Utility functions for the PC prior for a correlation matrix

Functions to evaluate and sample from the PC prior for a correlation matrix.

The parameterisation of a correlation matrix of dimension p has dim parameters: theta which are in the interval -pi to pi. The alternative parameterisation is through the off-diagonal elements r of the correlation matrix R. The functions inla.pc.cormat.<A>2<B> convert between parameterisations <A> to parameterisations <B>, where both <A> and <B> are one of theta, r and R, and p and dim.

inla.pc.cormat.dim2p(dim)

inla.pc.cormat.p2dim(p)

inla.pc.cormat.theta2R(theta)

inla.pc.cormat.R2theta(R)

inla.pc.cormat.r2R(r)

inla.pc.cormat.R2r(R)

inla.pc.cormat.r2theta(r)

inla.pc.cormat.theta2r(theta)

inla.pc.cormat.permute(R)

inla.pc.cormat.rtheta(n = 1, p, lambda = 1)

inla.pc.cormat.dtheta(theta, lambda = 1, log = FALSE)

Arguments

dim: The dimension of theta, the parameterisatin of the correlation matrix
p: The dimension the correlation matrix
theta: A vector of parameters for the correlation matrix
R: A correlation matrix
r: The off diagonal elements of a correlation matrix
n: Number of observations
lambda: The rate parameter in the prior
log: Logical. Return the density in natural or log-scale.

Value

inla.pc.cormat.rtheta generate samples from the prior, returning a matrix where each row is a sample of theta. inla.pc.cormat.dtheta evaluates the density of theta. inla.pc.cormat.permute randomly permutes a correlation matrix, which is useful if an exchangable sample of a correlation matrix is required.

Author

Havard Rue hrue@r-inla.org

Examples


  p = 4
  print(paste("theta has length", inla.pc.cormat.p2dim(p)))
#> [1] "theta has length 6"
  theta = inla.pc.cormat.rtheta(n=1, p=4, lambda = 1)
  print("sample theta:")
#> [1] "sample theta:"
  print(theta)
#>          [,1]    [,2]     [,3]     [,4]     [,5]     [,6]
#> [1,] 1.517243 1.61125 1.521007 1.552252 1.538682 1.651778
  print(paste("log.dens", inla.pc.cormat.dtheta(theta, log=TRUE)))
#> [1] "log.dens 8.02815372418386"
  print("r:")
#> [1] "r:"
  r = inla.pc.cormat.theta2r(theta)
  print(r)
#> [1]  0.05352802 -0.04044307  0.04976899  0.01633623  0.03468732 -0.08208997
  print("A sample from the non-exchangable prior, R:")
#> [1] "A sample from the non-exchangable prior, R:"
  R = inla.pc.cormat.r2R(r)
  print(R)
#>             [,1]       [,2]        [,3]        [,4]
#> [1,]  1.00000000 0.05352802 -0.04044307  0.04976899
#> [2,]  0.05352802 1.00000000  0.01633623  0.03468732
#> [3,] -0.04044307 0.01633623  1.00000000 -0.08208997
#> [4,]  0.04976899 0.03468732 -0.08208997  1.00000000
  print("A sample from the exchangable prior, R:")
#> [1] "A sample from the exchangable prior, R:"
  R = inla.pc.cormat.permute(R)
  print(R)
#>             [,1]        [,2]        [,3]        [,4]
#> [1,]  1.00000000  0.04976899  0.03468732 -0.04044307
#> [2,]  0.04976899  1.00000000 -0.08208997  0.01633623
#> [3,]  0.03468732 -0.08208997  1.00000000  0.05352802
#> [4,] -0.04044307  0.01633623  0.05352802  1.00000000