# Covariate effect in the OR1 model This function computes the average covariate effect for different outcomes of the OR1 model at a specified quantile. The covariate effects are calculated marginally of the parameters and the remaining covariates. ```r covEffectOR1(modelOR1, y, xMat1, xMat2, p, verbose) ``` ## Arguments - `modelOR1`: output from the quantregOR1 function. - `y`: observed ordinal outcomes, column vector of size $(n x 1)$. - `xMat1`: covariate matrix of size $(n x k)$ including a column of ones with or without column names. If the covariate of interest is continuous, then the column for the covariate of interest remains unchanged (xMat1 = x). If it is an indicator variable then replace the column for the covariate of interest with a column of zeros. - `xMat2`: covariate matrix x with suitable modification to an independent variable including a column of ones with or without column names. If the covariate of interest is continuous, then add the incremental change to each observation in the column for the covariate of interest. If the covariate is an indicator variable, then replace the column for the covariate of interest with a column of ones. - `p`: quantile level or skewness parameter, p in (0,1). - `verbose`: whether to print the final output and provide additional information or not, default is TRUE. ## Returns Returns a list with components: - **`avgDiffProb`:**: vector with change in predicted probability for each outcome category. ## Details This function computes the average covariate effect for different outcomes of the OR1 model at a specified quantile. The covariate effects are computed, using the MCMC draws, marginally of the parameters and the remaining covariates. ## Examples ```r set.seed(101) data("data25j4") y <- data25j4$y xMat1 <- data25j4$x k <- dim(xMat1)[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) modelOR1 <- quantregOR1(y = y, x = xMat1, b0, B0, d0, D0, burn = 10, mcmc = 40, p = 0.25, tune = 1, accutoff = 0.5, maxlags = 400, verbose = FALSE) xMat2 <- xMat1 xMat2[,3] <- xMat2[,3] + 0.02 res <- covEffectOR1(modelOR1, y, xMat1, xMat2, p = 0.25, verbose = TRUE) # Summary of Covariate Effect: # Covariate Effect # Category_1 -0.0072 # Category_2 -0.0012 # Category_3 -0.0009 # Category_4 0.0093 ``` ## References Rahman, M. A. (2016). `"Bayesian Quantile Regression for Ordinal Models."` Bayesian Analysis, 11(1): 1-24. DOI: 10.1214/15-BA939 Jeliazkov, I., Graves, J., and Kutzbach, M. (2008). `"Fitting and Comparison of Models for Multivariate Ordinal Outcomes."` Advances in Econometrics: Bayesian Econometrics, 23: 115`-`156. DOI: 10.1016/S0731-9053(08)23004-5 Jeliazkov, I. and Rahman, M. A. (2012). `"Binary and Ordinal Data Analysis in Economics: Modeling and Estimation"` in Mathematical Modeling with Multidisciplinary Applications, edited by X.S. Yang, 123-150. John Wiley `&` Sons Inc, Hoboken, New Jersey. DOI: 10.1002/9781118462706.ch6

covEffectOR1 function