A Poisson ridge regression estimator

The standard statistical method for analyzing count data is the Poisson regression model, which is usually estimated using maximum likelihood (ML) method. The ML method is very sensitive to multicollinearity. Therefore, we present a new Poisson ridge regression estimator (PRR) as a remedy to the problem of instability of the traditional ML method. To investigate the performance of the PRR and the traditional ML approaches for estimating the parameters of the Poisson regression model, we calculate the mean squared error (MSE) using Monte Carlo simulations. The result from the simulation study shows that the PRR method outperforms the traditional ML estimator in all of the different situations evaluated in this paper.

Research Highlights► Multicollinearity leads to instable maximum likelihood estimates of Poisson regression models. ► To reduce the instability we propose a ridge regression estimator. ► We also propose some methods of estimating the ridge parameter. ► Using Monte Carlo simulations we show that the ridge regression estimator reduces the instability. ► We also show in the simulation study the optimal way of estimating the ridge parameter.