# Inefficiency factor in the OR1 model This function calculates the inefficiency factor from the MCMC draws of $(\beta, \delta)$ in the OR1 model (ordinal quantile model with 3 or more outcomes). The inefficiency factor is calculated using the batch-means method. ```r ineffactorOR1(x, betadraws, deltadraws, 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 MCMC draws of $\beta$, size $(k x nsim)$. - `deltadraws`: dataframe of the MCMC draws of $\delta$, size $((J-2) x nsim)$. - `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 $\delta$. ## Details Calculates the inefficiency factor of $(\beta, \delta)$ using the batch-means method based on MCMC 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("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) betadraws <- output$betadraws deltadraws <- output$deltadraws inefficiency <- ineffactorOR1(xMat, betadraws, deltadraws, 0.5, 400, TRUE) # Summary of Inefficiency Factor: # Inef Factor # beta_1 1.1008 # beta_2 3.0024 # beta_3 2.8543 # delta_1 3.6507 # delta_2 3.1784 ``` ## 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

ineffactorOR1 function