(untitled) (Statistics, Optimization & Information Computing, 2025)
The diagnosing of influence is essential to assist in detecting influential observations, which influences the inference, especially estimation of the model. Classical diagnostic tools like Cooks Distance and DFFITS are well established and it is possible that less appropriate in model complexities or under different dispersion conditions of data. In the current paper, a novel effort to advance the area of influence diagnostics to the Gamma regression models (GRM) is proposed to utilize the metaheuristic approach as called the Secretary Bird Optimization Algorithm (SBOA). To compare the GRM detection ability of TC and MRE of Cook s Distance and DFFITS and the SBOA based SMOX approach, we run an extensive simulation study across sample sizes and dispersion parameters. The results of the simulations prove that the Cook Distance and the DFFITS are reliable but SBOA-ameliorated diagnostic scheme perform better to detect influential cases particularly in high dispersion scenarios and a limited to moderate samples. Viewed through compared analysis, it can be said SBOA offers a more thorough detection mechanism.