lkjcorr_marginal: Marginal distribution of a single correlation from an LKJ...

Description Usage Arguments Details References See Also Examples

Description

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

Usage

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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.

See Also

parse_dist and marginalize_lkjcorr for parsing specs that use the LKJ correlation distribution and the stat_dist_slabinterval family of stats for visualizing them.

Examples

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library(dplyr)
library(ggplot2)

data.frame(prior = "lkjcorr_marginal(2, 3)") %>%
  parse_dist(prior) %>%
  ggplot(aes(y = prior, dist = .dist, args = .args)) +
  stat_dist_halfeyeh() +
  xlim(-1, 1) +
  xlab("Marginal correlation for LKJ(3) prior on 2x2 correlation matrix")

mjskay/tidybayes documentation built on Oct. 18, 2019, 3:23 a.m.