mipfp (version 3.2.3)

Corr2PairProbs: 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)

Value

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

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 \(P(X_i = 1)\).

Author

Thomas Suesse.

Maintainer: Johan Barthelemy .

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)