Corr2PairProbs {mipfp}

Converting correlation to pairwise probability

Description

For K binary (Bernoulli) random variables X_1, ..., X_K, this function transforms the correlation measure of association C_{ij} between every pair (X_i, X_j) to the pairwise probability P(X_i = 1, X_j = 1), where C_{ij} is defined as

C_{ij} = \frac{cov(X_i, X_j)}{\sqrt(var(X_i) * var(X_j))}.

Usage

Corr2PairProbs(corr, marg.probs)

Arguments

corr

A K \times K matrix where the i-th row and the j-th column represents the correlation C_{ij} between variables i and j.

marg.probs

A vector with K elements of marginal probabilities where the i-th entry refers to P(X_i = 1).

Value

A matrix of the same dimension as corr containing the pairwise probabilities

Author(s)

Thomas Suesse.

Maintainer: Johan Barthelemy [e-mail].

References

Lee, A.J. (1993). Generating Random Binary Deviates Having Fixed Marginal Distributions and Specified Degrees of Association The American Statistician 47 (3): 209-215.

Qaqish, B. F., Zink, R. C., and Preisser, J. S. (2012). Orthogonalized residuals for estimation of marginally specified association parameters in multivariate binary data. Scandinavian Journal of Statistics 39, 515-527.

See Also

Odds2PairProbs for converting odds ratio to pairwise probability.

Examples

# correlation matrix from Qaqish et al. (2012)
corr <- matrix(c( 1.000, -0.215, 0.144, 0.107,
                 -0.215,  1.000, 0.184, 0.144,
                  0.144,  0.184, 1.000, 0.156,
                  0.107,  0.144, 0.156, 1.000), 
                  nrow = 4, ncol = 4, byrow = TRUE)
rownames(corr) <- colnames(corr) <- c("Parent1", "Parent2", "Sibling1", 
                                      "Sibling2")

# hypothetical marginal probabilities
p <- c(0.2, 0.4, 0.6, 0.8)

# getting the pairwise probabilities
pp <- Corr2PairProbs(cor = corr, marg.probs = p)
print(pp)