# Deviance Information Criterion in the OR1 model Function for computing the Deviance Information Criterion (DIC) in the OR1 model (ordinal quantile model with 3 or more outcomes). ```r dicOR1(y, x, betadraws, deltadraws, postMeanbeta, postMeandelta, 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 $(k x nsim)$. - `deltadraws`: dataframe of the MCMC draws of $\delta$, size is $((J-2) x nsim)$. - `postMeanbeta`: posterior mean of the MCMC draws of $\beta$. - `postMeandelta`: posterior mean of the MCMC draws of $\delta$. - `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 $$ DIC = 2*avgdDeviance - dev $$ $$ pd = avgdDeviance - dev $$ $$ dev = -2*(logLikelihood) $$ . ## 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("data25j4") y <- data25j4$y xMat <- data25j4$x k <- dim(xMat)[2] J <- dim(as.array(unique(y)))[1] b0 <- array(rep(0, k), dim = c(k, 1)) B0 <- 10*diag(k) d0 <- array(0, dim = c(J-2, 1)) D0 <- 0.25*diag(J - 2) output <- quantregOR1(y = y, x = xMat, b0, B0, d0, D0, burn = 10, mcmc = 40, p = 0.25, tune = 1, accutoff = 0.5, maxlags = 400, verbose = FALSE) mcmc <- 40 deltadraws <- output$deltadraws betadraws <- output$betadraws burn <- 0.25*mcmc nsim <- burn + mcmc postMeanbeta <- output$postMeanbeta postMeandelta <- output$postMeandelta dic <- dicOR1(y, xMat, betadraws, deltadraws, postMeanbeta, postMeandelta, burn, mcmc, p = 0.25) # DIC # 1375.329 # pd # 139.1751 # dev # 1096.979 ``` ## 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

dicOR1 function