# 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.

`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.
 ```1 2 3 4 5 6 7 8 9``` ```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") ```