# Deviance Information Criterion in the OR2 model Function for computing the DIC in the OR2 model (ordinal quantile model with exactly 3 outcomes). ```r 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). ## Returns Returns a list with components $$ DIC = 2*avgdeviance - dev $$ $$ pd = avgdeviance - dev $$ $$ dev = -2*(logLikelihood) $$ . ## 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. ## Examples ```r 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 ``` ## 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

dicOR2 function