Flexible Bayesian Quantile Regression in Ordinal Models

We propose an estimation technique for the flexible Bayesian quantile regression in ordinal (FBQROR) models --- an ordinal quantile regression where the error is assumed to follow a generalized asymmetric Laplace (GAL) distribution. The GAL distribution allows to fix specific quantiles while simultaneously letting the mode, skewness and tails to vary; a characteristic nonexistent in the asymmetric Laplace (AL) distribution since a single parameter defines both the quantile and the skewness. We also introduce the cumulative distribution function and the moment generating function of the GAL distribution. Our proposed algorithm for FBQROR model is illustrated in multiple simulation studies and implemented to analyze ordinal categorization of journals. Model comparison exhibit the practical utility of the proposed model.