dlkjcorr: LKJ correlation matrix probability density
In joepowers16/rethinking: Statistical Rethinking book package

Description Usage Arguments Details Author(s) References Examples

Functions for computing density and producing random samples from the LKJ onion method correlation matrix distribution.

1 2	dlkjcorr( x , eta=1 , log=TRUE ) rlkjcorr( n , K , eta=1 )

`x`	Matrix to compute probability density for
`eta`	Parameter controlling shape of distribution
`K`	Dimension of correlation matrix
`log`	If `TRUE`, returns log-probability instead of probability
`n`	Number of random matrices to sample

The LKJ correlation matrix distribution is based upon work by Lewandowski, Kurowicka, and Joe. When the parameter eta is equal to 1, it defines a flat distribution of correlation matrices. When eta > 1, the distribution is instead concentrated towards to identity matrix. When eta < 1, the distribution is more concentrated towards extreme correlations at -1 or +1.

It can be easier to understand this distribution if we recognize that the individual correlations within the matrix follow a beta distribution defined on -1 to +1. Thus eta resembles theta in the beta parameterization with a mean p and scale (sample size) theta.

The function rlkjcorr returns an 3-dimensional array in which the first dimension indexes matrices. In the event that n=1, it returns instead a single matrix.

Richard McElreath

Lewandowski, Kurowicka, and Joe. 2009. Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis. 100:1989-2001.

Stan Modeling Language User's Guide and Reference Manual, v2.6.2

R <- rlkjcorr(n=1,K=2,eta=4)
dlkjcorr(R,4)

# plot density of correlation
R <- rlkjcorr(1e4,K=2,eta=4)
dens( R[,1,2] )

# visualize 3x3 matrix
R <- rlkjcorr(1e3,K=3,eta=2)
plot( R[,1,2] , R[,1,3] , col=col.alpha("black",0.2) , pch=16 )