Odds2Corr: Converting odds ratio to correlation

In mipfp: Multidimensional Iterative Proportional Fitting and Alternative Models

Description

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).

Usage

Odds2Corr(odds, marg.probs)

Arguments

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).

Value

The function return a list with the correlations and the pairwise probabilities.

corr	A matrix of the same dimension as odds containing the correlations
pair.proba	A matrix of the same dimension as odds 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

Corr2Odds for converting correlation to odds ratio.

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)

# converting odds ratio to correlation
corr <- Odds2Corr(odds = or, marg.probs = p)
print(corr)

Example output

Loading required package: cmm
Loading required package: Rsolnp
Loading required package: numDeriv
$corr
            Parent1    Parent2  Sibling1  Sibling2
Parent1   1.0000000 -0.2156821 0.1445775 0.1076353
Parent2  -0.2156821  1.0000000 0.1847014 0.1445775
Sibling1  0.1445775  0.1847014 1.0000000 0.1563619
Sibling2  0.1076353  0.1445775 0.1563619 1.0000000

$pair.proba
            Parent1    Parent2  Sibling1  Sibling2
Parent1  0.20000000 0.03773512 0.1483313 0.1772216
Parent2  0.03773512 0.40000000 0.2843283 0.3483313
Sibling1 0.14833129 0.28432833 0.6000000 0.5106405
Sibling2 0.17722164 0.34833129 0.5106405 0.8000000

mipfp documentation built on May 2, 2019, 6:01 a.m.