Converting odds ratio to correlation
For K binary (Bernoulli) random variables X_1, ..., X_K, this function transforms the odds ratios measure of association O_ij between every pair (X_i, X_j) to the correlation C_ij where
C_ij = cov(X_i, X_j) / sqrt(var(X_i) * var(X_j))
and
O_ij = P(X_i = 1, X_j = 1) * P(X_i = 0, X_j = 0) / P(X_i = 1, X_j = 0) * P(X_i = 0, X_j = 1).
Odds2Corr(odds, marg.probs)
odds |
A K x K matrix where the i-th row and the j-th column represents the odds ratio O_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). |
The function return a list with the correlations and the pairwise probabilities.
corr |
A matrix of the same dimension as |
pair.proba |
A matrix of the same dimension as |
Thomas Suesse.
Maintainer: Johan Barthelemy johan@uow.edu.au.
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.
Corr2Odds for converting correlation to odds ratio.
# from Qaqish et al. (2012)
or <- matrix(c(Inf, 0.281, 2.214, 2.214,
0.281, Inf, 2.214, 2.214,
2.214, 2.214, Inf, 2.185,
2.214, 2.214, 2.185, Inf), nrow = 4, ncol = 4, byrow = TRUE)
rownames(or) <- colnames(or) <- c("Parent1", "Parent2", "Sibling1", "Sibling2")
# hypothetical marginal probabilities
p <- c(0.2, 0.4, 0.6, 0.8)
# converting odds ratio to correlation
corr <- Odds2Corr(odds = or, marg.probs = p)
print(corr)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.