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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

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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: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, volume 40, pages 211-251, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-90532019000040b011
    DOI: 10.1108/S0731-90532019000040B011
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    Citations

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    Cited by:

    1. Yu-Zhu Tian & Man-Lai Tang & Wai-Sum Chan & Mao-Zai Tian, 2021. "Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings," Computational Statistics, Springer, vol. 36(2), pages 1289-1319, June.
    2. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    3. Arjun Gupta & Soudeh Mirghasemi & Mohammad Arshad Rahman, 2021. "Heterogeneity in food expenditure among US families: evidence from longitudinal quantile regression," Indian Economic Review, Springer, vol. 56(1), pages 25-48, June.
    4. Mohit Batham & Soudeh Mirghasemi & Mohammad Arshad Rahman & Manini Ojha, 2021. "Modeling and Analysis of Discrete Response Data: Applications to Public Opinion on Marijuana Legalization in the United States," Papers 2109.10122, arXiv.org, revised May 2023.

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