* complete overlap */
else if r = 0 then return( 2 ); /* completely disjoint */
else do; /* intersecting circles */
pi = 3.14159;
lo = 0; hi = pi; /* angle theta, 0 <= theta <= pi radians */
q = r # pi; /* sector area of overlap */
old = 0;
alpha = pi/2;
delta = 1;
iter=0;
do until (delta < .001);
iter = iter + 1;
if iter > 20 then goto done;
z = alpha - sin(alpha);
if z = q then delta = 0;
else do; /* adjust */
old = alpha;
if z > q then do;
alpha = alpha - (alpha-lo)/2;
hi = old;
end;
else do;
alpha = alpha + (hi-alpha)/2;
lo = old;
end;
delta = abs(old-alpha);
end;
end;
done:
* print iter alpha delta lo hi;
alpha = alpha/2;
dist = 2 # cos(alpha);
end;
return( dist );
finish;
start partial( r12, r13, r23 );
*-- find partial correlation between vars 1&2, partialling 3;
r = (r12 - r13#r23) / sqrt( (1-r13##2)#(1-r23##2) );
return(r);
finish;
start spartial( r12, r13, r23 );
*-- semi-partial correlation between vars 2&3, partialling 1 from 3;
r = (r23 - r13#r12) / sqrt( (1-r13##2) );
return(r);
finish;
start bardiag( lx, ly, wx, wy, p, label);
lp= 0 || cusum(p) || 1;
print 'Bar diagram proportions of variance', p, lp;
x = lx + wx # lp;
y = ly + wy # { 0 1 };
call ggrid (x, y);
tp = "0.0" ||char(cusum(p),3,2) || "1.0";
call gstrlen(len,tp);
xl = x-len/2;
if p[2]<.05 then do;
xl[3]=xl[2]+len[2]/2;
xl[2]=xl[2]-len[2]/2;
end;
call gscript(xl, ly-3, tp);
call gscript(x[1],y[2]+1,'% Variance Accounted for');
call gstrlen(len,label);
do i=1 to 1+ncol(p);
xx = (x[i]+x[i+1]-len[i])/2;
yy = (y[1]+y[2])/2 - 1;
call gscript(xx, yy, label[i]);
end;
finish;
start twocirc(cx, cy, radius, r, labels, colors, patterns);
*-- Draw two circles showing partial relations;
rsq = r##2;
d = centdist( rsq ) # radius;
x = (cx - d/2)//
(cx + d/2);
y = cy // cy;
print 'Circle centers', x y radius rsq;
call gpie(x, y, radius, 0, 360, colors, , patterns);
call gpiexy(lx1, ly1, 1.25, 240, x[1]||y[1], radius);
call gpiexy(lx2, ly2, 1.25, 300, x[2]||y[2], radius);
call gstrlen(len,labels);
lx = lx1-len[1] // lx2;
ly = ly1 // ly2;
call gscript(lx, ly, labels);
finish;
start threcirc(cx, cy, radius, r, labels, colors, patterns);
*-- Draw three circles showing pairwise correlations;
rsq = r##2;
d =(centdist( rsq[1] ) //
centdist( rsq[2] ) //
centdist( rsq[3] )) ;
print d;
*reset print;
/*
s = sum( d )/2;
v = ((s-d)[#])/s;
v = sqrt(v);
xx = s - d[1];
theta = 2 # atan( v/xx);
*/
dsq = d##2;
cosa = min(1,( {1 1 -1}*dsq / (2#d[1]#d[2]) ));
theta = arcos( cosa );
*print theta (theta#45/atan(1));
dy = sin(theta)#d[2];
dx = cos(theta)#d[2];
cc = j(3,2,0);
cc[1,1] = cx - radius # d[1]/2;
cc[1,2] = cy + radius # dy/2;
cc[2,1] = cx + radius # d[1]/2;
cc[2,2] = cc[1,2];
cc[3,1] = cc[1,1] + radius # dx;
cc[3,2] = cc[1,2] - radius # dy;
print 'Circle centers', cc[r=labels c={X Y}];
call gpie(cc[,1], cc[,2], radius, 0, 360, colors, , patterns);
call gpoint(cc[,1], cc[,2], 'point');
ang= choose(cosa<.95,{120 60 270},
{270 90 270});
call gpiexy(lx1, ly1, 1.25, ang[1], cc[1,], radius);
call gpiexy(lx2, ly2, 1.25, ang[2], cc[2,], radius);
call gpiexy(lx3, ly3, 1.25, ang[3], cc[3,], radius);
call gstrlen(len,labels);
lx = lx1 || lx2 || lx3;
ly = ly1 || ly2 || ly3;
lx = lx - len/2;
call gscript(lx, ly, labels, 0,0);
