Mixed Poisson regression models are widely used for analyzing count data across diverse disciplines, owing to their ability to accommodate overdispersion. A persistent challenge in such models, however, is multicollinearity among explanatory variables, which undermines the reliability of regression coefficient estimates obtained via the maximum likelihood estimator (MLE), inflates parameter variances, and substantially increases the mean squared error. The Poisson-modified Quasi-Lindley regression model (PMQLRM), a recently introduced mixed Poisson regression model, has demonstrated promising performance in analyzing overdispersed count data. This paper proposes a James-Stein estimator for the PMQLRM as a means of addressing multicollinearity. The theoretical superiority of the proposed estimator is established through analytical comparisons with competing estimators, and the conditions under which it outperforms the MLE, ridge, and Liu estimators with respect to the MSE criterion are derived. The finite-sample performance of the proposed estimator is further assessed through Monte Carlo simulation studies and a real data application. Both the simulation results and the empirical analyses consistently indicate that the James-Stein estimator outperforms the MLE and other biased estimators in the presence of multicollinearity, which provides more stable and reliable estimates, particularly in settings where multicollinearity is present among the explanatory variables.
O. Alqasem, A. Hammad, M. A. El-Qurashi et al.· International Journal of Unc...· 0 citations
Count data are widely encountered in many scientific fields, particularly in healthcare and epidemiology. One of the most commonly used approaches for analyzing such data is the negative binomial regression model (NBRM), due to its simplicity and effectiveness in modeling event frequencies. Despite its popularity, the presence of severe multicollinearity among explanatory variables can substantially inflate the variance of parameter estimates and reduce the reliability of statistical inference. To address this issue, this study proposes an improved shrinkage estimator for the NBRM, referred to as a novel class of negative binomial Liu-type estimator. The proposed estimator combines the advantages of ridge regression and the Liu estimator, aiming to reduce estimation variance while maintaining stable parameter estimates under conditions of multicollinearity. The proposed estimator is compared with the traditional maximum likelihood estimator, as well as existing ridge and Liu-type estimators, using performance measures such as the mean squared error. Its performance is evaluated through extensive Monte Carlo simulation experiments under different levels of multicollinearity and sample sizes. The simulation results demonstrate that the proposed estimator provides more accurate and stable estimates than the competing methods, particularly in the presence of high multicollinearity. To illustrate the practical applicability of the proposed approach, the method is applied to a real-world healthcare dataset related to COVID-19 cases in the Kingdom of Saudi Arabia. The empirical results confirm the effectiveness of the proposed estimator in improving estimation accuracy and model stability when modeling multivariate healthcare count data. Overall, the proposed estimator offers a useful alternative for modeling multicollinear healthcare count data and enhances the reliability of statistical analysis in applied health research.
E. H. Hafez, A. Hammad, R. Aldallal et al.· Statistics, Optimization &am...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
