Simulate phi-coefficient

From: "Bliese, Paul D LTC USAMH" <paul.bliese at us.army.mil>

Given a sample of zeros and ones, for example:

VECTOR1<-rep(c(1,0),c(15,10))

How would I create a new sample (VECTOR2) also containing zeros and
ones, in which the phi-coefficient between the two sample vectors was
drawn from a population with a known phi-coefficient value?

I know there are ways to do this with normally distributed numbers (for
example the mvrnorm function in MASS), but am stumped when dealing with
dichotomous variables.

Paul

One way is to sample from the 2x2 table with the specified means and pearson
correlation (phi):

for a fourfold table, a b
                      c d
with marginal proportions p1 and p2
cov <- phi * sqrt(p1*(1-p1)*p2*(1-p2))
a <- p1*p2 + cov
b <- p1*(1-p2) - cov
c <- (1-p1)*p2 - cov
d <- (1-p1)*(1-p2) + cov
expand.grid(0:1,0:1)[sample(1:4, size=25, replace=TRUE, prob=c(a,b,c,d)),]

David.

| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v