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Last data update: 2014.03.03

R: Generating a multivariate Bernoulli joint-distribution

ObtainMultBinaryDist

R Documentation

Generating a multivariate Bernoulli joint-distribution

Description

This function applies the IPFP procedure to obtain a joint distribution of K multivariate binary (Bernoulli) variables X_1, ..., X_K.

It requires as input the odds ratio or alternatively the correlation as a measure of association between all the binary variables and a vector of marginal probabilities.

This function is useful when one wants to simulate and draw from a multivariate binary distribution when only first order (marginal probabilities) and second order moments (correlation or odds ratio) are available.

Usage

ObtainMultBinaryDist(odds = NULL, corr = NULL, marg.probs, ...)

Arguments

`odds`	A K x K matrix where the i-th row and the j-th column represents the Odds ratio between variables i and j. Must be provided if `corr` is not.
`corr`	A K x K matrix where the i-th row and the j-th column represents the correlation between variables i and j. Must be provided if `odds` is not.
`marg.probs`	A vector with K elements of marginal probabilities where the i-th entry refers to P(X_i = 1).
`...`	Additional arguments that can be passed to the `Ipfp` function such as `tol`, `iter`, `print` and `compute.cov`.

Value

A list whose elements are mainly determined by the Ipfp function.

`joint.proba`	The resulting multivariate joint-probabilities (from `Ipfp`).
`stp.crit`	The final value of the `Ipfp` stopping criterion.
`conv`	Boolean indicating whether the `Ipfp` algorithm converged to a solution.
`check.margins`	A list returning, for each margin, the absolute maximum deviation between the desired and generated margin. Ideally the elements should approximate 0 (from `Ipfp`).
`label`	The names of the variables.

Note

It is important to note that either the odds ratio defined in odds or the correlations described in corr must be provided.

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.

Examples

# initial odds ratios 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)

# estimating the joint-distribution
p.joint <- ObtainMultBinaryDist(odds = or, corr = NULL, marg.probs = p)
print(p.joint$joint.proba)

# obtain identical solution when providing correlation
corr <- Odds2Corr(odds = or, marg.probs = p)$corr
p.joint.alt <- ObtainMultBinaryDist(corr = corr, marg.probs = p)

# checking if the results are truly identicals
diff <- sum(abs(p.joint.alt$joint.proba - p.joint$joint.proba))
cat('Sum of the absolute deviations: ', diff, '\n')