Odds2PairProbs {mipfp} | R Documentation |
Converting odds ratio to pairwise probability
Description
For binary (Bernoulli) random variables
, ...,
, this function transforms the odds ratios
measure of association
between every pair
to the pairwise probability
, where
is
defined as
Usage
Odds2PairProbs(odds, marg.probs)
Arguments
odds |
A |
marg.probs |
A vector with |
Value
A matrix of the same dimension as odds
containing the pairwise
probabilities
Note
If we denote by
, and
by
, then it
can be shown that
Author(s)
Thomas Suesse.
Maintainer: Johan Barthelemy johan@uow.edu.au.
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
Corr2PairProbs
for converting the
correlation to pairwise probability.
Examples
# 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)
# getting the pairwise probabilities
pp <- Odds2PairProbs(odds = or, marg.probs = p)
print(pp)