ggdist: lkjcorr_marginal – R documentation

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lkjcorr_marginal

Marginal distribution of a single correlation from an LKJ distribution

Description

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

Usage

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).

Value

dlkjcorr_marginal gives the density
plkjcorr_marginal gives the cumulative distribution function (CDF)
qlkjcorr_marginal gives the quantile function (inverse CDF)
rlkjcorr_marginal generates random draws.

The length of the result is determined by n for rlkjcorr_marginal, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

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.

Examples

library(dplyr)
library(ggplot2)
library(forcats)

theme_set(theme_ggdist())

expand.grid(
  eta = 1:6,
  K = 2:6
) %>%
  ggplot(aes(y = fct_rev(ordered(eta)), dist = "lkjcorr_marginal", arg1 = K, arg2 = eta)) +
  stat_dist_slab() +
  facet_grid(~ paste0(K, "x", K)) +
  labs(
    title = paste0(
      "Marginal correlation for LKJ(eta) prior on different matrix sizes:\n",
      "dlkjcorr_marginal(K, eta)"
    ),
    subtitle = "Correlation matrix size (KxK)",
    y = "eta",
    x = "Marginal correlation"
  ) +
  theme(axis.title = element_text(hjust = 0))

ggdist

Visualizations of Distributions and Uncertainty

v2.4.0

GPL (>= 3)

Authors

Matthew Kay [aut, cre]

Initial release

2021-01-03