Modified Ridge Estimator for Poisson Regression

Poisson regression is a statistical model used to model the relationship between a count-valued-dependent variable and one or more independent variables. A frequently encountered problem when modeling such relationships is multicollinearity, which occurs when the independent variables are highly correlated with each other. Multicollinearity can affect the maximum likelihood (ML) estimates of unknown model parameters, making them unstable and inaccurate. In this study, we propose a modified ridge parameter estimator to combat multicollinearity in Poisson regression. We conducted extensive simulations to evaluate the performance of our proposed estimator using the mean squared error (MSE). We also apply our estimator to real data. The results show that our proposed estimator outperforms the ML estimator in both simulations and real data applications.