This study compares the performance of link functions for diagnostic methods to diagnose influential observations in the Gamma-Pareto regression model (G-PRM). Three link functions, i.e. inverse, identity, and log are considered to identify which link function gives the best results. For our investigation, we employed standardized deviance residuals (SDR) and adjusted deviance residuals (ADR). We used Cook’s distance (CD) and Difference of fit (DIFFITS) as diagnostic methods. We compare the performance of influence diagnostics with the link functions using the simulation study and a real-life application. Results show that the CD with the log link function is a good method for small dispersion. For large dispersion and small sample sizes, the performance of the DIFFITS with inverse and identity link functions is better than the CD method. Similarly, for large dispersion and sample sizes, the CD (with identity and log link functions) and DFFITS with inverse link function give the same performance.