Utility functions for the PC prior for a correlation matrix

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

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

The off diagonal elements of a correlation matrix

R

A correlation matrix

n

Number of observations

lambda

The rate parameter in the prior

log

Logical. Return the density in natural or log-scale.

Details

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.

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,] 1.723156 1.777821 1.898138 1.781326 2.02427 1.421615
print(paste("log.dens", inla.pc.cormat.dtheta(theta, log=TRUE)))
#> [1] "log.dens -0.929410740343662"
print("r:")
#> [1] "r:"
r = inla.pc.cormat.theta2r(theta)
print(r)
#> [1] -0.1517706 -0.2055492 -0.3215266 -0.1709504 -0.3612244  0.2720060
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,]  1.0000000 -0.1517706 -0.2055492 -0.3215266
#> [2,] -0.1517706  1.0000000 -0.1709504 -0.3612244
#> [3,] -0.2055492 -0.1709504  1.0000000  0.2720060
#> [4,] -0.3215266 -0.3612244  0.2720060  1.0000000
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,]  1.0000000 -0.1517706  0.2720060 -0.1709504
#> [2,] -0.1517706  1.0000000 -0.3215266 -0.2055492
#> [3,]  0.2720060 -0.3215266  1.0000000 -0.3612244
#> [4,] -0.1709504 -0.2055492 -0.3612244  1.0000000