# drawnu_or2: Samples the scale factor nu for ordinal quantile model with 3... In bqror: Bayesian Quantile Regression for Ordinal Models

## Description

This function samples the ν from a generalized inverse Gaussian (GIG) distribution for ordinal quantile model with 3 outcomes.

## Usage

 `1` ```drawnu_or2(z, x, beta, sigma, tau2, theta, lambda) ```

## Arguments

 `z` Gibbs draw of latent response variable, a column vector. `x` covariate matrix of dimension (n x k) including a column of ones. `beta` Gibbs draw of coefficients of dimension (k x 1). `sigma` scale factor, a scalar. `tau2` 2/(p(1-p)). `theta` (1-2p)/(p(1-p)). `lambda` index parameter of GIG distribution which is equal to 0.5.

## Details

Function samples the ν from a GIG distribution.

## Value

Returns a row vector of the ν from GIG distribution.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```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) sigma <- 3.749524 tau2 <- 10.6667 theta <- 2.6667 lambda <- 0.5 output <- drawnu_or2(z, x, beta, sigma, tau2, theta, lambda) # output # 5.177456 4.042261 8.950365 # 1.578122 6.968687 1.031987 # 4.13306 0.4681557 5.109653 # 0.1725333 ```