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This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.

The paper presents a general approach to modeling and estimating time series models with discrete outcomes, where the errors are autoregressive and lagged dependence may be present in either the observed discrete outcomes or a latent dependent variable. Within such a general framework, estimation is challenging due to the high dimensionality of the latent variable and strong correlation in Markov chain Monte Carlo (MCMC) draws. To address these estimation issues, the paper introduces efficient MCMC algorithms that employ a novel blocking technique for sampling the latent variable. The importance of modeling autoregressive errors is demonstrated by comparing these models with counterparts that assume independent errors. The performance of the proposed algorithms is evaluated through multiple simulation studies, and the advantages of the proposed models are illustrated in an application to US business cycles.

This article develops a random effects quantile regression model for panel data that allows for increased distributional flexibility, multivariate heterogeneity, and time-invariant covariates in situations where mean regression may be unsuitable. Our approach is Bayesian and builds upon the generalized asymmetric Laplace distribution to decouple the modeling of skewness from the quantile parameter. We derive two efficient simulation-based estimation algorithms, demonstrate their properties and performance in targeted simulation studies, and employ them in the computation of marginal likelihoods to enable formal Bayesian model comparisons. The methodology is applied in a study of U.S. residential rental rates following the Global Financial Crisis. Our empirical results provide interesting insights on the interaction between rents and economic, demographic and policy variables, weigh in on key modeling features, and overwhelmingly support the additional flexibility at all quantiles and across several sub-samples. The practical differences that arise as a result of allowing for flexible modeling can be nontrivial, especially for quantiles away from the median.