Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka.
Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka.
ScientificWorldJournal. 2022 Jul 20;2022:8171461. doi: 10.1155/2022/8171461. eCollection 2022.
The mixed Poisson regression models are commonly employed to analyze the overdispersed count data. However, multicollinearity is a common issue when estimating the regression coefficients by using the maximum likelihood estimator (MLE) in such regression models. To deal with the multicollinearity, a Liu estimator was proposed by Liu (1993). The Poisson-Modification of the Quasi Lindley (PMQL) regression model is a mixed Poisson regression model introduced recently. The primary interest of this paper is to introduce the Liu estimator for the PMQL regression model to mitigate the multicollinearity issue. To estimate the Liu parameter, some exiting methods are used, and the superiority conditions of the new estimator over the MLE and PMQL ridge regression estimator are obtained based on the mean square error (MSE) criterion. A Monte Carlo simulation study and applications are used to assess the performance of the new estimator in the scalar mean square error (SMSE) sense. Based on the simulation study and the results of the applications, it is shown that the PMQL Liu estimator performs better than the MLE and some other existing biased estimators in the presence of multicollinearity.
混合泊松回归模型常用于分析过离散计数数据。然而，在这种回归模型中，使用最大似然估计（MLE）估计回归系数时，通常会出现多重共线性问题。为了解决多重共线性问题，Liu（1993）提出了Liu 估计量。最近引入了一种新的混合泊松回归模型，即泊松修正拟林德利（PMQL）回归模型。本文的主要目的是引入 PMQL 回归模型的 Liu 估计量，以减轻多重共线性问题。为了估计 Liu 参数，使用了一些现有的方法，并基于均方误差（MSE）准则，得到了新估计量相对于 MLE 和 PMQL 岭回归估计量的优势条件。通过蒙特卡罗模拟研究和应用实例评估了新估计量在标量均方误差（SMSE）意义下的性能。基于模拟研究和应用结果，表明在存在多重共线性的情况下，PMQL Liu 估计量比 MLE 和其他一些现有的有偏估计量表现更好。
