# [R] Simulate phi-coefficient (correlation between dichotomous vars)

David Duffy David.Duffy at qimr.edu.au
Tue Sep 27 23:38:49 CEST 2005

```On Tue, 27 Sep 2005, Bliese, Paul D LTC USAMH wrote:
> My situation is a bit more complicated and I'm not sure it is easily
> solved.  The problem is that I must assume one of the vectors is
> constant and generate one or more vectors that covary with the constant
> vector.
>
>> 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
>

Calculate the conditional probabilities from the above

P(X2=1|X1=1)= a/(a+b) = p2 + cov/p1
P(X2=1|X1=0)= c/(c+d) = p2 - cov/(1-p1)

condsim <- function(X, phi, p2, p1=NULL) {
if (!all(X %in% c(0,1))) stop("expecting 1's and 0's")
if (is.null(p1)) p1 <- mean(X)
covar <- phi  * sqrt(p1*(1-p1)*p2*(1-p2))
if (covar>0 && covar>(min(p1,p2)-p1*p2)) {
warning("Specified correlation too large for given marginal proportions")
covar <- min(p1,p2)-p1*p2
}else if (covar<0 && covar < -min(p1*p2,(1-p1)*(1-p2))) {
warning("Specified correlation too small for given marginal proportions")
covar <- -min(p1*p2,(1-p1)*(1-p2))
}
Y <- X
i1 <- X==1
i0 <- X==0
Y[i1] <- rbinom(sum(i1),1, p2 + covar/p1)
Y[i0] <- rbinom(sum(i0),1, p2 - covar/(1-p1))
data.frame(X,Y)
}

David Duffy.

```

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