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

## Description

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

## Usage

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

## Arguments

 `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

## Details

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.

## Author(s)

Richard McElreath

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 ) ```

rmcelreath/rethinking documentation built on May 1, 2020, 5:10 p.m.