drawsigmaOR2 {bqror}

Samples \sigma in the OR2 model

Description

This function samples \sigma from an inverse-gamma distribution in the OR2 model (ordinal quantile model with exactly 3 outcomes).

Usage

drawsigmaOR2(z, x, beta, nu, tau2, theta, n0, d0)

Arguments

z

Gibbs draw of continuous latent values, a column vector of size n x 1.

x

covariate matrix of size (n x k) including a column of ones with or without column names.

beta

Gibbs draw of \beta, a column vector of size (k x 1).

nu

modified latent weight, column vector of size (n x 1).

tau2

2/(p(1-p)).

theta

(1-2p)/(p(1-p)).

n0

prior hyper-parameter for \sigma.

d0

prior hyper-parameter for \sigma.

Details

This function samples \sigma from an inverse-gamma distribution.

Value

Returns a list with components

sigma:

\sigma, a scalar, sampled from an inverse gamma distribution.

dtilde:

scale parameter of the inverse-gamma distribution.

References

Rahman, M. A. (2016). '"Bayesian Quantile Regression for Ordinal Models."' Bayesian Analysis, 11(1): 1-24. DOI: 10.1214/15-BA939

Devroye, L. (2014). '"Random variate generation for the generalized inverse Gaussian distribution."' Statistics and Computing, 24(2): 239'-'246. DOI: 10.1007/s11222-012-9367-z

See Also

rgamma, Gibbs sampling

Examples

set.seed(101)
z <- c(21.01744, 33.54702, 33.09195, -3.677646,
 21.06553, 1.490476, 0.9618205, -6.743081, 21.02186, 0.6950479)
x <- matrix(c(
     1, -0.3010490, 0.8012506,
     1,  1.2764036, 0.4658184,
     1,  0.6595495, 1.7563655,
     1, -1.5024607, -0.8251381,
     1, -0.9733585, 0.2980610,
     1, -0.2869895, -1.0130274,
     1,  0.3101613, -1.6260663,
     1, -0.7736152, -1.4987616,
     1,  0.9961420, 1.2965952,
     1, -1.1372480, 1.7537353),
     nrow = 10, ncol = 3, byrow = TRUE)
beta <- c(-0.74441, 1.364846, 0.7159231)
n <- dim(x)[1]
nu <- array(5 * rep(1,n), dim = c(n, 1))
tau2 <- 10.6667
theta <- 2.6667
n0 <- 5
d0 <- 8
output <- drawsigmaOR2(z, x, beta, nu, tau2, theta, n0, d0)

# output$sigma
#   3.749524