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 - Ali M. Ali; Basheer Jameel Khaleel (Academia Open, 2025)
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: Multilevel regression applied for hierarchical data with two-level structure. Bayesian analysis outperformed generalized least squares using AIC and BIC measures. Study analyzed wheat data (2000–2021) in Iraq governorates effectively. Keywords: Multilevel Regression, Bayesian Analysis, Generalized Least Squares, AIC, BIC