Modified ridge-type for the Poisson regression model: simulation and application

The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood estimator (PMLE). There is a tendency that the explanatory variables grow together, which results in the problem of multicollinearity. The variance of the PMLE becomes inflated in the presence of multicollinearity. The Poisson ridge regression (PRRE) and Liu estimator (PLE) have been suggested as an alternative to the PMLE. However, in this study, we propose a new estimator to estimate the regression coefficients for the PRM when multicollinearity is a challenge. We perform a simulation study under different specifications to assess the performance of the new estimator and the existing ones. The performance was evaluated using the scalar mean square error criterion and the mean squared error prediction error. The aircraft damage data was adopted for the application study and the estimators' performance judged by the SMSE and the mean squared prediction error. The theoretical comparison shows that the proposed estimator outperforms other estimators. This is further supported by the simulation study and the application result.

Automated summary

A new estimator is proposed in this study to estimate the regression coefficients for the Poisson regression model when multicollinearity is a challenge. The theoretical comparison, simulation study, and application results demonstrate that the proposed estimator outperforms other estimators in terms of performance.