Hi George,

I know this is a late response, but I recently encountered the same quandary. Specifically, I wanted to create a simulation dataset, specifying the correlations between a dichotomous variable and two additional continuous variables. To do so, I ended up adapting the 'corr2data' macro found here: http://www.ats.ucla.edu/stat/sas/macros/corr2data.sas. If not for the dichotomous variable, this task would be much easier (see this blog for a really simple explanation: http://malaiseprecis.blogspot.com/2009/12/generating-correlated-random-variables.html). In any case, here's the code that I used:

*Goal is to create dataset with one dichotomous variable, A, and two continuous variables, B and C;

*First define the following variables:

1) P - proportion of '1s' for B

2) AB - correlation between A and B

3) AC - correlation between A and C

4) BC - correlation between B and C

5) N - desired number of cases in simulated dataset;

%let P = .50;

%let AB = .05;

%let AC = .44;

%let BC = .15;

%let N = 10000;

proc iml ;

C={1 &AB &AC, &AB 1 &BC, &AC &BC 1}; *setting up correlation matrix;

p = root(C); *using a Cholesky transformation;

dim = nrow(C);

A = j(&N,1,.); *setting up an initial vector for variable A to be filled later;

B = j(&N,1,.); *ditto for variable B;

C = j(&N,1,.); *ditto for variable C;

call randgen(A, 'BERNOULLI', &P); *filling vector A with random dichotomous data;

call randgen(B, 'NORMAL'); *filling vector B with random normally distributed data. You can specify the mean and variance by editing this line a bit;

call randgen(C, 'NORMAL'); *ditto for vector C;

myvar = A||B||C; *merging the three vectors into a single matrix;

do i = 1 to dim; *these are the steps that transform your data such that it has the correlation matrix that you specified;

myvar[, i] = myvar[,i]-(sum(myvar[,i])/&n);

end;

XX = (t(myvar)*myvar)/(&n-1);

U = root(inv(XX));

Y = myvar*T(U);

T = Y*p;

create outdata from T; *creates dataset, 'outdata';

append from T;

quit;

*by transforming the data in the above steps, the dichotomous variable is now a continuous bimodal variable. the steps below convert the bimodal variable back to a dichotomous variable and renames all of the variables to A, B, and C;

data outdata; set outdata;

if col10 then a=1;

b=col2;

c=col3;

drop col1-col3;

run;

Note that the proportions for A and the intercorrelations for AB and AC will not perfectly match what you specified, but they'll be close. There is likely a way to clean this up a bit, but I'll leave that to the real statisticians. Until then, hopefully this can be of help!

Paul

Thanks Paul for this very insightful piece of information.