Alqasem Ohud A, Hammad Ali T, El-Raouf M M Abd, Yousuf Abdirashid M, Gemeay Ahmed M
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt.
Sci Rep. 2025 May 30;15(1):19042. doi: 10.1038/s41598-025-00948-w.
Mixed Poisson regression models (MPRMs) are widely used for analyzing overdispersed count data. However, the presence of multicollinearity among explanatory variables poses challenges when estimating regression coefficients using the maximum likelihood estimator (MLE), leading to inflated variances. The Poisson Modification of the Quasi-Lindley regression model (PMQLRM), a recently introduced alternative within MPRMs, faces similar issues. To address this, we propose a Liu-type estimator for the PMQLRM as an effective remedy for multicollinearity. Several existing methods are utilized to estimate the Liu-type parameter, and the theoretical superiority conditions of the proposed estimator over the MLE, ridge regression estimator, and Liu estimator are established using the scalar mean squared error (MSE) criterion. A Monte Carlo simulation study is conducted to compare the performance of different estimators based on the MSE. Additionally, a real-world dataset is analyzed to demonstrate the practical advantages of the proposed method. The findings indicate that the Poisson-modification of the Quasi-Lindley Liu-type estimator outperforms the MLE and other biased estimators when multicollinearity is present, offering a more stable and reliable alternative for parameter estimation in mixed Poisson regression models.
混合泊松回归模型（MPRMs）被广泛用于分析过度分散的计数数据。然而，当使用最大似然估计器（MLE）估计回归系数时，解释变量之间的多重共线性会带来挑战，导致方差膨胀。拟林德利回归模型的泊松修正（PMQLRM）是最近在MPRMs中引入的一种替代方法，也面临类似问题。为解决此问题，我们提出了一种用于PMQLRM的刘型估计器，作为解决多重共线性的有效补救措施。利用几种现有方法来估计刘型参数，并使用标量均方误差（MSE）准则建立了所提出的估计器相对于MLE、岭回归估计器和刘估计器的理论优势条件。进行了蒙特卡罗模拟研究，以基于MSE比较不同估计器的性能。此外，分析了一个真实世界的数据集，以证明所提出方法的实际优势。研究结果表明，当存在多重共线性时，拟林德利刘型估计器的泊松修正优于MLE和其他有偏估计器，为混合泊松回归模型中的参数估计提供了一种更稳定可靠的替代方法。
