# Turn spec for LKJ distribution into spec for marginal LKJ distribution

Source:`R/lkjcorr_marginal.R`

`marginalize_lkjcorr.Rd`

Turns specs for an LKJ correlation matrix distribution as returned by
`parse_dist()`

into specs for the marginal distribution of
a single cell in an LKJ-distributed correlation matrix (i.e., `lkjcorr_marginal()`

).
Useful for visualizing prior correlations from LKJ distributions.

## Usage

```
marginalize_lkjcorr(
data,
K,
predicate = NULL,
dist = ".dist",
args = ".args",
dist_obj = ".dist_obj"
)
```

## Arguments

- data
A data frame containing a column with distribution names (

`".dist"`

by default) and a list column of distribution arguments (`".args"`

by default), such as output by`parse_dist()`

.- K
Dimension of the correlation matrix. Must be greater than or equal to 2.

- predicate
a bare expression for selecting the rows of

`data`

to modify. This is useful if`data`

contains more than one row with an LKJ prior in it and you only want to modify some of the distributions; if this is the case, give row a predicate expression that evaluates to`TRUE`

on the rows you want to modify. If`NULL`

(the default), all`lkjcorr`

distributions in`data`

are modified.- dist
The name of the column containing distribution names. See

`parse_dist()`

.- args
The name of the column containing distribution arguments. See

`parse_dist()`

.- dist_obj
The name of the column to contain a distributional object representing the distribution. See

`parse_dist()`

.

## Value

A data frame of the same size and column names as the input, with the `dist`

, and `args`

,
and `dist_obj`

columns modified on rows where `dist == "lkjcorr"`

such that they represent a
marginal LKJ correlation distribution with name `lkjcorr_marginal`

and `args`

having
`K`

equal to the input value of `K`

.

## Details

The LKJ(eta) prior on a correlation matrix induces a marginal prior on each correlation
in the matrix that depends on both the value of `eta`

*and* `K`

, the dimension
of the \(K \times K\) correlation matrix. Thus to visualize the marginal prior
on the correlations, it is necessary to specify the value of `K`

, which depends
on what your model specification looks like.

Given a data frame representing parsed distribution specifications (such
as returned by `parse_dist()`

), this function updates any rows with `.dist == "lkjcorr"`

so that the first argument to the distribution (stored in `.args`

) is equal to the specified dimension
of the correlation matrix (`K`

), changes the distribution name in `.dist`

to `"lkjcorr_marginal"`

,
and assigns a distributional object representing this distribution to `.dist_obj`

.
This allows the distribution to be easily visualized using the `stat_slabinterval()`

family of ggplot2 stats.

## Examples

```
library(dplyr)
library(ggplot2)
# Say we have an LKJ(3) prior on a 2x2 correlation matrix. We can visualize
# its marginal distribution as follows...
data.frame(prior = "lkjcorr(3)") %>%
parse_dist(prior) %>%
marginalize_lkjcorr(K = 2) %>%
ggplot(aes(y = prior, xdist = .dist_obj)) +
stat_halfeye() +
xlim(-1, 1) +
xlab("Marginal correlation for LKJ(3) prior on 2x2 correlation matrix")
# Say our prior list has multiple LKJ priors on correlation matrices
# of different sizes, we can supply a predicate expression to select
# only those rows we want to modify
data.frame(coef = c("a", "b"), prior = "lkjcorr(3)") %>%
parse_dist(prior) %>%
marginalize_lkjcorr(K = 2, coef == "a") %>%
marginalize_lkjcorr(K = 4, coef == "b")
#> coef prior .dist .args .dist_obj
#> 1 a lkjcorr(3) lkjcorr_marginal 2, 3 lkjcorr_marginal(2, 3)
#> 2 b lkjcorr(3) lkjcorr_marginal 4, 3 lkjcorr_marginal(4, 3)
```