The College of Administration and Economics at the University of Baghdad discussed, a PhD dissertation in field of Statistics by the student (Luay Adil Abduljabbar ) and tagged with (Influence Diagnostics in Gamma Regression Model Using Hybrid Meta-heuristic Algorithm ) , Under supervision of (Prof. Dr. Sabah Manfi Ridha )
The existence of influential observations is an important issue in statistical modelling as it adversely affects the precision of parameter estimates, model adequacy and statistical inference. In Gamma Regression Models (GRM), inappropriate treatment of these observations often leads to biased estimates and unreliable conclusions. This dissertation aims to develop an efficient and robust diagnostic framework for detecting and treating influential observations in the GRM. To achieve this, a novel metaheuristic algorithm, named the Hybrid Secretary–Osprey Optimization Algorithm (HSOOA), is proposed by integrating the global exploration capability of the Secretary Bird Optimization Algorithm (SBOA) with the local exploitation strategy of the Osprey Optimization Algorithm (OOA). To enhance estimation accuracy without removing critical data, the proposed optimization framework is incorporated into a robust M-estimation procedure utilizing a newly developed dynamic weighting function, to bound the severe impact of influential points.
The methodology was comprehensively evaluated through an extensive Monte Carlo simulation study under various sample sizes (n=50, 100, 200, and 500), numbers of explanatory variables (p=1, 3, and 7), and Gamma shape parameters (v=0.75, 1, 2, and 5).
In the practical application, the proposed framework was used to estimate the parameters of the model based on real medical data collected from the Iraqi Ministry of Health / Medical City / Baghdad Teaching Hospital, which consisted of 200 observations of Fasting Blood Glucose (FBG) concentrations adopting the optimal methodology identified in the simulation study. The empirical results show the high efficiency of the proposed framework as it succeeded in identifying 18 influential observations and reducing their severe impact efficiently. The robust treatment resulted in a significant decrease in MSE values and a considerable improvement in the stability and accuracy of the Gamma Regression Model parameter estimates. These results suggest promising opportunities for the extension of this hybrid optimization framework to other Generalized Linear Models (GLMs).
