Developing a Bayesian technique employing a posterior based on mode to estimate parameters in multiple linear regression   : simulation study

Bekhal Samad Sedeeq; Hogr Mohammed Qader; Dashty Ismail Jamil

doi:10.25212/lfu.qzj.9.1.54

Authors

Bekhal Samad Sedeeq Department of Statistics and Informatics, College of Administration and Economics, University of Salahaddin, Erbil, Kurdistan Region, Iraq
Hogr Mohammed Qader Paytakht technical institute- private - Erbil, Kurdistan Region, Iraq
Dashty Ismail Jamil Department of Marketing, College of Administration and Economics, Lebanese French University, Kurdistan Region, Iraq

DOI:

https://doi.org/10.25212/lfu.qzj.9.1.54

Keywords:

Multiple Linear Model, Bayesian approach, posterior, OLS, RMSE.

Abstract

The process of estimating the parameters of regression is still one of the most important. Despite the large number of papers and studies written on this subject, these studies differ in the techniques followed in the process of estimation, whether they are classic or Bayesian. In this study, we developed a Bayesian technique employing a posterior-based mode to estimate parameters in multiple linear regression. The best multiple linear regression model for the data may be obtained based on the mean squared error after comparing the Bayesian posterior based on mode and the traditional method (ordinary least squares) by combining simulated and real data with a MATLAB program made especially for this purpose. The study finds that, compared to the traditional approach, the Bayesian posterior based on mode approach yields more accurate parameter estimates and In terms of the RMSE statistical criterion, the best results for estimating the multiple linear regression model

Downloads

Download data is not yet available.

References

- Box, G.E.P, & Tiao, G. (1992): "Bayesian Inference in Statistical Analysis", John Wiley & Sons, New York.

- Chang, T. & Eaves, D. M. (1992): "Posterior Mode Estimation for the Generalized Linear Model" Annals Institute of Statistical Mathematics, Vol. 44, No. 3, pp. 417 – 434.

- Chib, S., Griffiths, W., Koop, G. & Terrell, D. (2008): "Bayesian Econometrics" Howard House, Wagon Lane, Bingley BD16 1WA, UK.

- D.M. Saleh, D. H. Kadir and D. I. Jamil (2023). A Comparison between Some Penalized Methods for Estimating Parameters: Simulation Study. QALAAI ZANIST JOURNAL, 8(1), 1122–1134. https://doi.org/10.25212/lfu.qzj.8.1.44

- Geweke J. (2005): "Contemporary Bayesian Econometrics and Statistics" John Wiley & Sons, Inc.

- Goldstein, M., (1976): "Bayesian Analysis of Regression Problems", Biometrika, Vol.63, No.1, P.51-58.

- Koop, G. (2003): "Bayesian Econometrics" John Wiley & Sons Ltd.

- Lindley, D.V. & Smith, A. F. M. (1972): "Bayes Estimation for Linear Model and Distribution", Journal of Royal Statistical Society, Ser. B, Vol. 43, No.1, P.1-41.

- Martz, H. F. & Krutchkoff, R.G. (1969): "Empirical Bayes Estimation in a Multiple Linear Regression Model", Biometrika, Vol .56, No.2. P.367.

- O'Hagan, A. (1973): "Bayes Estimation of Convex Quadratic" Biometrika, Vol. 60, No.3. PP. 565-571.

- Oman, S. D. (1978): "A Bayesian Comparesion of Some Used in Linear Regression with Multicollinear Data", Communications in Statistics: Theory and Method, Vol. 7, No. 6, P.517-534.

- Philippe G, Alain D. and Mylene B., (2020) “A New Bayesian Approach to Robustness Against Outliers in Linear Regression” International Society for Bayesian Analysis (2020). pp. 389–414.

- Raftery, E., Maigan, D. & Hoeting, J.A. (1997): "Bayesian Model Averaging for Linear Regression Model", Jasa, Vol.75, No.327, P.801-816.

- Rousseeuw, P. J., & Leroy, A. M. (1987). Robust regression and outlier detection (Vol. 1): Wiley Online Library.

- Shelemyahu Zacks, (1971): "The Theory of Statistical Inference", John Wiley and sons, Inc, Case Westen Reserve University.

- T. H. Ali & D. M., Salah (2021). COMPARISON BETWEEN WAVELET BAYESIAN AND BAYESIAN ESTIMATORS TO REMEDY CONTAMINATION IN LINEAR REGRESSION MODEL. PalArch’s Journal of Archaeology of Egypt/ Egyptology, 18(10), 3388-3409. Retrieved from https://archives.palarch.nl/index.php/jae/article/view/10382.

- T. H., Ali & D. M. Salah (2022), Proposed Hybrid Method for Wavelet Shrinkage with Robust Multiple Linear Regression Model With Simulation Study, QALAAI ZANISTSCIENTIFIC JOURNAL A Scientific Quarterly Refereed Journal Issued by Lebanese French University – Erbil, Kurdistan, Iraq, Vol. (7), No (1), Winter 2022 ISSN 2518-6566 (Online) - ISSN 2518-6558 (Print), Doi:10.25212/lfu.qzj.7.1.36.

- Zellner, A. (1971): "An Introduction to Bayesian Inference in Econometrics", John Wiley and Sons, Inc.

- S. A. Obed, D. M. Saleh & D. I. Jamil. (2023). The Impact of Social Media Advertising on Customer Performance Using Logistic Regression Analysis. QALAAI ZANIST JOURNAL, 8(3), 1304–1324. https://doi.org/10.25212/lfu.qzj.8.3.54