# Inefficiency factor in the OR2 model This function calculates the inefficiency factor from the MCMC draws of $(\beta, \sigma)$ in the OR2 model (ordinal quantile model with exactly 3 outcomes). The inefficiency factor is calculated using the batch-means method. ```r ineffactorOR2(x, betadraws, sigmadraws, accutoff, maxlags, verbose) ``` ## Arguments - `x`: covariate matrix of size $(n x k)$ including a column of ones with or without column names. This input is used to extract column names, if available, but not used in calculation. - `betadraws`: dataframe of the Gibbs draws of $\beta$, size $(k x nsim)$. - `sigmadraws`: dataframe of the Gibbs draws of $\sigma$, size $(1 x nsim)$. - `accutoff`: cut-off to identify the number of lags and form batches, default is 0.05. - `maxlags`: maximum lag at which to calculate the acf, default is 400. - `verbose`: whether to print the final output and provide additional information or not, default is TRUE. ## Returns Returns a column vector of inefficiency factors for each component of $\beta$ and $\sigma$. ## Details Calculates the inefficiency factor of $(\beta, \sigma)$ using the batch-means method based on the Gibbs draws. Inefficiency factor can be interpreted as the cost of working with correlated draws. A low inefficiency factor indicates better mixing and an efficient algorithm. ## 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 inefficiency <- ineffactorOR2(xMat, betadraws, sigmadraws, 0.5, 400, TRUE) # Summary of Inefficiency Factor: # Inef Factor # beta_1 1.5686 # beta_2 1.5240 # beta_3 1.4807 # sigma 2.4228 ``` ## References Greenberg, E. (2012). `"Introduction to Bayesian Econometrics."` Cambridge University Press, Cambridge. DOI: 10.1017/CBO9780511808920 Chib, S. (2012), `"Introduction to simulation and MCMC methods."` In Geweke J., Koop G., and Dijk, H.V., editors, `"The Oxford Handbook of Bayesian Econometrics"`, pages 183--218. Oxford University Press, Oxford. DOI: 10.1093/oxfordhb/9780199559084.013.0006 ## See Also pracma, acf

ineffactorOR2 function