1d:T762,# Samples $\beta$ in the OR1 model This function samples $\beta$ from its conditional posterior distribution in the OR1 model (ordinal quantile model with 3 or more outcomes). ```r drawbetaOR1(z, x, w, 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. - `w`: latent weights, column vector of size 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) data("data25j4") xMat <- data25j4$x p <- 0.25 n <- dim(xMat)[1] k <- dim(xMat)[2] w <- array( (abs(rnorm(n, mean = 2, sd = 1))), dim = c (n, 1)) theta <- 2.666667 tau2 <- 10.66667 z <- array( (rnorm(n, mean = 0, sd = 1)), dim = c(n, 1)) b0 <- array(0, dim = c(k, 1)) B0 <- diag(k) invB0 <- matrix(c( 1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3, ncol = 3, byrow = TRUE) invB0b0 <- invB0 %*% b0 output <- drawbetaOR1(z, xMat, w, tau2, theta, invB0, invB0b0) # output$beta # -0.2481837 0.7837995 -3.4680418 ``` ## 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, mvrnorm , inv

drawbetaOR1 function