lkjcorr_marginal: Marginal distribution of a single correlation from an LKJ... In mjskay/tidybayes: Tidy Data and 'Geoms' for Bayesian Models

Description

Marginal distribution for the correlation in a single cell from a correlation matrix distributed according to an LKJ distribution.

Usage

 1 2 3 4 5 6 7 dlkjcorr_marginal(x, K, eta, log = FALSE) plkjcorr_marginal(q, K, eta, lower.tail = TRUE, log.p = FALSE) qlkjcorr_marginal(p, K, eta, lower.tail = TRUE, log.p = FALSE) rlkjcorr_marginal(n, K, eta)

Arguments

 x vector of quantiles. K Dimension of the correlation matrix. Must be greater than or equal to 2. eta Parameter controlling the shape of the distribution log logical; if TRUE, probabilities p are given as log(p). q vector of quantiles. lower.tail logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. log.p logical; if TRUE, probabilities p are given as log(p). p vector of probabilities. n number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The LKJ distribution is a distribution over correlation matrices with a single parameter, eta. For a given eta and a KxK correlation matrix R:

R ~ LKJ(eta)

Each off-diagonal entry of R, r[i,j]: i != j, has the following marginal distribution (Lewandowski, Kurowicka, and Joe 2009):

(r[i,j] + 1)/2 ~ Beta(eta - 1 + K/2, eta - 1 + K/2)

In other words, r[i,j] is marginally distributed according to the above Beta distribution scaled into (-1,1).

References

Lewandowski, D., Kurowicka, D., & Joe, H. (2009). Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis, 100(9), 1989–2001. doi: 10.1016/j.jmva.2009.04.008.