# Samples $\beta$ in the OR2 model This function samples $\beta$ from its conditional posterior distribution in the OR2 model (ordinal quantile model with exactly 3 outcomes). ```r 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. ## Returns 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. ## Details This function samples $\beta$, a vector, from its conditional posterior distribution which is an updated multivariate normal 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) 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 ``` ## 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

drawbetaOR2 function