Corr2Odds: Converting correlation to odds ratio

In mipfp: Multidimensional Iterative Proportional Fitting and Alternative Models

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 odds ratio O_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

Corr2Odds(corr, marg.probs)

Arguments

corr	A K x 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

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

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

Corr2Odds for converting correlation to odds ratio.

Examples

# correlation matrix from Qaqish et al. (2012)
cr <- 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(cr) <- colnames(cr) <- c("Parent1", "Parent2", "Sibling1", "Sibling2")

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

# converting correlation to odds ratio and getting pairwise probabilities
or <- Corr2Odds(corr = cr, marg.probs = p)
print(or)

Example output

Loading required package: cmm
Loading required package: Rsolnp
Loading required package: numDeriv
$odds
           Parent1   Parent2 Sibling1 Sibling2
Parent1        Inf 0.2824182 2.206206 2.201278
Parent2  0.2824182       Inf 2.206989 2.206206
Sibling1 2.2062060 2.2069892      Inf 2.181030
Sibling2 2.2012775 2.2062060 2.181030      Inf

$pair.proba
            Parent1    Parent2  Sibling1  Sibling2
Parent1  0.20000000 0.03786878 0.1482181 0.1771200
Parent2  0.03786878 0.40000000 0.2841600 0.3482181
Sibling1 0.14821812 0.28416000 0.6000000 0.5105696
Sibling2 0.17712000 0.34821812 0.5105696 0.8000000

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