R help - Apr 2005 - Generating a binomial random variable correlated with a normal random variable

Hi All:
I would like to generate a binomial random variable that correlates with a
normal random variables with a specified correlation. Off course, the
correlation coefficient would not be same at each run because of randomness.
I greatly appreciate your input.
Ashraf

On 03-Apr-05 Ashraf Chaudhary wrote:
> Hi All:
> I would like to generate a binomial random variable that
> correlates with a normal random variables with a specified
> correlation. Off course, the correlation coefficient would
> not be same at each run because of randomness.
> I greatly appreciate your input.
> Ashraf
It's not at all clear what you mean by this. For example,
are you seeking:

A) X (continuous) and R (discrete, distributed on (0,n))
   are such that the marginal distribution of X is normal,
   the marginal distribution of R is binomial, and the
   correlation coefficient between X and R is specified?

B) Given X, R on (0,n) has a binomial distribution with
   probability parameter p which depends on X?

C) For each of n values of X, R is binary (0,1) with
   P[R=1] depending on X, such that sum(R from 1 to n)
   has a binomial distribution, and the correlation
   between X and R is specified?

And so on.

Also, it is not obvious what interpretation to put on
the correlation coefficient between a discrete variable
and a continuous variable.

How large is the "n" parameter in the binomial distribution
intended to be?

It would help if you described what you are really looking
for in much more explicit detail!

Bestg wishes,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 04-Apr-05                                       Time: 09:03:29
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one idea is to consider that the underlying (for ease normally 
distributed) latent variables that produce the Bernoulli trials are 
correlated with your original normal random variable.

I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat/
     http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Ashraf Chaudhary" <mchaudha at jhsph.edu>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, April 04, 2005 12:41 AM
Subject: [R] Generating a binomial random variable correlated with a 
normalrandom variable

> Hi All:
> I would like to generate a binomial random variable that correlates 
> with a
> normal random variables with a specified correlation. Off course, 
> the
> correlation coefficient would not be same at each run because of 
> randomness.
> I greatly appreciate your input.
> Ashraf
>
> ______________________________________________
> R-help at 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
>

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

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 at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 16-Apr-05                                       Time: 08:21:42
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