The gamma regression model explores the relationship between a skewed response variable and one or more independent variables. The method of maximum likelihood is popularly adopted to model the relationship. However, the method performance drops when linear dependency exists among the predictors (multicollinearity). In this article, we develop a new method to account for multicollinearity in gamma regression model. The proposed estimator theoretically dominates the existing estimators. The simulation studies and real-life application supports the theoretical findings.

Poisson regression model has been popularly used to model count data. However, over-dispersion is a threat to the performance of the Poisson regression model. The Bell Regression Model (BRM) is an alternative means of modelling count data with over-dispersion. Conventionally, the parameters in BRM is popularly estimated using the Method of Maximum Likelihood (MML). Multicollinearity posed challenge on the efficiency of MML. In this study, we developed a new estimator to overcome the problem of multicollinearity. The theoretical, simulation and application results were in favor of this new method.