Development of the generalized ridge estimator for the Poisson-Inverse Gaussian regression model with multicollinearity

The Poisson-Inverse Gaussian regression model is a widely used method for analyzing count data, particularly in over-dispersion. However, the reliability of parameter estimates obtained through maximum likelihood estimation in this model can be compromised when multicollinearity exists among the explanatory variables. Multicollinearity means that high correlations between explanatory variables inflate the variance of the maximum likelihood estimates and increase the mean squared error. To handle this problem, the Poisson-Inverse Gaussian ridge regression estimator has been proposed as a viable alternative. This paper introduces a generalized ridge estimator to estimate regression coefficients in the Poisson-Inverse Gaussian regression model under multicollinearity. The performance of the proposed estimator is evaluated through a comprehensive simulation study, covering various scenarios and employing the mean squared error as the evaluation criterion. Furthermore, the practical applicability of the estimator is demonstrated using two real-life datasets, with its performance again assessed based on mean squared error. Theoretical analyses, supported by simulation and empirical findings, suggest that the proposed estimator outperforms existing methods, offering a more reliable solution in multicollinearity.