The Wald-type Confidence Interval on the Mean Response Function of the Poisson Inverse Gaussian Ridge Regression

Accepted: October 2023

Abstract

The negative binomial (NB) regression model is commonly used to model overdispersed count data. However, the NB regression model is not suitable for highly overdispersed data, for which the Poisson-inverse Gaussian (PIG) regression model is often used instead. The maximum likelihood (ML) estimator is typically used to estimate the coeficients of the PIG regression model. However, when multicollinearity exists among the explanatory variables, the ML estimator's variance can become inflated. To address this issue, we propose PIG ridge regression (PIGRR) and quantile-based ridge regression estimators for the PIG regression model. We also suggest using a Waldtype method to calculate the confidence interval on the mean response function of the PIGRR. To evaluate the performance of these proposed methods, we conducted a Monte Carlo simulation study, considering mean squared error and average confidence lengths as performance criteria. Additionally, we analyzed the trafic fatalities dataset to demonstrate the benefits of the proposed estimators for practitioners dealing with multicollinearity issues in real datasets.