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Flexible Bayesian Quantile Regression in Ordinal Models

In: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B

Author

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  • Mohammad Arshad Rahman
  • Shubham Karnawat

Abstract

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.

Suggested Citation

  • Mohammad Arshad Rahman & Shubham Karnawat, 2019. "Flexible Bayesian Quantile Regression in Ordinal Models," Advances in Econometrics, in: Ivan Jeliazkov & Justin L. Tobias (ed.),Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, volume 40, pages 211-251, Emerald Publishing Ltd.
  • Handle: RePEc:eme:aecozz:s0731-90532019000040b011
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    Cited by:

    1. Arjun Gupta & Soudeh Mirghasemi & Mohammad Arshad Rahman, 2020. "Heterogeneity in Food Expenditure amongst US families: Evidence from Longitudinal Quantile Regression," Papers 2010.02614, arXiv.org.

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