Description Usage Arguments Details Author(s) References Examples

View source: R/distributions.r

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

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`x` |
Matrix to compute probability density for |

`eta` |
Parameter controlling shape of distribution |

`K` |
Dimension of correlation matrix |

`log` |
If |

`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

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