A construction of statistical inferences in geographically weighted univariate log-gamma regression

Log-gamma regression (LGR) is a non-linear regression model in which the response variable follows a log-gamma distribution. Previous studies have generally applied the two-parameter log-gamma distribution, consisting of shape and scale. This study extends the model by introducing an additional location parameter, forming a three-parameter log-gamma distribution. Since spatial heterogeneity often reduces the accuracy of conventional LGR, we propose the geographically weighted univariate log-gamma regression (GWULGR) to better account for spatial variation in the data. The objective of this study is to develop the GWULGR model, provide a statistical framework for its estimation and testing, and demonstrate its effectiveness through an application to regional life expectancy. The empirical results show that GWULGR provides a substantially better fit than the conventional LGR model, as reflected by a smaller corrected Akaike Information Criterion (AICc) value (162.4875 compared to 209.8250). These findings emphasize the importance of integrating spatial effects into log-gamma regression to capture local variation more accurately. Our approach involves:•Extending log-gamma regression into a three-parameter form.•Incorporating spatial effects using a geographically weighted regression (GWR) framework.•Evaluating model performance through an application to the 2023 life expectancy index across districts and cities in Sumatra.