International Journal of Nonlinear Analysis and Applications

The Bayesian Lasso of quantile structural equation model

Articles in Press

Document Type : Research Paper

Authors

1 Technical College of Management, Middle Technical University, Baghdad, Iraq

2 College of Administration and Economics, Department of Statistics, University of Baghdad, Baghdad, Iraq

Abstract

Structural equation models have been extensively applied to medical and social sciences, the most important latent variable models are structural equation models. Structural equation modelling (SEM) is a popular multivariate technique for analyzing the interrelationships between latent variables. In general, structural equation models include a measurement equation to characterize latent variables through multiple observable variables and a mean regression-type structural equation to investigate how the explanatory latent variables affect the outcomes of interest. In this study, we apply Bayesian least absolute shrinkage and selection operator (Lasso) procedure to conduct estimation in the Quantile SEM, and compare this estimator with estimator of Bayesian Quantile Structural equation model, and apply the use of the Markov chain Monte Carlo (MCMC) method by Gibbs sampler to conduct Bayesian inference. The simulation was implemented assuming different distributions of the error term for the structural equations model and values of the parameters for a small sample size.

[1] R. Alhamzawi, Model selection in quantile regression models, J. Appl. Stat. 42 (2015), no. 2, 445–458.
[2] D.F. Andrews and C.L. Mallows, Scale mixtures of normal distributions, J. Royal Stat. Soc.: Ser. B Method. 36 (1974), no. 1, 99–102.
[3] X. Feng, Y. Wang, B. Lub, and X. Song, Bayesian regularized quantile structural equation models, J. Multivariate Anal. 154 (2017), 234–248.
[4] R. Koenker and G. Bassett Jr., Regression quantiles, Econ.: J. Econ. Soc. 46 (1978), no. 1, 33–50.
[5] I. Komujer, Quasi-maximum likelihood estimation for conditional quantiles, J. Econ. 128 (2005), 137–164.
[6] H. Kozumi and G. Kobayashi, Gibbs sampling methods for Bayesian quantile regression, J. Stat. Comput. Simulat. 81 (2011), no. 11, 1565–1578.
[7] Q. Li, R. Xi, and N. Lin, Bayesian regularized quantile regression, Bayesian Anal. 5 (2010), 533–556.
[8] Y. Li and J. Zhu, L1-norm quantile regression, J. Comput. Graph. Statist. 17 (2008), no. 1, 163–185.
[9] T. Park and G. Casella, The Bayesian lasso, J. Amer. Statist. Assoc. 103 (2008), 681–686.
[10] X.Y. Song and S.Y. Lee, Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences, John Wiley and Sons, 2012.
[11] R. Tibshirani, Regression shrinkage and selection via the lasso, J. Royal Stat. Soc. Ser. B: Statist. Method. 58 (1996), no. 1, 267–288.
[12] Y. Wang, X.-N. Feng, and X.-Y. Song, Bayesian quantile structural equation models, Structural Equ. Model.: Multidiscip. J. 23 (2016), no. 2, 246–258.
[13] K. Yu and R.A. Moyeed, Bayesian quantile regression, Statist. Prob. Lett. 54 (2001), 437–447.
[14] A. Zellner, An Introduction to Bayesian Inference in Econometrics, John Wiley and Sons, New York, 1971.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 29 April 2025
  • Receive Date: 15 November 2021
  • Revise Date: 20 December 2021
  • Accept Date: 29 January 2022