For univariate density plots, you can plot the density for an LKJ prior for 2x2 correlation matrices, or marginal plots of LKJ priors for larger correlation matrices. Below are examples.

```
library(tidyverse)
theme_set(theme_bw() +
theme(plot.title=element_text(size=rel(1), hjust=0.5)))
library(ggdist)
# Plot LKJ Density
lkj_dfunc = function(K, etas=c(0.1, 0.5, 1, 1.5, 2, 5)) {
etas = set_names(etas)
cor = seq(-1,1,length=200)
etas %>%
map_df(
~ dlkjcorr_marginal(cor, K=K, eta=.x)
) %>%
bind_cols(x=cor) %>%
pivot_longer(cols=-x, names_to='eta', values_to='density') %>%
ggplot(aes(x=x, y=density)) +
geom_area(colour=hcl(240,100,30), fill=hcl(240,100,65)) +
facet_wrap(vars(eta)) +
scale_y_continuous(expand=expansion(c(0,0.05))) +
coord_cartesian(ylim=c(0,2)) +
labs(title=paste0(ifelse(K==2, "", "Marginal "),
"LKJ correlation distribution for K=", K,
" and various values of eta"),
x="Correlation")
}
lkj_dfunc(2)
```

```
lkj_dfunc(5)
```

```
# Plot density of random draws from LKJ distribution
lkj_rfunc = function(K, N=1000, etas=c(0.1, 0.5, 1, 1.5, 2, 5)) {
etas = set_names(etas)
etas %>%
map_df(
~ rlkjcorr_marginal(N, K=K, eta=.x)
) %>%
pivot_longer(cols=everything(), names_to='eta', values_to='corr') %>%
ggplot(aes(x=corr)) +
geom_density(colour=hcl(240,100,30), fill=hcl(240,100,65)) +
facet_wrap(vars(eta)) +
scale_y_continuous(expand=expansion(c(0,0.05))) +
labs(title=paste0(ifelse(K==2, "D", "Marginal d"),
"ensity of random draws from LKJ distribution for K=", K,
" and various values of eta"),
x="Correlation")
}
lkj_rfunc(2)
```

```
lkj_rfunc(5)
```

^{Created on 2021-08-14 by the reprex package (v2.0.1)}