*print 'three circles label positions', lx, ly, labels;
finish;
start demo;
cx = 20; cy=62; radius = 14;
rsq = r##2;
call gset('height',1.5);
call gscript(12,95,'Balantine',0,0,2.0);
colors = { 'CXFF00000080', 'black', 'CX0000FF80' };
colors = { &colors };
patterns = { &patterns};
*patterns = {'m2n45', 'empty', 'm2n135'};
run threcirc(cx, cy, radius, r, vars, colors, patterns);
r23_1 = partial(r[3], r[3], r[1]);
v_2 = trim(vars[2])+'.'+vars[1] || trim(vars[3])+'.'+vars[1] ;
cx = 75; cy=75;
rad = radius # (1-rsq[3]);
run twocirc(cx, cy, rad, r23_1, v_2, colors[{1 3}], patterns[{1 3}]);
r12_3 = partial(r[1], r[2], r[3]);
v_3 = trim(vars[2])+'.'+vars[3] || trim(vars[1])+'.'+vars[3] ;
cx = 75; cy=40;
rad = radius # (1-rsq[1]);
run twocirc(cx, cy, rad, r12_3, v_3, colors[{1 3}], patterns[{1 3}]);
call gscript(60,95,'Partial Relations',0,0,2.0);
p = spartial(r[1], r[2], r[3]);
p = rsq[1] || p##2;
label = vars[1] || trim(vars[3])+'.'+vars[1] || 'Error';
call bardiag(5,3, 85,10, p, label);
call gshow;
finish;
start cor (x);
d = dev(x); * correct for means;
xpx=t(d)*d; * crossproduct;
v = vecdiag(xpx); * diagonal values;
v = 1/sqrt(choose(v=0,.,v)); * account for constants;
v = choose(v=.,0,v);
corr= diag(v) * xpx * diag(v); * correlation matrix;
return(corr);
finish;
start dev(x);
* d = x - repeat(x[:,], nrow(x), 1);
return(x - repeat(x[:,], nrow(x), 1));
finish dev;
start nomiss(y, X, obsnames);
*-- Remove rows with any missing data from matrix and obsnames;
* (pass ' ' for obsnames if no row labels are present);
matrix = y || X;
miss = loc(matrix <=.Z);
if type(miss)='U'
then return; /* no missing data */
else do;
nr = nrow(matrix);
nc = ncol(matrix);
rows= 1+floor((miss-1)/nc);
rows= unique(rows);
keep=remove(1:nrow(matrix),rows);
deleted = nr - ncol(keep);
matrix = matrix[keep,];
reset noname;
print 'Warning:' deleted 'row(s) with missing data have been removed.';
reset name;
if obsnames ^={' '}
then do;
obs = obsnames[rows];
obs = shape(obs,1,nrow(obs)#ncol(obs));
if type(obs)='N' then obs=char(obs,3,0);
obsnames=obsnames[keep];
end;
end;
y = matrix[,1:ncol(y)];
X = matrix[,(1+ncol(y)):ncol(matrix)];
finish;
* r = {.60 .0513 .77974};
* vars={"PersTest" "Therapy" "IntExt"};
r = { &ryx1 &rx1x2 &ryx2 };
vars = {&vars};
r = {.60 .0513 .77974};
vars={"PersTest" "Therapy" "IntExt"};
* r = { .47 .42 .30 }; *-- Example from paper ;
* vars= { X1 Y X2 };
use &data;
read all var{&y &x1 &x2} into x[ colname=vars ];
obs = char(1:nrow(x),3,0);
y = x[,1];
X = x[,2:3];
run nomiss(y, X, obs);
x = y || X;
Ryx = cor(X);
print Ryx [r=vars c=vars];
r = Ryx[1,2] || Ryx[2,3] || Ryx[1,3];
call gstart;
call gwindow({-5 -5 , 104 104});
run demo;
call gwindow({0 0 , 100 100});
vars= { X1 Y X2 };
cx = 55; cy=58; radius = 20;
r = { .50 .0 .30 };
rsq = r##2;
call gopen;
call gset('height',3.2);
run threcirc(cx, cy, radius, rsq, vars, colors, patterns);
call gscript(30, 8,'X1, X2 Independent',0,0,3.5);
call gshow;
r = { .50 .40 .30 };
cx = 40;
rsq = r##2;
call gopen;
call gset('height',3.2);
run threcirc(cx, cy, radius, rsq, vars, colors, patterns);
call gscript(22, 8,'X1, X2 Correlated',0,0,3.5);
call gshow;
quit;
%mend;
%ballantine(data=therapy, y=Therapy, x1=PersTest, x2=IntExt);