A semiparametric Bayesian approach for joint-quantile regression with clustered data |
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Affiliation: | 1. SAS Institute Inc., 100 SAS Campus Drive, Cary, NC 27513, United States;2. Department of Statistics, George Washington University, Washington, DC, 20052, United States;1. Department of Economics, Business and Statistics, University of Palermo, Italy;2. Department of Political Sciences, University of Pisa, Italy |
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Abstract: | Based on a semiparametric Bayesian framework, a joint-quantile regression method is developed for analyzing clustered data, where random effects are included to accommodate the intra-cluster dependence. Instead of posing any parametric distributional assumptions on the random errors, the proposed method approximates the central density by linearly interpolating the conditional quantile functions of the response at multiple quantiles and estimates the tail densities by adopting extreme value theory. Through joint-quantile modeling, the proposed algorithm can yield the joint posterior distribution of quantile coefficients at multiple quantiles and meanwhile avoid the quantile crossing issue. The finite sample performance of the proposed method is assessed through a simulation study and the analysis of an apnea duration data. |
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Keywords: | Generalized Pareto distribution Markov chain Monte Carlo Mixed model Quantile regression Random effects |
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