A Comparison of Some Link Functions for Gamma-Pareto Regression Models: Simulation and Applications

The Gamma-Pareto Regression Model (G-PRM) is a suitable statistical approach for analyzing continuous and discrete response variables. The G-PRM is analyzed using Generalized Linear Models (GLM) through designated link functions. Three standard link functions, inverse, identity, and log, are investigated under the Akaike Information Criterion, Bayesian Information Criterion, and R² and adjusted R² statistical indicators. Simulations and the ARDENNES data (Biopsy) are used to evaluate the G-PRM with various link functions. Based on AIC, BIC, R², and adjusted R² assessments, the identity link outperforms the inverse and log links in analyzing ARDENNES data and simulation datasets. This research develops a novel technique for best model selection, evaluated through various sample size scenarios and dispersion levels, confirming the suitability of the identity link function.