A New Ridge Estimator for the Poisson Regression Model

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The Poisson regression model is a well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the Poisson regression coefficients. To address this problem, a Poisson ridge regression model has been proposed by numerous researchers. In this paper, a new Poisson ridge estimator (NPRRM) is proposed and derived. The idea behind the NPRRM is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter, and therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NPRRM estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NPRRM estimator outperforms both Poisson ridge regression and maximum likelihood estimators in terms of predictive performance.