From: Ashraf Chaudhary <mchaudha_at_jhsph.edu>

Date: Sun 17 Apr 2005 - 06:46:07 EST

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Apr 17 06:54:48 2005

Date: Sun 17 Apr 2005 - 06:46:07 EST

X <- rnorm(100) Y <- rnorm(100) r<- 0.7 Y1 <- X*r+Y*sqrt(1-r**2) cor(X,Y1) # Correlated normals using Cholesky decompositioncor(X>0.84,Y1) # Method I

##

X1 <- rbinom(100,1,0.5)

Y2 <- X1*r+Y*sqrt(1-r**2)

cor(X1,Y2); # Method II

I would like to thank Ben from whom I received the following response:

"Are you computing the correlation between the continuous variable and the dichotomized variable with the formula for the biserial correlation? If not, that is probably the root of your problem."

I looked at the biserial correlation which is a special case of Pearson correlation between a continuous and binomial random variable. I don't know how I can use it to generate the data. Any idea?

Regards,

Ashraf

-----Original Message-----

From: Ted Harding [mailto:Ted.Harding@nessie.mcc.ac.uk]
Sent: Saturday, April 16, 2005 3:22 AM

To: Ashraf Chaudhary

Cc: r-help@stat.math.ethz.ch

Subject: RE: [R] Generating a binomial random variable correlated with a

On 15-Apr-05 Ashraf Chaudhary wrote:

*> Hi,
*

> I am posting this problem again (with some additional detail)

*> as I am stuck and could not get it resolved as yet. I tried to
**> look up in alternative sources but with no success. Here it is:
**>
**> I need to generate a binomial (binary 0/1) random variable linearly
**> correlated with a normal random variable with a specified correlation.
**> Off course, the correlation coefficient would not be same at each run
**> because of randomness.
**>
**> If I generate two correlated normals with specified correlation and
**> dichotomize one, the correlation of a normal and the binomial random
**> variable would not be the same as specified.
**>
**> I greatly appreciate your help.
**> Ashraf
*

Hello Ashraf,

I do not know what you mean by "a binomial random variable linearly correlated with a normal random variable." You can certainly (and indeed your dichotomy method is one way) generate a binomial and a normal which are correlated. But apparently this gives a result which is "not the same as specified": however, I cannot see in your description a specification which would violated by the result of doing so.

You cannot expect a binomial variable to be such that, for instance, its expectation conditional on the value of a normal variable would be a linear function of the normal variable, since this would allow a situation where the expectation was greater than 1 or less than 0. But I wonder what else you could possibly mean by "linearly correlated".

Please therefore be more explicit about the specification of your problem!

Trying to help,

Ted.

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

Date: 16-Apr-05 Time: 08:21:42 ------------------------------ XFMail ------------------------------ ______________________________________________R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Apr 17 06:54:48 2005

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