dicOR2 {bqror}

Deviance Information Criterion in the OR2 model

Description

Function for computing the DIC in the OR2 model (ordinal quantile model with exactly 3 outcomes).

Usage

dicOR2(y, x, betadraws, sigmadraws, gammacp, postMeanbeta,
postMeansigma, burn, mcmc, 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.

betadraws

dataframe of the MCMC draws of \beta, size is (k x nsim).

sigmadraws

dataframe of the MCMC draws of \sigma, size is (nsim x 1).

gammacp

row vector of cut-points including -Inf and Inf.

postMeanbeta

posterior mean of the MCMC draws of \beta.

postMeansigma

posterior mean of the MCMC draws of \sigma.

burn

number of burn-in MCMC iterations.

mcmc

number of MCMC iterations, post burn-in.

p

quantile level or skewness parameter, p in (0,1).

Details

Deviance is -2*(log likelihood) and has an important role in statistical model comparison because of its relation with Kullback-Leibler information criterion.

This function provides the DIC, which can be used to compare two or more models at the same quantile. The model with a lower DIC provides a better fit.

Value

Returns a list with components

DIC = 2*avgdeviance - dev

pd = avgdeviance - dev

dev = -2*(logLikelihood)

.

References

Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Linde, A. (2002). '"Bayesian Measures of Model Complexity and Fit."' Journal of the Royal Statistical Society B, Part 4: 583-639. DOI: 10.1111/1467-9868.00353

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. '"Bayesian Data Analysis."' 2nd Edition, Chapman and Hall. DOI: 10.1002/sim.1856

See Also

decision criteria

Examples

set.seed(101)
data("data25j3")
y <- data25j3$y
xMat <- data25j3$x
k <- dim(xMat)[2]
b0 <- array(rep(0, k), dim = c(k, 1))
B0 <- 10*diag(k)
n0 <- 5
d0 <- 8
output <- quantregOR2(y = y, x = xMat, b0, B0, n0, d0, gammacp2 = 3,
burn = 10, mcmc = 40, p = 0.25, accutoff = 0.5, maxlags = 400, verbose = FALSE)
betadraws <- output$betadraws
sigmadraws <- output$sigmadraws
gammacp <- c(-Inf, 0, 3, Inf)
postMeanbeta <- output$postMeanbeta
postMeansigma <- output$postMeansigma
mcmc = 40
burn <- 10
nsim <- burn + mcmc
dic <- dicOR2(y, xMat, betadraws, sigmadraws, gammacp,
postMeanbeta, postMeansigma, burn, mcmc, p = 0.25)

# DIC
#   801.8191
# pd
#   6.608594
# dev
#   788.6019