# Samples $\sigma$ in the OR2 model This function samples $\sigma$ from an inverse-gamma distribution in the OR2 model (ordinal quantile model with exactly 3 outcomes). ```r 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 $\sigma$. ## Returns Returns a list with components - **`sigma`:**: $\sigma$, a scalar, sampled from an inverse gamma distribution. - **`dtilde`:**: scale parameter of the inverse-gamma distribution. ## Details This function samples $\sigma$ from an inverse-gamma distribution. ## Examples ```r 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 ``` ## 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

drawsigmaOR2 function