Academia Open
Vol 10 No 1 (2025): June (In Progress)
Computer Science

Statistical Study for the Estimators of Bayesian Analysis and Generalized Least Squares Method for the Parameters of the Multilevel Regression Model
Kajian Statistik untuk Estimator Analisis Bayesian dan Metode Kuadrat Terkecil Tergeneralisasi untuk Parameter Model Regresi Multilevel


View Article
  • Ali M. Ali*,
  • Basheer Jameel Khaleel
Ali M. Ali
Collage of Administration and Economic, Al Mustansiriyah University, Iraq *
Basheer Jameel Khaleel
Ministry of Education , Iraq

(*) Corresponding Author
Picture in here are illustration from public domain image or provided by the author, as part of their works
DOI: https://doi.org/10.21070/acopen.10.2025.10488
Published January 17, 2025
Keywords
  • Multilevel Regression,
  • Bayesian Analysis,
  • Generalized Least Squares,
  • AIC,
  • BIC
How to Cite
Ali, A. M., & Khaleel , B. J. (2025). Statistical Study for the Estimators of Bayesian Analysis and Generalized Least Squares Method for the Parameters of the Multilevel Regression Model. Academia Open, 10(1), 10.21070/acopen.10.2025.10488. https://doi.org/10.21070/acopen.10.2025.10488

Copyright (c) 2025 Ali M. Ali, Basheer Jameel Khaleel

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In this research, we dealt with the multilevel linear regression model, which is one of the most important models widely used and applied in analyzing data that is characterized by the fact that the observations in it take a hierarchical form. Two different methods were also applied to estimate the model parameters, namely the general least squares method and Bayesian analysis. A comparison was made between them and which is better in the estimation process through the Akaike information criterion and the Bayesian information criterion. It was found that the Bayesian analysis method is the most efficient in the estimation process. The Bayesian analysis method is the best method for estimating the parameters of a multilevel model (with two levels) for PMRM-2 panel data in general for any type of regression models for panel data and for different sample sizes. The method maintained the preference for estimation by adopting the AIC and BIC measures. This means that the Bayesian analysis method can be adopted for estimation in the applied aspect when estimating the parameters of a multilevel model (with two levels) for PMRM-2 panel data, such as wheat data in Some governorates of Iraq, according to the available time series extending from 2000 - 2021.

Highlights:

  1. Multilevel regression applied for hierarchical data with two-level structure.
  2. Bayesian analysis outperformed generalized least squares using AIC and BIC measures.
  3. Study analyzed wheat data (2000–2021) in Iraq governorates effectively.

Keywords: Multilevel Regression, Bayesian Analysis, Generalized Least Squares, AIC, BIC

View Article

Downloads

Download data is not yet available.

References

  1. . E. Aarts et al., "A Solution to Dependency: Using Multilevel Analysis to Accommodate Nested Data," Nature Neuroscience, vol. 17, no. 4, 2014.
  2. . M. R. Abonazel, "Generalized Estimators of Stationary Random-Coefficients Panel Data Models: Asymptotic and Small Sample Properties," REVSTAT – Statistical Journal, vol. 17, no. 4, pp. 493–521, Oct. 2019.
  3. . J. M. K. Aheto and G. A. Dagne, "Multilevel Modeling, Prevalence, and Predictors of Hypertension in Ghana: Evidence From Wave 2 of the World Health Organization’s Study on Global AGEing and Adult Health," Health Science Reports, vol. 4, p. e453, 2021.
  4. . A. D. Al-Nasser, O. M. Eidous, and L. M. Mohaidat, "Multilevel Linear Models Analysis Using Generalized Maximum Entropy," Asian Journal of Mathematics and Statistics, vol. 3, no. 2, pp. 111–118, 2010.
  5. . A. D. Al-Nasser, "Multilevel Linear Models Analysis Using Generalized Maximum Entropy," presented at MTISD, University of Salento, Lecce, 18–20 Jun. 2008.
  6. . J. Antonakis, N. Bastardoz, and M. Rönkkö, "On Ignoring the Random Effects Assumption in Multilevel Models: Review, Criticism, and Recommendations," Organizational Research Methods, vol. 24, no. 2, pp. 443–483, 2021.
  7. . M. M. Asadullah and M. M. Husian, "The Effect of Sample Size on Random Component in Multilevel Modeling," European Journal of Statistics, vol. 2, p. 7, 2022.
  8. . T. Asparouhov and B. Muthén, "Bayesian Estimation of Single and Multilevel Models With Latent Variable Interactions," Structural Equation Modeling: A Multidisciplinary Journal, vol. 27, no. 3, pp. 1–22, 2020, doi: 10.1080/10705511.2020.1761808.