drawbetaOR2 {bqror}

Samples \beta in the OR2 model

Description

This function samples \beta from its conditional posterior distribution in the OR2 model (ordinal quantile model with exactly 3 outcomes).

Usage

drawbetaOR2(z, x, sigma, nu, tau2, theta, invB0, invB0b0)

Arguments

z

continuous latent values, vector of size (n x 1).

x

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

sigma

\sigma, a scalar value.

nu

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

tau2

2/(p(1-p)).

theta

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

invB0

inverse of prior covariance matrix of normal distribution.

invB0b0

prior mean pre-multiplied by invB0.

Details

This function samples \beta, a vector, from its conditional posterior distribution which is an updated multivariate normal distribution.

Value

Returns a list with components

beta:

\beta, a column vector of size (k x 1), sampled from its condtional posterior distribution.

Btilde:

variance parameter for the posterior multivariate normal distribution.

btilde:

mean parameter for the posterior multivariate normal distribution.

References

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

See Also

Gibbs sampling, normal distribution , rgig, inv

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)
sigma <- 1.809417
n <- dim(x)[1]
nu <- array(5 * rep(1,n), dim = c(n, 1))
tau2 <- 10.6667
theta <- 2.6667
invB0 <- matrix(c(
     1, 0, 0,
     0, 1, 0,
     0, 0, 1),
     nrow = 3, ncol = 3, byrow = TRUE)
invB0b0 <- c(0, 0, 0)

output <- drawbetaOR2(z, x, sigma, nu, tau2, theta, invB0, invB0b0)

# output$beta
#   -0.74441 1.364846 0.7159231