# Samples $\delta$ in the OR1 model This function samples the cut-point vector $\delta$ using a random-walk Metropolis-Hastings algorithm in the OR1 model (ordinal quantile model with 3 or more outcomes). ```r drawdeltaOR1(y, x, beta, delta0, d0, D0, tune, Dhat, p) ``` ## Arguments - `y`: observed ordinal outcomes, 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 $\beta$, column vector of size $(k x 1)$. - `delta0`: initial value for $\delta$. - `d0`: prior mean for $\delta$. - `D0`: prior covariance matrix for $\delta$. - `tune`: tuning parameter to adjust MH acceptance rate. - `Dhat`: negative inverse Hessian from maximization of log-likelihood. - `p`: quantile level or skewness parameter, p in (0,1). ## Returns Returns a list with components - **`deltaReturn`:**: $\delta$, a column vector of size $((J-2) x 1)$, sampled using MH algorithm. - **`accept`:**: indicator for acceptance of the proposed value of $\delta$. ## Details Samples the cut-point vector $\delta$ using a random-walk Metropolis-Hastings algorithm. ## Examples ```r set.seed(101) data("data25j4") y <- data25j4$y xMat <- data25j4$x p <- 0.25 beta <- c(0.3990094, 0.8168991, 2.8034963) delta0 <- c(-0.9026915, -2.2488833) d0 <- matrix(c(0, 0), nrow = 2, ncol = 1, byrow = TRUE) D0 <- matrix(c(0.25, 0.00, 0.00, 0.25), nrow = 2, ncol = 2, byrow = TRUE) tune <- 0.1 Dhat <- matrix(c(0.046612180, -0.001954257, -0.001954257, 0.083066204), nrow = 2, ncol = 2, byrow = TRUE) p <- 0.25 output <- drawdeltaOR1(y, xMat, beta, delta0, d0, D0, tune, Dhat, p) # deltareturn # -0.9025802 -2.229514 # accept # 1 ``` ## References Rahman, M. A. (2016). `"Bayesian Quantile Regression for Ordinal Models."` Bayesian Analysis, 11(1): 1-24. DOI: 10.1214/15-BA939 Chib, S., and Greenberg, E. (1995). `"Understanding the Metropolis-Hastings Algorithm."` The American Statistician, 49(4): 327-335. DOI: 10.2307/2684568 Jeliazkov, I., and Rahman, M. A. (2012). `"Binary and Ordinal Data Analysis in Economics: Modeling and Estimation"` in Mathematical Modeling with Multidisciplinary Applications, edited by X.S. Yang, 123-150. John Wiley & Sons Inc, Hoboken, New Jersey. DOI: 10.1002/9781118462706.ch6 ## See Also NPflow, Gibbs sampling, mvnpdf

drawdeltaOR1 function