correl: Build the correlation matrix parametrized from the hypershere...

In graphpcor: Models for Correlation Matrices Based on Graphs

Build the correlation matrix parametrized from the hypershere decomposition, see details.

Description

Build the correlation matrix parametrized from the hypershere decomposition, see details.

Usage

theta2correl(theta, fromR = TRUE)

theta2gamma2L(theta, fromR = TRUE)

rcorrel(p, lambda)

Arguments

theta	numeric vector with length equal n(n-1)/2
fromR	logical indicating if theta is in R. If FALSE, assumes \theta[k] \in (0, pi).
p	integer to specify the matrix dimension
lambda	numeric as the penalization parameter. If missing it will be assumed equal to zero. The lambda=0 case means no penalization and a random correlation matrix will be drawn. Please see section 6.2 of the PC-prior paper, Simpson et. al. (2017), for details.

Details

The hypershere decomposition, as proposed in Rapisarda, Brigo and Mercurio (2007) consider \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 compute x[k] = pi/(1+exp(-theta[k])) organize it as a lower triangle of a n \times n matrix

| cos(x[i,j]) , j=1

B[i,j] = | cos(x[i,j])prod_{k=1}^{j-1}sin(x[i,k]), 2 <= j <= i-1

| prod_{k=1}^{j-1}sin(x[i,k]) , j=i

| 0 , j+1 <= j <= n

Result

\gamma[i,j] = -log(sin(x[i,j]))

KLD(R) = \sqrt(2\sum_{i=2}^n\sum_{j=1}^{i-1} \gamma[i,j]

Value

a correlation matrix

Lower triangular n x n matrix

Functions

• theta2gamma2L(): Build a lower triangular matrix from a parameter vector. See details.

• rcorrel(): Drawn a random sample correlation matrix

References

Rapisarda, Brigo and Mercurio (2007). Parameterizing correlations: a geometric interpretation. IMA Journal of Management Mathematics (2007) 18, 55-73. <doi 10.1093/imaman/dpl010>

Simspon et. al. (2017). Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statist. Sci. 32(1): 1-28 (February 2017). <doi: 10.1214/16-STS576>

graphpcor documentation built on June 8, 2025, 10:37 a.m.